Seminar series

<p>Individual lectures and seminars are announced <a href="/en/current/calendar/" title="Calender">in the calendar</a>.</p>

<p>Seminars are usually held on Wednesdays, 13.15-14-15, but day and time may vary. <a rel="noopener" href="/en/current/calendar/?event.organisations.name=Department%20of Mathematical Sciences" target="_blank" title="Link to calendar for Mathematical Sciences." data-anchor="?event.organisations.name=Department of Mathematical Sciences">Check the calendar</a> to keep track. </p>
<p>You can also contact the organizers for information. </p>

<h2>Seminars 2024</h2>
<h3>12.4.2024 - Adam Keilthy, Chalmers/GU: Deformations of modular forms and multiple L-values</h3>
<p>Abstract: By considering variations of the uniformising differential equation of a genus 0 modular curve, Bogo defines a notion of a deformation of a modular form in terms of iterated integrals of modular forms, whose first order transformation properties are given in terms of period polynomials.</p>
<p>In this talk, we will provide a cohomological formalism for such deformations, establish the existence and near uniqueness of such deformations, and give an explicit example in terms of both critical and non critical totally holomorphic multiple L values, establishing a geometric interpretation for non-critical multiple L-values.</p>
<h3>6.3.2024 - Martin Raum, Chalmers/GU: Moduli of Flat Surfaces and Affine Modular Forms</h3>
<p>Abstract: I will discuss the relation between moduli of two-marked tori and modular forms for a special affine group, which is non-reductive and thus outside of reach of the Langlands Program. The connection is made by the Siegel-Veech transform, which I will explain. In general, the Siegel-Veech transform yields a supply of square-integrable functions on strata of abelian differentials, of which moduli of marked tori are a special case. Before our work, only the case of one-marked tori was understood. In particular, even in the case of two-marked tori spectral properties of the image were unknown. To reveal them we require three differential operators associated with various group actions or foliations. This yields a surprisingly detailed understanding of the L2-space surpassing what we know for the special linear group. On the geometric side, we need to identify novel configurations of relative saddle connections, which I will explain as well. This is based on work with Jayadev Athreya, Jean Lagacé, and Martin Möller.</p>
<h3>23.2.2024 - Sebastián Herrero, ETH Zürich and University of Santiago de Chile: Special values of Green's functions on hyperbolic 3-space</h3>
<p>Abstract: In 1986 Gross and Zagier stated an algebraicity conjecture for special values of higher Green's functions on modular curves, which resembles the properties of the modular j function in the theory of complex multiplication. This conjecture has recently been demonstrated by Bruinier, Li and Yang. In this talk I will present new results on an analogous problem for special values of Green's functions on hyperbolic 3-space. We prove that their averages can be computed in terms of logarithms of primes and logarithms of units in real quadratic fields. This is work in collaboration with Özlem Imamoglu, Anna von Pippich and Markus Schwagenscheidt.</p>
<h3>7.2.2024 - Douglas Molin, Chalmers/GU: On a conjecture of Venkatesh (also half-way seminar)</h3>
<p>Abstract: Let F be a CM field and g an automorphic form of PGL(2,F). A conjecture of Venkatesh describes the structure of the contribution of g to the singular homology with rational coefficients of the locally symmetric spaces associated to PGL(2,F). I will introduce this conjecture and the main ingredients of my conditional proof of its p-adic realisation, wherein the coefficents are p-adic instead of rational.</p>
<h3>2.2.2024 - Vivan Kuperberg, ETH Zürich: Sums of odd-ly many fractions and the distribution of primes</h3>
<p>Abstract: In this talk, I will discuss new bounds on constrained sets of fractions. Specifically, I will discuss the answer to the following question, which arises in several areas of number theory: for an integer $k \ge 2$, consider the set of $k$-tuples of reduced fractions $\frac{a_1}{q_1}, \dots, \frac{a_k}{q_k} \in I$, where $I$ is an interval around $0$. How many $k$-tuples are there with $\sum_i \frac{a_i}{q_i} \in \mathbb Z$?</p>
<p>When $k$ is even, the answer is well-known: the main contribution to the number of solutions comes from “diagonal” terms, where the fractions $\frac{a_i}{q_i}$ cancel in pairs. When $k$ is odd, the answer is much more mysterious! In work with Bloom, we prove a near-optimal upper bound on this problem when $k$ is odd. I will also discuss applications of this problem to estimating moments of the distributions of primes and reduced residues.</p>
<h3>24.1.2024 - Mykola Pochekai, Chalmers/GU: Chow Rings of Unimodular Triangulations</h3>
<p>Abstract: The concept of associating a Chow-ring-like structure with a combinatorial object to extract combinatorial information is not new. The earliest successful instance of this approach was R. Stanley's proof of the g-conjecture in the 1970s. A more recent iteration of this idea is found in J. Huh's works on the Chow rings of matroids. Drawing inspiration from these ideas, I have defined Chow rings for unimodular triangulations. I will demonstrate how these constructions can be used to update the longstanding conjecture regarding the unimodality of the delta-vector of polytopes that admit triangulations of a special kind.</p>
<h3>17.1.2024 - Emil Jacobsen, Stockholm University: On the motivic fundamental group</h3>
<p>Abstract: I will introduce the motivic fundamental group of a smooth variety, and explain its relation to the usual fundamental group. The main result can also be phrased as follows: local systems of motivic origin are stable under extension in the category of local systems. I will also present a motivic version of a classical theorem of Hain, on Malcev completions of monodromy representations. At the end, I'll explain some of the group/representation theoretic tools that go into these result.</p>

<p>The seminar is joint for the division of Analysis and Probability and its main themes are Mathematical Physics, Probability Theory and Harmonic and Functional Analysis.</p>
<p>The seminar is encouraged to be aimed at a broader audience, but some talks may be of a more specialised nature. The talks in the seminar are usually 60 minutes, including questions.</p>
<p>The seminar is held on campus with possibility to attend online via Zoom (subject to technology working). Please contact one of the organizers for the Zoom link.</p>

<h2>Upcoming seminars</h2>
<p>(always at 13:15 in MV:L14, unless otherwise stated)</p>
<h3>2024-04-23 Håkan Andreasson, Chalmers/GU</h3>
<h4>Existence of a minimizer to the particle number-Casimir functional for the Einstein-Vlasov system</h4>
<p>Abstract: In 2001 Wolansky introduced a particle number-Casimir functional for the Einstein-Vlasov system. Two open questions are associated with this functional. First, a meaningful variational problem should be formulated and the existence of a minimizer to this problem should be established. The second issue is to show that a minimizer, for some choice of the parameters, is a static solution of the Einstein-Vlasov system. I will present a solution to the first problem by proving the existence of a minimizer. On the technical side, it is a main achievement that we are able to bypass the non-compactness of minimizing sequences by new arguments in both $v$-space and $x$-space. We note that such compactness results for the Einstein-Vlasov system have been absent in the literature, whereas similar results have been known in the Newtonian case. We also provide arguments which give strong support that minimizers corresponding to small masses are static solutions of the Einstein-Vlasov system. Furthermore, our analysis leads us to propose a new stability criterion for static solutions: We conjecture that a static solution for which the Casimir-binding energy is positive is stable for mass-preserving perturbations.</p>
<h3>2024-04-30 Robin van Haastrecht, Chalmers/GU</h3>
<h4>Limit formulas for the trace of the functional calculus of quantum channels for $SU(2)$</h4>
<p>Lieb and Solovej (2014) studied traces of quantum channels, defined by the leading component in the decomposition of the tensor product of two irreducible representations of $SU(2)$, to establish a Wehrl-type inequality for integrals of convex functions of matrix coefficients. It is proved that the integral is the limit of the trace of the functional calculus of quantum channels. I introduce new quantum channels for all the components in the tensor product and generalize their limit formula. I prove that the limit can be expressed using Berezin transforms.</p>
<h3>2024-05-07 Søren Fournais, Copenhagen</h3>
<h4>TBA</h4>
<h3>2024-05-28</h3>
<h3>Wojciech Szymanski, Syddansk Universitet</h3>
<h4>TBA</h4>
<h3>2024-06-11<span> </span>Jorge Castillejos, UNAM, Cuernavaca</h3>
<h4>TBA</h4>

