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 2023</h2>
<h3>27.09.2023 - Nancy Abdallah, Högskolan i Borås: Lefschetz properties of Artin Gorenstein algebras in codimensions 3 and 4</h3>
<p>Abstract: The weak and strong Lefschetz properties (WLP and SLP) has been much studied for Artinian algebras. Codimension two Artinian algebras over a field of characteristic zero have the strong Lefschetz property. It is open whether Artin Gorenstein (AG) algebras of codimension <em>c</em> = 3 satisfy the weak or strong Lefschetz properties. Harima, Migliore, Nagel, and Watanabe proved that complete intersection algebras of codimension three satisfy the weak Lefschetz property. For <em>c</em> = 4, Gondim showed that WLP always holds for regularity <em>r</em> ≤ 4 and gives a family where WLP fails for any <em>r</em> ≥ 7, building on an earlier example of Ikeda of failure for<br /><em>r</em> = 5.</p>
<p>In this talk we go through an overview of Lefschetz properties over AG algebras and we give some recent results in codimensions 3 and 4. In codimension 4 we explore relations between Lefschetz properties of an AG algebra A and the free resolutions of A.</p>
<h3>20.09.2023 - Lars Halle, University of Bologna: Degenerations of Hilbert schemes and relative VGIT</h3>
<p>Abstract: Let G be a reductive group acting on a projective variety X.  In Mumford's Geometric Invariant Theory (GIT),  the formation of a quotient in this situation depends on the choice of a G-linearized ample line bundle on X. In "Variation of GIT" (VGIT), one studies various aspects of this dependence. </p>
<p>I will report on joint work with K. Hulek and Z. Zhang, and explain how some central results in VGIT can be extended to a relative (and equivariant) setting. Our