<h2>Previous seminars (most recent on top)</h2>
<h3>2024-04-16 Eric Ling, Copenhagen</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">Rigidity aspects of Penrose's singularity theorem</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">In this talk, we present some rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our arguments to cosmological spacetimes (i.e., spacetimes with compact Cauchy surfaces) and scenarios involving topological censorship. This is joint work with Greg Galloway.</p>
<h3 class="zfr3Q CDt4Ke " dir="ltr">2024-04-10 David Rule, Linköping (MV:L15)</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">Multilinear and Weighted Estimates for Oscillatory Integral Operators</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">In this talk we will discuss a couple of boundedness theorems for oscillatory integral operators. Firstly, we study the weighted L^p boundedness of linear operators whose amplitudes do not have sufficient decay to allow for weighted boundedness for all A_p Muckenhoupt weights. In this situation we can obtain weighted L^p boundedness for a smaller class of Muckenhoupt weights. Secondly, we look at the boundedness of multilinear oscillatory integrals on local Hardy spaces. Here vector-valued inequalities allow us to study quasi-Banach spaces (where 0&lt;p&lt;1). This is a combination of joint work with Aksel Bergfeldt, Solange Mukeshimana, Salvador Rodriguez-Lopez and Wolfgang Staubach.</p>
<h3>2024-04-02 Malin Palö Forsström, Chalmers/GU</h3>
<h4>Poisson coverage processes</h4>
<p>Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a&nbsp; Poisson process on a collection of sets. Our main focus is to determine which processes are representable in this way. The models we consider include percolation, Markov chains, and the Ising model. This talk is based on joint work with Nina Gantert and Jeffrey E. Steif.</p>
<h3>2024-03-20 Tobias Weich, Paderborn</h3>
<h4>Polyhedral bounds on the joint spectrum on higher rank locally symmetric spaces</h4>
<p>We consider the joint spectrum of the algebra of invariant differential operators on a general higher rank locally symmetric space. We prove that the supremum of the real part of the joint spectrum with respect to a natural polyhedral norm is exactly described by the growth indicator function of the discrete subgroup. This generalizes a classical result by Elstrod, Patterson and Corlette which states that in the rank one case the bottom of the Laplace spectrum is determined by the critical exponent of the discrete subgroup.</p>
<h3>2024-03-14 Erik Duse, KTH</h3>
<h4>Generic ill-posedness of the energy-momentum equations in the vectorial calculus of variations</h4>
<p>Abstract: This talk is about the energy-momentum equations in calculus of variations. These arises from inner variations, i.e., domain variations, as opposed to outer variations that give rise to the Euler-Lagrange equations. For minimisation problems involving vector valued functions the energy-momentum equations become important. In recent work I proved that the they are generically ill-posed with respect to Dirichlet data using convex integration theory. I also showed that they poses Lipschitz solutions that are nowhere continuously differentiable. A similar result for the Euler-Lagrange equations was proven by Müller and Several in 2003. Besides reporting on my work I will explain various fundamental notions for vectorial problems like quasiconvexity and rank-one convexity.</p>
<h3 class="zfr3Q CDt4Ke " dir="ltr">2024-03-12 Peter Sjögren, Chalmers/GU</h3>
<h4>Variation inequalities for the Ornstein-Uhlenbeck semigroup</h4>
<p>Abstract: We consider the Ornstein-Uhlenbeck semigroup H<sub>t</sub>, t&gt;0, in dimension one. It is known that H<sub>t</sub>&nbsp;f -&gt; f as t -&gt; 0, in L<sup>p</sup>&nbsp;and almost everywhere.</p>
<p>To measure the speed of convergence, one introduces the variation seminorm, taken with respect to t. This notion has been studied in many different contexts.</p>
<p>We show that this seminorm for H<sub>t</sub>&nbsp;defines an operator of weak type (1,1) with respect to the relevant Gaussian measure. The analogous L<sup>p</sup> estimates for 1 &lt; p &lt; ∞ were already known.</p>
<h3>2024-03-05 Are Austad, Syddansk Universitet, Odense</h3>
<h4>Ideal intersection properties for group-graded Banach *-algebras</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">A central problem at the intersection of operator algebras and dynamical systems is understanding the ideal structure of reduced crossed products. While great effort has gone in to understand simplicity of the crossed product, sometimes this is too much to ask for. A different approach is needed to venture beyond the simple case.</p>
<p dir="ltr" class="zfr3Q CDt4Ke ">In this talk, we introduce the $\ell^1$-ideal intersection property for $C^*$-dynamical systems, which says that ideals in the reduced crossed product are detected by the $\ell^1$-algebra sitting inside, giving us a better handle on the ideal structure. We will present classes of discrete groups $\Gamma$ for which $(C(X), \Gamma, \alpha)$ has the $\ell^1$-ideal intersection property for all choices of $C(X)$ and action $\alpha$. As a by-product, we are also able to add to the list of groups $\Gamma$ for which $\ell^1(\Gamma)$ has unique $C^*$-norm. This is based on joint work with Sven Raum (University of Potsdam).</p>
<p dir="ltr" class="zfr3Q CDt4Ke ">If time permits, I will also report on some ongoing work on ideal intersection properties for spectral interpolation triples coming from locally compact groups.</p>
<h3>2024-02-27 Eduard Vilalta, Chalmers/GU</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">Nowhere scattered multiplier algebras</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">The multiplier algebra of a C*-algebra is the non-commutative generalization of the Stone–Čech compactification of a topological space. An interesting and often deep question about this construction is the preservation of certain properties, that is, given a C*-algebra A that satisfies a certain property P, when does its multiplier M(A) satisfy P?</p>
<p dir="ltr" class="zfr3Q CDt4Ke ">In this talk, I will recall the construction of the multiplier algebra and focus on the question above for the property of nowhere scatteredness. This notion, which ensures sufficient noncommutativity of a C*-algebra, does not always pass to multiplier algebras. Surprisingly, regularity properties play a role in this study. During the talk, I will give sufficient conditions under which nowhere scatteredness is preserved. I will also give some examples of nowhere scattered C*-algebras whose multiplier algebra is not nowhere scattered.</p>
<h3>2024-02-13 Johan Wästlund, Chalmers/GU</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">Billiards, Checkers, and Quadratic Reciprocity</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">I will discuss fairly simple proofs of the famous Law of Quadratic Reciprocity through two activities: In Arithmetic Billiards, a ball is bouncing around in a rectangle. In Parity Checkers we place checkers on a checkerboard under certain parity constraints. Both activities turn out to capture the division of congruence classes modulo a prime into squares and non-squares.</p>
<h3>2024-02-07 Lashi Bandara, Deakin University, Melbourne</h3>
<h4>Trace, Regularity, Fredholmness: the story of non-compact boundary for first-order elliptic operators</h4>
<p>Abstract: The study of boundary value problems on smooth manifolds with boundary is a classic and well studied subject. A significant development which highlighted the importance of the subject was the celebrated index formula of Atiyah-Patodi-Singer in the 1970s. This, in particular, enshrined the place of non-local boundary conditions in geometry, as local boundary conditions were discovered to be topologically obstructed for index formulae. However, much of the study in the subject has been restricted to compact boundary and for Dirac-type operators or their close cousins.<br><br>More recently, Bär-Bandara extended the study beyond Dirac-type operators, assuming only ellipticity of the operator, though retaining the restriction of compact boundary. This was made possible through the introduction of the H-infinity functional calculus as the central analytic instrument. An unintended consequence of the use of this "global" technique was that it suggested the possibility of understanding non-local boundary conditions for the non-compact case.<br><br>This talk will focus on recent results and advancements when the boundary is non-compact. A trace theorem is obtained on the maximal extension of the operator, ensuring the possibility to understand *all* possible boundary conditions, which is in particular significant in the study of regularity and perturbations of boundary conditions. Fredholmness is studied in contexts where the operator is invertible outside of a compact set. These results are obtained under a set of assumptions, which are shown to be satisfied under second fundamental form and scalar curvature bounds&nbsp; for the Spin-Dirac operator.</p>
<h3>2024-01-30 Pieter Spaas, Copenhagen</h3>
<h4>Local Hilbert-Schmidt stability</h4>
<p>We will introduce a local notion of Hilbert-Schmidt stability (HS-stability), partially motivated by the recent introduction of local permutation stability by Bradford. We will discuss some basic properties, and then establish a local character criterion for local HS-stability of amenable groups, by analogy with the character criterion for HS-stability of Hadwin and Shulman. We will then discuss further examples of (flexible versions of) local HS-stability. Finally, we show that infinite sofic (resp. hyperlinear) property (T) groups are never locally permutation (resp. HS-) stable, answering a question by Lubotzky. This is based on joint work with Francesco Fournier-Facio and Maria Gerasimova.</p>
<h3>2024-01-23 at 13:15, MVL14 Ulrik Enstad, Oslo</h3>
<h4>Classifiability of C*-algebras associated with point sets</h4>
<p>A common construction in operator algebras associates to a discrete group a full and reduced group C*-algebra. In particular, this can be done for a lattice in a locally compact group. This talk concerns a more general construction that associates a (full or reduced) C*-algebra to a discrete point set in a locally compact group, for instance an approximate lattice. The main result I will present gives conditions for when this C*-algebra is classifiable by its Elliott invariant. In particular, this is the case for certain aperiodic point sets in nilpotent Lie groups</p>
<h3>2023-12-20 at 13:15, MVL14 Simon Larson, GU/Chalmers</h3>
<h4>Two-term spectral asymptotics in Lipschitz domains</h4>
<p dir="ltr" class="zfr3Q CDt4Ke ">In this talk I will discuss some recent developments concerning spectral asymptotics for Dirichlet and Neumann Laplace operators in a bounded domain with Lipschitz-regular boundary. More specifically, we will prove two-term asymptotic expansions for positive order Riesz-means. If time permits I will also outline some applications in the realm of spectral shape optimization.</p>
<p dir="ltr" class="zfr3Q CDt4Ke ">The talk is based on joint work with Rupert Frank.</p>
<h3>2023-12-06 at 13:15, MVF31 – joint KASS and AP seminar, Bingyuan Liu, University of Texas Rio Grande Valley</h3>
<h4 class="m-8029141829898839010gmail-zfr3q" style="margin-bottom: 12.0pt;">The Diederich–Fornæss index and the ∂¯-Neumann problem</h4>
<p>A domain Ω ⊂ ℂn is said to be pseudoconvex if − log(−δ(z)) is plurisubharmonic in Ω, where δ is a signed distance function of Ω. The study of global regularity of <em>∂¯-</em>Neumann problem on bounded pseudoconvex domains is dated back to the 1960s. However, a complete understanding of the regularity is still absent. On the other hand, the Diederich–Fornæss index was introduced in 1977 originally for seeking bounded plurisubharmonic functions. Through decades, enormous evidence has indicated a relationship between global regularity of the <em>∂¯-</em>Neumann problem and the Diederich–Fornæss index. Indeed, it has been a long-lasting open question whether the trivial Diederich–Fornæss index implies global regularity. In this talk, we will introduce the backgrounds and motivations. The main theorem of the talk proved recently by Emil Straube and me answers this open question for (0, n − 1) forms.</p>
<h3>2023-11-28 at 13:15, MV:L14 Mia Deijfen, Stockholm</h3>
<h4>Percolation in geometric random intersection graphs</h4>
<h3>2023-11-14 at 13:15, MV:L14 Marco Fraccaroli, BCAM</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">The <em>L<sup>p</sup></em> theory for outer measure spaces</h4>
<h3 class="zfr3Q CDt4Ke " dir="ltr">23-11-21 at 13:15, MV:L14 Nadine Ansorge, Bayreuth University</h3>
<h4 class="zfr3Q CDt4Ke " dir="ltr">On linear stability of isochrone steady states of the Vlasov-Poisson system</h4>
<h3>2023-11-07 Jacob Stordal Christiansen, Lund</h3>
<h4>Chebyshev polynomials and Widom factors</h4>
<h3>2023-10-24 Nico Michele Schiavone<br>(BCAM, Bilbao)</h3>
<h4>Spectral enclosures for perturbed Dirac operators</h4>
<h3>2023-10-17 Frederik Ravn Klausen<br>(Copenhagen)</h3>
<h4>Phase transitions of the graphical representations of the Ising model</h4>
<h3>2023-10-10 Daniel Ueltschi <br>(Warwick, UK)</h3>
<h4>The Kac-Ward solution of the 2D Ising model</h4>
<h3>2023-10-03 at 13:15, MV:L14 Alexandru Aleman<br>(Lund)</h3>
<h4>Cyclicity in weighted Besov spaces</h4>
<h3>2023-09-26 Andreas Rosén<br>(Chalmers/University of Gothenburg)</h3>
<h4>Dirichlet and Neumann vs. Atiyah-Singer-Patodi</h4>
<h3>2023-09-19 Nachi Avram Re'em<br>(Chalmers/University of Gothenburg)</h3>
<h4>α-stable stationary processes</h4>
<h3>2023-09-12 Nina Gantert (Technical University of Munich / Jubilee Professor)</h3>
<h4>Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation</h4>
<h3>2023-08-29 Jakob Björnberg (Chalmers/University of Gothenburg)</h3>
<h4>Dimerisation in mirror models and quantum spin chains</h4>
<h3>2023-06-08 Miroslav Englis (Czech Academy of Sciences)</h3>
<h4>M-harmonic Bergman kernels</h4>
<h3>2023-05-30 Mattias Byléhn (Chalmers/University of Gothenburg)</h3>
<h4>Towards hyperuniformity on hyperbolic spaces</h4>
<h3>2023-05-23 Kevin Schnelli (KTH)</h3>
<h4>Quantitative Tracy-Widom law for Wigner random matrices</h4>
<h3>2023-05-16 Matej Brešar (Ljubljana and Maribor)</h3>
<h4>The Waring problem for noncommutative algebras</h4>
<h3>2023-05-11 Charlotte Dietze (LMU)</h3>
<h4>Semiclassical estimates for Schrödinger operators with Neumann boundary conditions on Hölder domains</h4>
<h3>2023-05-09 Nina Gantert, jubilee professor (Technical University of Munich)</h3>
<h4>Branching random walks with annihilation</h4>
<h3>2023-05-02 Stein Andreas Bethuelsen (Universitetet i Bergen)</h3>
<h4>Random walk on random walks in high dimensions: non-perturbative results</h4>
<h3>2023-04-25 Kevin Brix (Glasgow University)</h3>
<h4>Symbolic dynamics, groups, and C*-algebras</h4>
<h3>2023-04-20 Pascal Auscher (Université Paris-Saclay)</h3>
<h4>A variational approach for parabolic Cauchy problems</h4>
<h3>2023-04-18 Anna Sakovich (Uppsala)</h3>
<h4>Towards a Spacetime Intrinsic Flat Convergence</h4>
<h3>2023-04-04 Lauren Köhler-Schindler (ETH Zürich)</h3>
<h4>Scaling limits and arm exponents for the planar fuzzy Potts model</h4>
<h3>2023-03-28 Alireza Ataei (Uppsala)</h3>
<h4>The Kato square root problem for weighted parabolic operators</h4>
<h3>2022-03-14 Simon Schmidt (Copenhagen)</h3>
<h4>Quantum symmetry vs nonlocal symmetry</h4>
<h3>2022-02-28 Jasmin Matz (Copenhagen)&nbsp;</h3>
<h4>Analytic torsion for congruence quotients of SL(n,R)</h4>
<h3>2023-02-14 Alexei Iantchenko (Malmö)</h3>
<h4>Semiclassical surface-wave imaging and leaking modes in seismology​</h4>
<h3>2023-02-07 Sergey Neshveyev (Oslo) Semigroup</h3>
<h4>C*-algebras and faithful representations of groupoid C*-algebras</h4>
<h3>2023-02-03 Urban Larsson (IIT Bombay)</h3>
<h4>Bidding Combinatorial Games</h4>
<p><a href="https://arxiv.org/abs/2207.08073%20and https://arxiv.org/abs/2207.11596" title="Link to publication">Link to more information</a>.</p>
<h3>2023-01-31 Sanaz Pooya (Stockholm)</h3>
<h4>On a generalisation of Kazhdan projections</h4>
<h3>2023-01-17 Sven Raum (Stockholm)</h3>
<h4>Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems</h4>
<h3>2022-12-13 Caleb Eckhardt (Miami University)</h3>
<h4>Dimension theory of group C*-algebras</h4>
<h3>2022-11-22 Nadia Larsen (Oslo)</h3>
<h4>Equilibrium states of C*-algebras associated to right LCM monoids</h4>
<h3>2022-11-15 Stas Volkov (Lund)</h3>
<h4>Conservative random walk and related topics</h4>
<h3>2022-11-08 Fredrik Viklund (KTH)</h3>
<h4>The Loewner-Kufarev energy and foliations by Weil-Petersson curves</h4>

<p>The colloquium runs roughly once every month on Mondays, usually in Euler or Pascal at 15:15-16:15.</p>
<p>The ambition of the colloquium is to gather students and employees from all divisions for overview talks by renowned experts about exciting mathematical topics.</p>
<p>Feel free to contact any the organizers for questions or suggestions for colloquia speakers. Even if the colloquium for the term is fully booked, suggestions for the Mathematical Sciences Seminar are always welcome.</p>
<h3>Upcoming</h3>
<p>&nbsp;</p>

<h2>Previous colloquia</h2>
<h3>2024</h3>
<h4>12/3 Rupert Frank, LMU Munich: The Wehrl entropy problem: mathematical physics meets complex analysis and representation theory</h4>
<p>Euler, 15.30-16.30 (fika in the lunch room from 15.00)</p>
<p>Abstract: The coherent state transform, under various names, appears in many fields of mathematics and physics. It is associated to representations of a group. In this talk we are concerned with the problem of minimizing the entropy of the coherent state transform and we explain how complex analysis can be used to achieve this in certain settings. We discuss various open questions.</p>
<h4>19/2 Olle Häggström, Chalmers/GU: A role for mathematicians in a future with advanced AI?</h4>
<p>Pascal, 15.30-16.30 (fika in the lunch room from 15.00)</p>
<p>It is very unlikely that AI progress is about to come to a sudden halt, leaving GPT-4 forever as the apex of human efforts to build AI. Much more plausible is to expect AI to continue to develop in ways that will radically transform all professions and all sectors of society, including higher education and mathematical research. Filling in the details in such predictions is a more delicate matter.</p>
<h3>2023</h3>
<h4>11/9 Pavel Kurasov, Stockholm: <strong>Crystalline measures and Fourier quasicrystals: from metric graphs to stable polynomials</strong></h4>
<p>Abstract: The classical Poisson's summation formula establishes a relation between a function and its Fourier transform. Crystalline measures are tempered distributions given by locally finite purely atomic measures whose Fourier transform is also a purely atomic measure. Such measures were studied by J.-P. Kahane, A.-P. Guinand, and S. Mandelbrojt in the fifties.</p>
<p>Differential operators on metric graphs surprised researchers by their extraordinary spectral properties and possibility to carry out explicit analysis. One such example is given by the trace formula connecting spectra of quantum graphs to the set of periodic orbits on the underlying metric graph (without any additional correction terms). It appears that the corresponding spectral measure provides an explicit example of so-called crystalline measures generalising classical Dirac comb and Poisson summation formula.</p>
<p>We are going to show how to construct a wide family of crystalline measures using quantum graphs (differential operators on metric graphs) and more generally via stable polynomials.</p>
<h4>23/10 Klas Modin, Chalmers/University of Gothenburg: Abel Laureate Luis Caffarelli: a glimpse of his work</h4>
<p>Abstract: This year’s Abel Prize winner is Luis Caffarelli from the University of Texas at Austin. The motivation is: "For his seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge-Ampère equation.”</p>
<p>In this talk, I shall present some of his results related to optimal mass transport and regularity of solutions to the Monge-Ampère equation.</p>
<h3>2022</h3>
<h4>24/1 Jan Gerken, Chalmers and University of Gothenburg: <strong>Geometric deep learning: On the interplay between mathematics and deep neural networks</strong></h4>
<p>The field of geometric deep learning has gained a lot of momentum in recent years and attracted people with different backgrounds such as deep learning, theoretical physics and mathematics. This is also reflected by the considerable research activity in this direction at our department. In this talk, I will give an introduction into neural networks and deep learning and mention the different branches of mathematics relevant to their study. Then, I will focus more specifically on the subject of geometric deep learning where symmetries in the underlying data are used to guide the construction of network architectures. This opens the door for mathematical tools such as representation theory and differential geometry to be used in deep learning, leading to interesting new results. I will also comment on how the cross-fertilization between machine learning and mathematics has recently benefited (pure) mathematics.</p>
<h4>11/10 Jakob Björnberg, University of Gothenburg/Chalmers: <strong>Mathematical works of Hugo Duminil-Copin</strong></h4>
<p>Abstract: Hugo Duminil-Copin is one of the four Fields-medal winners of 2022. He received the prize "for solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four." In this talk I will give an introduction to a selection of his works in this area, and place them within a larger context.</p>
<h3>2020 </h3>
<h4>20/1 Tobias Ekholm, Uppsala University: <strong>Skeins on Branes</strong></h4>
<p>The HOMFLY polynomial is an invariant of knots in the 3-sphere allowing one to distinguish different knots. It is a two variable polynomial which is defined combinatorially, via so called skein-relations. We give a geometric interpretation of the coefficients of the polynomial as a count of certain holomorphic curves associated to the knot. One of the variables in the HOMFLY accounts for the area or homological degree of the curves, the other for their Euler characteristic. This is in line with predictions by Ooguri and Vafa based on topological string theory. The proof embodies a new method to define invariant counts of holomorphic curves with Lagrangian boundary. This is a mathematically rigorous incarnation of the fact that boundaries of open topological strings create line defects in Chern-Simons theory as described by Witten.</p>
<h4><strong>17/2 Olle Häggström, Chalmers/GU: </strong><strong>AI Alignment, Embedded Agency and Decision Theory</strong></h4>
<p>The term artificial intelligence (AI) had not yet been coined in the days of Alan Turing. Nevertheless, he did foresee the field, and famously predicted that machines would eventually become so capable as to surpass human general intelligence, in which case he suggested that "we should have to expect the machines to take control". The (small but growing) research area known as AI Alignment takes this ominous prediction as a starting point, and aims to work out how to instil the AI with goals that lead to a good outcome (for humans) despite their taking control. Attempts to solve AI Alignment lead to many intriguing philosophical and mathematical questions involving, e.g., the notion of embedded agency, and the fundamentals of decision theory.</p>
<h4>9/3 Laura Mancinska, University of Copenhagen: <strong>Harnessing Quantum Entanglement</strong></h4>
<p>Entanglement is one of the key features of quantum mechanics. It lies at the heart of most cryptographic applications of quantum technologies and is necessary for computational speed-ups. However, given a specific information processing task, it is challenging to find the best way to harness entanglement and we are yet to uncover the full range of its potential applications.</p>
<p>We will see that the so-called nonlocal games provide a rigorous mathematical framework for studying entanglement and the advantage that it can offer. On the one hand, we will take a closer look at specific applications of entanglement, including protocols for certifying proper functioning of untrusted quantum devices. While on the other hand, we will attempt to gain a better understanding of the mathematical structure of entanglement by considering a restricted class nonlocal games. This class will give rise to a natural quantum relaxation for the notion of graph isomorphism.</p>
<h4>20/4 Tom Britton, Stockholm University: <strong>Mathematical modelling of infectious disease outbreaks like covid-19</strong> <br /><a href="https://play.chalmers.se/media/Colloquium+at+the+Mathematical+Sciences+with+Tom+Britton/0_zeabjfyx">(link to video from the seminar at Chalmers Play)</a></h4>
<p>Abstract: Mathematical models for the spread of infectious diseases are used to: better understand spreading mechanisms, determine if a big outbreak is likely to occur and how big it will be, determine if a disease will become endemic, and investigate how various preventive measures can reduce spreading hopefully preventing a major pandemic outbreak or make an endemic disease vanish. Making inference is harder than usual in that the basic events, transmissions, are rarely observed but instead proxies like onset of symptoms are recorded, and also by the fact that these events are dependent rather than independent (as is usually the case).</p>
<p>In the talk I will give an overview of the area with particular focus on emerging outbreaks, including illustrations from the current coronavirus outbreak.</p>

<p>Upcoming seminars are also posted in the <a rel="noopener" href="/en/current/calendar/?event.organisations.name=Department%20of%20Mathematical%20Sciences" target="_blank" title="Link to calendar for Mathematical Sciences" data-anchor="?event.organisations.name=Department%20of%20Mathematical%20Sciences">department calendar</a>.</p>

<h2>Previous seminars</h2>
<p>(Most recent on top.)</p>
<h3>2024-03-05 Lars Martin Sektnan, Chalmers/University of Gothenburg</h3>
<h4>On semistable perturbation problems for canonical metrics</h4>
<p><strong>Abstract:</strong> In this talk, I will discuss perturbation problems for canonical metrics (such as Hermite-Einstein metrics on vector bundles or constant scalar curvature metrics on Kähler manifolds), where the goal is to produce new such metrics from old, in perturbed situations. I will focus on certain “semistable” cases, where one is infinitesimally close to being able to solve the original equation, but does not actually have a solution to begin with. This results in an obstructed perturbation problem - solutions do not always exist. I will try to highlight what the new challenges are in this situation and techniques to overcome them, in order to produce solutions to the perturbed equations assuming a necessary algebro-geometric criterion. This is based on joint works with Tipler, Dervan and McCarthy, and Ortu.</p>
<h3>2024-02-23 Duc Viet Vu, University of Cologne</h3>
<h4>Volume of big cohomology classes</h4>
<p>Abstract: We prove that the partial derivative of the volume function of big classes along a prime divisor in a compact Kaehler manifold is equal to the numerical restricted volume of that class to the divisor.  This extends a previous result by Witt Nystroem in the case where the divisor is smooth and not included in the non-Kahler locus of the cohomology class.  A consequence of our main result is that the divisorial components of the non-Kaehler locus of a big class lie  in the null locus of that class.</p>
<h3>2024-02-20 Martin Sera, Kyoto University of Advanced Science</h3>
<h4>Applications of generalized Monge–Ampère products</h4>
<p>Abstract: In this presentation, we consider generalized (mixed) Monge–Ampère products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several articles written by subsets of M. Andersson, Z. Błocki, R. Lärkäng, H. Raufi, J. Ruppenthal, E. Wulcan and the speaker. Continuing our last presentation, we discuss their applications using Lelong number estimates of them. Among others, we obtain the following generalization of a result by X. Wu. If the nonnef locus of a pseudoeffective vector bundle E on a Kähler manifold is contained in a countable union of k-codimensional analytic sets, and if the k-power of the first Chern class of E is trivial, then E is nef.</p>
<h3>2024-01-23 Gerard Freixas i Montplet, École Polytechnique</h3>
<h4>Positivity properties of the BCOV invariant</h4>
<p>Abstract: The BCOV invariant is a real valued invariant of Calabi-Yau manifolds (CY's), constructed by Fang-Lu-Yoshikawa in dimension 3 and Eriksson-F.-Mourougane in general. It builds on a combination of holomorphic analytic torsions of sheaves of holomorphic differentials, first studied by string theorists Bershadsky-Cecotti-Ooguri-Vafa. The BCOV invariant induces a smooth function on the moduli space of polarized CY's, and it satisfies a differential equation relating it to the Weil-Petersson form and the curvatures of the Griffiths bundles. In previous works with D. Eriksson and C. Mourougane, we studied the singularities of the BCOV invariant for one-parameter degenerations of CY’s. This can be interpreted as the boundary conditions of the differential equation. Motivated by mirror symmetry, we asked ourselves about the positivity properties of these singularities, and whether the BCOV invariant provides a psh exhaustion function on the moduli space. In this talk I will report on work in progress with D. Eriksson on these questions. </p>
<h3>2024-01-11 Rémi Reboulet</h3>
<h4>Flats in the space of Kähler metrics</h4>
<p>Abstract: We investigate the space of positive metrics on an ample line bundle over a complex projective manifold from the point of view of metric geometry. It has been known since the work of Mabuchi, Chen and Sun that it can be endowed with the structure of a negatively curved, geodesic metric space. In spaces of negative curvature, one is naturally interested in areas that are isometric to a flat space. Those flat subspaces vastly generalise the notion of geodesics, which are one-dimensional examples. I will explain how one can construct flat subspaces of infinite dimension in the space of positive metrics. This is joint work with David Witt Nyström.</p>
<h3>2023-12-14<br>Theodoros Papazachariou, University of Cambridge</h3>
<h4>On divisorial stability of finite covers</h4>
<p>Abstract: Divisorial stability of a polarised variety is a stronger - but conjecturally equivalent - variant of uniform K-stability introduced by Boucksom-Jonsson. Whereas uniform K-stability is defined in terms of test configurations, divisorial stability is defined in terms of convex combinations of divisorial valuations on the variety. In this talk, I will give a quick account on divisorial stability, and then I will describe the behaviour of divisorial stability under finite group actions. In particular, I will show that equivariant divisorial stability of a polarised variety is equivalent to log divisorial stability of its quotient. I will then use this result to give a general construction of equivariantly divisorially stable polarised varieties. This is joint work with R. Dervan.</p>
<h3>2023-11-23<br>Noémie Legout</h3>
<h4>A Fukaya category of Lagrangian cobordisms</h4>
<p>Abstract: In the late 80's, motivated by questions of Hamiltonian dynamics, Floer used the theory of pseudo-holomorphic curves in order to define a chain complex associated to a pair of Lagrangian submanifolds in a compact symplectic manifold. This led later to the definition of the Fukaya category of a symplectic manifold: an A-infinity category whose objects are Lagrangians and morphisms spaces are given in terms of Floer complexes. These categories are extremely studied because their derived versions appear for example in one "side" of the homological mirror symmetry conjecture.</p>
<p>In this talk, I will give some ideas about how to define such a Fukaya category for a non-compact symplectic manifolds with "nice" boundary, i.e. contact type boundary. The objects of this category are Lagrangian cobordisms between Legendrian submanifolds (living in the boundary). There will be more pictures than formulas!</p>
<h3>2023-10-24<br>Antonio Trusiani, Chalmers and University of Gothenburg</h3>
<h4>Modifications of cscK classes</h4>
<p>Abstract: The study of constant scalar curvature Kähler (cscK) metrics on compact complex manifolds is a classical topic that has attracted enormous interest since the 1950s. However, detecting the existence of cscK metrics is a difficult task, which in the projective case conjecturally amounts to proving an important algebro-geometric stability notion.</p>
<p>In 2006, Arezzo and Pacard showed that having cscK metrics is a property that is preserved by blowing-up distint points on compact Kähler manifolds with discrete automorphism groups. This result has been recently extended by Seyyedali and Székélyhidi to blow-ups along submanifolds. In the talk, I will present a further "optimal" generalization that replaces blow-ups along submanifolds with modifications (holomorphic bimeromorphic maps). The proof only uses pluripotential-theoretical techniques and it can be very likely adapted to other situations. Time permitting, in the last part of the talk I will discuss applications and future developments.</p>
<h3>2023-10-12<br>Aurélio Menegon, Mid Sweden University</h3>
<h4>Singular complex analytic spaces: let’s fiber them, deform them, cut them… until we get some information!</h4>
<p>We are going to talk about singularities of complex analytic spaces and maps defined on them. First, we will discuss whether it is possible to use Milnor's approach to study these maps. Then, for isolated singularities, we will talk about deformations, while for non-isolated singularities we will explore the topology of their links.</p>
<h3>2023-10-05<br>Richard Lärkäng, Chalmers/GU</h3>
<h4>Chern classes of coherent analytic sheaves</h4>
<h3>2023-09-26<br>David Witt Nyström, Chalmers/GU</h3>
<h4>Transcendental Okounkov bodies</h4>
<p>Abstract: In the 90's Okounkov showed how one can associate convex bodies to ample line bundles, generalizing the classical correspondence in toric geometry between polarized toric manifolds and Delzant polytopes. In 2008 Lazarsfeld-Mustata and independently Kaveh-Khovanskii showed that Okounkovs construction works more generally for e.g. big line bundles. Just as in the toric case, the Euclidean volume of the Okounkov body is equal to the volume of the line bundle divided by n! (n being the complex dimension), which means that results in convex analysis can be used in the study of the volume of line bundles. In their paper Lazarsfeld-Mustata asked if one could similarly define the Okounkov body of a big (1,1)-cohomology class on a compact Kähler manifold, and if then the Euclidean volume of the Okounkov body would be equal to the volume of the class divided by n! In 2015 Deng Ya proposed how to define the Okounkov body of a big class, but only managed to prove the conjectured volume equality in dimension one and two. In a recent preprint Tamas Darvas, Remi Reboulet, Mingchen Xia, Kewei Zhang and myself prove the volume equality for all dimensions. In my talk I will explain the construction of the Okounkov body, both in the line bundle case and in the "transcendental" case of a cohomology class, and maybe give some ideas of the proof of the volume equality. </p>
<h3>2023-09-14 <br>Bo Berndtsson, Chalmers/GU</h3>
<h4>What I did on my summer vacation</h4>
<p>The formalism of superforms and supercurrents on $\R^n$ is a real variable analog of positive closed forms and currents. It was studied first in the thesis of Aron Lagerberg and has found applications in tropical geometry and the theory of Berkovich spaces. I will discuss its applications to convex geometry, developing the masters thesis of Simon Larsson. The main points are a new proof of the Alexandrov-Fenchel theorem -- mimicking Gromov's proof of the Khovanski-Teissier theorem -- and some tentative applications to Monge-Ampere equations on the boundaries of convex polytopes.</p>
<h3>2023-05-10 <br>Nikolay Shcherbina, Wuppertal</h3>
<h4>On cores and hyperbolicity of complex manifolds</h4>
<p>We define a notion of the core of a complex manifold and discuss its main properties. Then we indicate some applications of the core to the question of hyperbolicity of a given manifold.</p>
<h3>2023-05-04 <br>Mingchen Xia, IMJ-PRG </h3>
<h4>A transcendental approach to non-Archimedean metrics</h4>
<p>The pluripotential theory on a normal projective variety is closely related to the pluripotential theory on its Berkovich analytification. In particular, thanks to the celebrated work of Berman--Boucksom--Jonsson, we know that the space of finite energy non-Archimedean metrics associated with an ample line bundle is isomorphic to a subspace of the space of geodesic rays in the space Archimedean potentials. In this talk, I will explain an extension of this point of view to transcendental big classes. We show that Boucksom--Jonsson's envelope conjecture holds in our transcendental theory and our theory coincides with Boucksom--Jonsson's on smooth projective varieties.</p>
<p>Part of the talk is based on a joint work with Tamás Darvas and Kewei Zhang.</p>
<h3>2023-04-27 <br>Aron Wennman, Stockholm University </h3>
<h4>Random Weierstrass zeta functions</h4>
<p>In this talk, I will describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary (i.e. translation invariant) point process in the plane. These functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions, or equivalently as electric fields generated by a random configuration of point charges.</p>
<p>I plan to describe for which point processes these electric fields, after subtracting the mean, become translation invariant, and discuss how they may be used to study the growth of the number variance (“charge fluctuations”) of stationary point processes in dilations of Jordan domains with quite irregular boundaries.</p>
<p>This talk is based on recent joint work with Misha Sodin and Oren Yakir (Tel Aviv) (see <a href="https://arxiv.org/abs/2210.09882">https://arxiv.org/abs/2210.09882</a> and <a href="https://arxiv.org/abs/2211.01312">https://arxiv.org/abs/2211.01312</a>)</p>
<h3>2023-04-20 <br>Ludvig Svensson</h3>
<h4>Finite Parts of Certain Divergent Integrals and Their Dependence on Regularization Method</h4>
<p>Let X be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on X that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle <br>E-&gt;X. We consider two different regularizations of such integrals, both depending on a choice of smooth Hermitian metric on E. Given such a choice, for each of the two regularizations there is a natural way to define a finite part of the divergent integral, and I will explain that they coincide. Furthermore, I'll present an explicit formula for the dependence on the choice of metric of the finite part, and briefly talk about how it was obtained.</p>
<h3>2023-03-09 <br>Siarhei Finski, École polytechnique</h3>
<h4>Submultiplicative norms and filtrations on section rings</h4>
<p>A graded norm on a section ring of a polarised projective manifold is called submultiplicative if the norm of products of holomorphic sections is no bigger than the products of norms. Such norms arise naturally in complex geometry and functional analysis. For example, in the former context, they appear in the study of holomorphic extension problems, submultiplicative filtrations (related to K-stability) and Narasimhan-Simha pseudonorms. In the latter context, they appear in the study of projective tensor norms on polynomial rings.</p>
<p>We show that submultiplicative norms on section rings of polarised projective manifolds are asymptotically equivalent to sup-norms associated with metrics on the polarising line bundle. We then derive several applications of this result to the aforementioned problems. The holomorphic extension theorem of Ohsawa and Takegoshi, semiclassical analysis in complex geometry and pluripotential theory play a prominent role in our work.</p>
<p>This is joint work with Zakarias Sjöström-Dyrefelt (Aarhus).</p>
<h3>2023-03-03 <br>Martin Sera, Kyoto University of Advanced Science</h3>
<h4>Lelong numbers of direct images of generalized Monge-Ampère products</h4>
<p>In this presentation, we consider generalized (mixed) Monge-Ampère products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several articles written by subsets of M. Andersson, Z. Błocki, R. Lärkäng, H. Raufi, J. Ruppenthal, E. Wulcan and the speaker. We continue these studies and present estimates for the Lelong numbers of pushforwards of such products by proper holomorphic submersions. Furthermore, we apply these estimates to Chern and Segre currents of pseudoeffective vector bundles. Among other corollaries, we obtain the following generalization of a recent result by X. Wu. If the non-nef locus of a pseudoeffective vector bundle E on a Kähler manifold is contained in a countable union of k-codimensional analytic sets, and if the k-power of the first Chern class of E is trivial, then E is nef.</p>
<p>This is joint work with Zakarias Sjöström-Dyrefelt (Aarhus).</p>
<h3>2023-03-02 <br>Sohaib Khalid, SISSA</h3>
<h4>The Z-critical equation on surfaces</h4>
<p>Introduced by Dervan-McCarthy-Sektnan, the Z-critical equations are conjectural complex differential-geometric analogues of Bridgeland stability conditions and seek to strengthen the classical Hitchin-Kobayashi correspondence: a holomorphic vector bundle over a smooth projective variety is slope polystable if and only if it admits a Hermite-Einstein metric. In this talk, I will briefly discuss the motivation and setting of the Z-critical equations, before specialising to the case of line bundles on projective surfaces. In this special case, I will attempt to explain how certain facts from the classical geometry of surfaces give a PDE analogue of a wall-and-chamber decomposition.</p>
<p>This is joint work with Zakarias Sjöström-Dyrefelt (Aarhus).</p>
<h3>2023-02-23 <br>Álfheiður Edda Sigurðardóttir, University of Iceland</h3>
<h4>Weighted and graded pluripotential theory</h4>
<p>The Green function has a higher dimensional version called the pluricomplex Green function. The Siciak-Zakharjuta theorem states that the pluricomplex Green function is equal to the Siciak function, which is written in terms of polynomials. The usual grading of polynomials is the smallest dilate of the unit simplex containing its support. If the unit simplex is replaced by any compact convex set, a new grading of polynomials arises and a new Siciak function. We study when a generalization of the Siciak-Zakharjuta theorem applies in this setting.</p>
<h3>2023-02-16 <br>Rémi Reboulet, Chalmers and University of Gothenburg</h3>
<h4>The birational geometry of GIT quotients</h4>
<p>If X is a projective variety with an action of a reductive group G, Geometric Invariant Theory (GIT) yields a projective quotient of X by G. This construction depends on the choice of a G-linearised ample line bundle L on X. Varying L, it is known that we obtain birational GIT quotients, but only finitely many varieties arise in this way. Borrowing from the theory of Zariski--Riemann spaces, we explain how to construct a "universal" GIT quotient capturing all possible varieties birational to a given GIT quotient.</p>
<p>This is based on joint work with Ruadhaí Dervan.</p>
<h3>2023-02-09 <br>David Witt Nyström, Chalmers and University of Gothenburg</h3>
<h4>Competitive Hele-Shaw flows and quadratic differentials</h4>
<p>This talk is based on joint work in progress with Fredrik Viklund at KTH.</p>
<p>In the classical Hele-Shaw flow a domain in the complex plane grows according to Darcy's Law, thus modelling the propagation of a viscous fluid trapping in a thin layer. We introduce a competitive version of the flow where several domains on a compact Riemann surface similarly strive to expand but at the same time hinder each other. We conjecture that, with some easily understood exceptions, this flow will exist for all time and converge to an equilibrium configuration. Interestingly, such an equilibrium gives rise to a very special kind of quadratic differential on the Riemann surface, which is best understood in terms of its associated half-translation surface. In this talk I will try to explain all this, and time permitting maybe also say something about a connection to wall-crossing, and/or a related discrete model called competitive erosion.</p>

<p>The seminar usually meets on Mondays 13.15-14.00 CEST in room MVL:14. Talks are usually 25-30 minutes long and 10 minutes for discussion (\pm 5 minutes).</p>
<p>Send an email to the organizer if you want to be added to the seminar's mailling list.</p>
<p><a href="https://chalmers.zoom.us/j/69309989575" title="Zoom-link to CAM-seminar">Zoom meetings link​</a>. Send an email to the organizer if you need the password.</p>
<p>Please <a href="https://researchseminars.org/seminar/cam" title="Link to information about the CAM-seminar.">follow this link</a> for abstract and information about the seminar series.</p>
<p>Further interesting seminars in numerical analysis in Sweden <a href="https://sites.google.com/view/numerics-sverige/" title="Link to seminars in numerical analysis">can be found here</a>.</p>

<h2>Upcoming seminars</h2>
<h3>(always at 13:15 in MV:L14 unless otherwise stated)</h3>
<h3>2024-04-22 Eddie Wadbro, Karlstad University: Material distribution topology optimization for boundary-effect-dominated problems</h3>
<p>Abstract: In the classical design optimization using the material distribution method (density-based topology optimization), a material indicator function represents the presence or absence of material within the domain. The first part of this talk provides an introduction to material distribution topology optimization with an emphasis on mathematical morphology, non-linear filters, and length scale control.</p>
<p>To use the material distribution approach for boundary-effect-dominated problems, we need to identify the boundary of the design at each iteration; this talk discusses two methods to achieve this. The first is to use a boundary strip indicator function defined on the elements of the computational mesh. The second is to use a boundary indicator function defined on the mesh faces (edges in 2D and facets in 3D). The second part of my presentation covers the main ideas behind both approaches and showcases results from two applications, one suitable for each approach.</p>
<h3>2024-04-29 Ragnar Winther: What about <em>p</em>?</h3>
<p>Abstract: The title of this talk refers to a question frequently asked by Ivo Babuska, from the late 1980s and on, following various talks on finite element methods. More precisely, what can we say about the properties of finite element methods as we raise the polynomial degree? Even today the so called $p$-method is less understood,and the corresponding analysis is less canonical, than the traditional approach of mesh refinement, i.e., the $h$-method. In recent years Rick Falk and I have developed a theory which represents a new tool to analyze finite element methods of high polynomial degree, which we refer to as the bubble transform. The key idea is to construct a decomposition into local bubbles which simultaneously covers all possible polynomial degrees. The purpose of this talk is to give a review of this theory, and to discuss potential applications.</p>
<h3>2024-05-06 Axel Ringh</h3>

<p>What is geometric deep learning? It includes several directions within the foundations of machine learning.</p>
<p>One direction is “geometrization” of neural networks, driven by the need to deal with data defined on non-Euclidean domains, for example graphs or manifolds. Efforts here are in full focus due to the abundance of non-Euclidean data in biology, physics, network science, and computer vision.</p>
<p>Another direction is to study the geometry of spaces of probability measures. This paves the way for geometric developments and mathematical understanding of deep learning. An example is to analyze the Riemannian gradient flow structure of Sinkhorn and other algorithms used within neural networks.</p>
<p>Research about geometric structures in deep learning is still in its infancy. But it is rapidly developing, as witnessed by the diversity of subjects covered at recent workshops and conferences. At ICLR 2021, Bronstein gave a keynote talk entitled <em>Geometric deep learning – the Erlangen program of machine learning</em>. He outlined his grand vision for geometric deep learning and compared it to the famous <strong>Erlangen program</strong> in mathematics, proposed by Klein in 1872 as a <em>unified theory of geometry</em>, connecting group theory, and geometry in profound ways. In a similar way, geometric deep learning brings geometry, PDE, group theory, and representation theory into the realm of machine learning.</p>
<p>The research at the Department of Mathematical Sciences at Chalmers and the University of Gothenburg has close links to many different parts of geometric deep learning, in particular, optimal transport, information geometry, stochastic differential equations and representation theory. An important forum in this research is our <strong>Geometric Deep Learning Seminar</strong>, as a platform for discussion and engagement.</p>
<p><a rel="noopener" href="/en/current/calendar/?event.organisations.name=Department%20of Mathematical Sciences" target="_blank" title="Link to calendar for Mathematical Sciences." data-anchor="?event.organisations.name=Department of Mathematical Sciences">Check the department calendar</a> for the next planned seminar. </p>

<p>The aims of this seminar series on teaching and pedagogy are to</p>
<ul>
<li>increase the collegial discussion of basic education,</li>
<li>spread good examples within the faculty and</li>
<li>inspire to develop ones teaching.</li>
</ul>
<p>We have seminars with varying themes and a large part of the time will be devoted to discussion.</p>
<p>Previous seminars in the series is listed further down on the page. </p>
<p><a href="/institutioner/mv/forskning/seminarieserier/" title="Länk till sidan på svenska.">For abstracts in Swedish, go to the Swedish page</a>. </p>

<h3>Program for spring 2024</h3>
<p><strong>29 January at 9.00–10.00 – Anders Gustavsson, Nanyang Technological University, Singapore, joins via Zoom: Hur främjar vi konceptuellt lärande?</strong></p>
<p>Room: MV:L14 and <a href="https://chalmers.zoom.us/j/63991155899">https://chalmers.zoom.us/j/63991155899</a></p>
<p>Abstract in Swedish.</p>
<p><strong>26 February at 15.15–16.15 – Katarina Blom: Från Matlab till Python</strong></p>
<p>Room: MV:L14</p>
<p>Abstract in Swedish.</p>
<p><strong>25 March at 15:15-16:15 – CANCELLED</strong><span style="color: black; background: white;"></span></p>
<p><strong>29 April at 15.15-16.15&nbsp;– </strong><strong>Jan Stevens: Datorövningar i undervisningen</strong></p>
<p>Lokal: MV:L14</p>
<p>Abstract in Swedish.</p>
<p><strong>27 May at 15.15-16.15 – </strong><strong>Carl Lindberg: The Three Math Skills Our Students Need in Industry</strong></p>
<p>Room: MV:L14</p>
<p style="background: white;" class="elementtoproof">Abstract: I argue that in order for our students to one day become productive and competent engineers and applied mathematicians when they're working in industry, they need other mathematical skills than the skill of being able to solve standard problems posed to them by others, eg on exams. I suggest how we as teachers can help our students further develop these abilities.</p>

<h3>Program 2023</h3>
<h4>30 January – Olow Sande, Umeå universitet<br />Formativa grupparbeten på nybörjarkurser i matematik</h4>
<p>Abstract in Swedish. </p>
<h4>6 March – Burkhard Alpers, Aalen University of Applied Science<br />Making mathematics relevant for engineering students</h4>
<p>Often engineering students do not see in which ways their mathematical education is relevant for their engineering study course (“Why and where do I need this?”).</p>
<p>In my talk I will outline different ways to let students experience the relevance starting with classical learning settings like lectures and assignments and moving on to project tasks where more self-organised student activity is required. I will also talk about ways to find suitable tasks for students.</p>
<h4>4 April – Annoesjka Cabo, TU Delft<br />The Mathematics of Education - Integrate, Differentiate, Transform</h4>
<p>At TU Delft service mathematics is provided by mathematicians. About 40 staff members deliver basic mathematics courses to 20.000 students per year. In this talk I share the material developed in the Programme of Innovation in Mathematics Education (PRIME): applets, online exercises, slides, videos, etc . Moreover I would like to discuss what it takes for such a large-scale innovation with tailored approaches to different study programmes to succeed and keep on doing so.</p>
<h4>24 April – Ulla Dinger, Chalmers/University of Gothenburg<br />Mentorprogram för nya lärare och doktorander.</h4>
<p>Abstract in Swedish.</p>
<h4>29 Ma – Irina Pettersson, Chalmers/University of Gothenburg<br />Aktiv inlärning och andra knep</h4>
<p>Abstract in Swedish.</p>
<h4>30 October – Laura Fainsilber and Linnea Hietala<br />Gruppuppgifter för matematisk diskussion på distansbasåret</h4>
<p>Abstract in Swedish.</p>
<h4>27 November – Karl de Fine Licht, TME<br />AI in Higher Education</h4>
<p>Abstract: In the past year, there has been intense discussion surrounding the use of "generative AI" in higher education. While some have advocated for a complete ban, most suggest a more nuanced approach, proposing that we allow certain uses under specific circumstances while disallowing others. In this seminar, we will explore the tools that are relevant in an academic context, understand their capabilities and limitations, and discuss some prospects about what the future may hold.</p>
<h4>18 December – Staffan Frid, Klara Teoretiska Gymnasium, Stockholm<br />Skärmlös spelifikation som ett verktyg för ökad aktivitet i matematikklassrummet på gymnasiet</h4>
<p>Abstract in Swedish.</p>
<h3>Program 2022</h3>
<h4>28 februari – Seidon Alsaody, Uppsala Universitet<br />Linjär algebra, aktivt och konceptuellt</h4>
<p>Abstract in Swedish.</p>
<h4>28 mars – Jonas Månsson, Lunds Tekniska Högskola<br />Matematik på YouTube</h4>
<p>Abstract in Swedish. </p>
<h4>25 april – Olle Häggström<br />Bildningskurser på universitetsnivå</h4>
<p>Abstract in Swedish. </p>
<h4>30 maj – Julie Rowlett<br />Erfarenheter av att använda Inspera för online examination</h4>
<h4>26 september – Jonny Lindström<br />Lärandeaktiviteter i stora föreläsningsgrupper</h4>
<p>Abstract in Swedish.</p>
<h4>24 oktober – Samuel Bengmark<br />Pragmatic Research on Pedagogical Practice-PREP</h4>
<p>Abstract in Swedish.</p>
<h4>1 december – Elin Götmark, Martin Hallnäs, Andreas Rosén, Ulla Dinger<br />Kommunikationsspåret</h4>
<p>Abstract in Swedish.</p>
<h4>19 december – Meike Akveld, ETH<br />Improving mathematics diagnostic tests using item analysis</h4>
<p>Many universities use diagnostic tests to assess incoming students’ preparedness for mathematics courses. Diagnostic test results can help students to identify topics where they need more practice, and give lecturers a summary of strengths and weaknesses in their class. We demonstrate a process that can be used to make improvements to a mathematics diagnostic test, so that it provides better information about students’ abilities. To identify questions that could be improved, our process uses item response theory to analyse student data. We provide an accessible introduction to the key ideas of item response theory, and demonstrate applying the process to make improvements to diagnostic tests at two universities. Our method provides a model for others wishing to make improvements to mathematics diagnostic tests.</p>
<h3>Program 2021</h3>
<h4>22 februari – Jonas Enger, Fysik <br />Didaktiskt inriktad högskolepedagogisk kurs</h4>
<p>Abstract in Swedish.</p>
<h4>7 april – Klas Modin<br />Using Jupyter Notebook and Canvas in combination</h4>
<p>Ideas on how to integrate Jupyther Notebook in Canvas.</p>
<h4>26 april – Stefan Lemurell<br />Högskolepedagogiska kurser</h4>
<p>Abstract in Swedish.</p>
<h4>31 maj – Elin Götmark<br />Erfarenheter av Flipped Classroom</h4>
<p>Abstract in Swedish. </p>
<h4>27 september – Åke Fäldt, Fysik<br />Gruppduggor som ett effektivt pedagogiskt hjälpmedel</h4>
<p>Abstract in Swedish. </p>
<h4>25 oktober – Hossein Raufi<br />Erfarenheter av aktiv undervisning</h4>
<p>Abstract in Swedish. </p>
<h4>22 november – Max Lyles, jurist på GU<br />Distansundervisning: juridiska frågor</h4>
<p>Abstract in Swedish.</p>
<h3>Program 2020</h3>
<h4>27 januari – Marija Cvijovic<br />Teaching math to non-mathematicians: one size does not fit all</h4>
<h4>24 februari – Samuel Bengmark<br />Bevisens roll i undervisningen</h4>
<p>Abstract in Swedish.</p>
<h4>30 mars – Stefan Lemurell<br />Dela erfarenheter av distansundervisning</h4>
<p>Seminar to share experiences after the first week of distance teaching.</p>
<h4>27 april – Stefan Lemurell<br />Erfarenheter av examination på distans</h4>
<h4>18 maj – Jana Madjarova<br />Tråckelstygn och efterstygn, eller hur man förlänger en läsperiod.</h4>
<h4>26 oktober – Elin Götmark, Torbjörn Lundh och Serik Sagitov Bildningskurser i matematik</h4>
<p>Abstract in Swedish. </p>
<h4>14 december – Jan-Fredrik Olsen, Lund<br />Programmering som verktyg i undervisningen av gränsvärdesbegreppet</h4>
<p>Abstract in Swedish. </p>
<h3>Seminarier 2019</h3>
<h4>18 februari – Julie Rowlett <br />(klein)-Kleindagarna</h4>
<p>The "Kleindagarna" is a workshop held bi-annually at the Mittag-Leffler Institute. This workshop brings together teachers from Swedish high schools and universities, with the aim of working together to create interesting, engaging, and educational lesson plans. I was invited this January to give one of four "inspirational lectures". In the end, though, I was no less inspired than the other participants, coming away with new energy and ideas for teaching. Here, we will have a klein-Kleindag together! To start, I will explain what we did in the Kleindagarna. Then, we will work together in the same way:  we shall split into groups based on choosing one of four topics. Each group will work together to create a pilot lesson plan inspired by their chosen topic. A key and guiding element will be the "5 Es". At the end, each group will share their pilot lesson plan. The group work can be either Swedish or English, as people prefer!</p>
<h4>18 mars – Bo Berndtsson<br />Kursen Perspektiv på matematik</h4>
<p>Abstract in Swedish.</p>
<h4>29 april – Sonja Bjelobaba, GU och Uppsala universitet<br />Designa bort plagiering</h4>
<p>Abstract in Swedish. </p>
<h4>27 maj – Laura Fainsilber<br />Höstmatte: ett försök med självstudier för repetition inför den första matematikkursen, med hjälp av filmer och test i Möbius</h4>
<p>Abstract in Swedish. </p>
<h4>30 september – Ulla Dinger<br />Mentorsprogram för nya lärare</h4>
<p>Abstract in Swedish. </p>
<h4>28 oktober – Linda Mattsson, BTH<br />Hur kan vi öka civilingenjörsstudenters fokus på kreativa matematiska lösningsstrategier?</h4>
<p>Abstract in Swedish.</p>
<h4>25 november – David Witt Nyström<br />"How I wish I'd taught maths"- tankar om boken av Craig Barton</h4>
<h3>Program 2018</h3>
<h4>19 februari – Samuel Bengmark<br />En modell för undervisningskompetenser</h4>
<p>Abstract in Swedish.</p>
<h4>12 mars – Torbjörn Lundh<br />Fermatpedagogik – en metod att underlätta studenters föreläsningsantecknande</h4>
<p>Abstract in Swedish.</p>
<h4>16 april – Erik Broman<br />Mina budord för undervisning</h4>
<p>Abstract in Swedish.</p>
<h4>14 maj – Samuel Bengmark<br />Vad skulle få dig att söka Excellent Teaching Practitioner</h4>
<p>Abstract in Swedish.. </p>
<h4>24 september – Lars Filipsson, KTH<br />Interaktiva föreläsningar</h4>
<p>Abstract in Swedish. </p>
<h4>29 oktober - Samuel Bengmark<br />Om kursutvärderingar inte mäter kursens effektivitet, hur skall vi då använda dem?</h4>
<p>Discussion about studies from Department of Statistics at UC Berkeley.<br />(<a href="https://www.scienceopen.com/document?vid=42e6aae5-246b-4900-8015-dc99b467b6e4">Stark 2014</a>, <a href="https://www.scienceopen.com/document?vid=818d8ec0-5908-47d8-86b4-5dc38f04b23e">Boring 2016</a>). </p>
<h4>26 november – Anders Logg<br />Matematikundervisning på M</h4>
<p>Abstract in Swedish. </p>
<h4>17 december – Thomas Wernstål<br />Examination av Matlab med Möbius</h4>
<p>Abstract in Swedish. </p>
<h3>Program 2017</h3>
<h4>20 mars – Vilhelm Adolfsson och Daniel Persson<br />Filmer i undervisningen</h4>
<p>Abstract in Swedish. </p>
<h4>24 april – Samuel Bengmark<br />Tentarättning – hur gör vi, och hur gör man bäst?</h4>
<p>Abstract in Swedish. </p>
<h4>22 maj – Sergey Zuev <br />VLE</h4>
<h4>18 september – Samuel Bengmark<br />Vad krävs för att lyckas i övergången från gymnasie- till högskolematematik?</h4>
<p>Abstract in Swedish. </p>
<h4>16 oktober – Damiano Ognissanti <br />Möbius</h4>
<p>Abstract in Swedish. </p>
<h4>20 november – Jonny Lindström och Jan Stevens<br />Examination av Matlab med Maple T.A.</h4>
<h4>11 december – Elin Götmark <br />Studenters matematiska skrivande​</h4>
<p>Abstract in Swedish. </p>
<h3>Program 2016</h3>
<h4>14 mars – Stefan Lemurell <br />Kursplaner och examination</h4>
<p>Abstract in Swedish. </p>
<h4>25 april – Thomas Wernstål<br />Ping Pong/GUL</h4>
<p>Abstract in Swedish. </p>
<h4>9 maj – Ulla Dinger<br />Studentansvar</h4>
<p>Abstract in Swedish. </p>
<h4>23 maj – Ulla Dinger<br />Akademisk ärlighet</h4>
<p>Abstract in Swedish. </p>
<h4>24 oktober – Samuel Bengmark<br />Om föreläsningar</h4>
<p>Abstract in Swedish. </p>
<h4>21 november – Ann-Brith Strömberg och Kerstin Wiklander<br />Inslag om hållbar utveckling i våra kurser</h4>
<p>Abstract in Swedish. </p>
<h4>19 december – Jan Stevens<br />Maple T.A.</h4>
<p>Examples of the use of Maple T.A. in teaching. </p>

<p>Please <a href="https://researchseminars.org/seminar/gbgstats" title="Link to information about Gothenburg statistical seminar.">follow this link</a> for abstract and information about the seminar series. You will also find information about the next seminar in the calendar.</p>

<p>Most of the seminars are in Swedish, and information is on <a href="/institutioner/mv/forskning/seminarieserier/" title="Link to seminar page in Swedish">the Swedish page</a>. Any seminars held in English will be published here.&nbsp;</p>
<h3>02.11.2023 – <a rel="noopener" href="https://www.gse.harvard.edu/directory/faculty/jon-star" target="_blank" title="Jon Star">Jon Star</a>, Harvard: Mathematical flexibility: A promising focus for research and practice</h3>
<p>Abstract: Mathematical flexibility is increasingly recognized as an important construct of interest for both researchers and practitioners in mathematics education. Flexibility can be characterized as a learner’s willingness to change strategies based on the particular problem-solving conditions or goals. In this talk, I first provide an introduction to flexibility. I then explore different ways that flexibility has been assessed, highlighting successes and challenges in the various forms of assessment. I then present recent empirical research results on flexibility, and I conclude by suggesting some promising areas for future research on flexibility.</p>
<h3>28.08.2023 - Javier Marmolejo and Sebastian Kilde: Visualizing the spherical well potential:&nbsp;The missing analogy on the path toward teaching the hydrogen atom</h3>
<p><strong>Abstract</strong>: An important milestone in teaching quantum mechanics is modeling the hydrogen atom. Usually, the path starts with solving the Schrödinger equation for the square well potential, placing the electron inside a one-dimensional box. It then moves up in complexity and closer to the hydrogen atom through the harmonic potential, the cubic well, and maybe even the quantum rotor. However, the most intuitive approximation to an atom, that of placing the electron inside a spherical box, is rarely included in textbooks, and important concepts, such as angular momentum, are lost. Here we introduce a graphical method of teaching the spherical well potential using an analogy between optics and quantum mechanics. It is backed up by recent experimental data on the optical resonances of an evaporating droplet. The explanation helps build a quantum mechanical intuition based on the shape of the potentials and the resulting resonances. As opposed to the square and harmonic potentials, it includes the concept of quantized angular momentum, while staying in one dimension, the radial one. The model can also highlight other quantum concepts such as tunneling, ground and excited states, and Fano resonances. This approach is akin to the analogy between a square well potential and a Fabry-Perot cavity and provides the missing link on the path to teaching the hydrogen atom.</p>
<p>This research seminar is arranged together with the research group PER at the Department of Physics.</p>

Algebraic geometry and number theory

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<p>Mathematical Science is a joint department between Chalmers and the University of Gothenburg.</p>

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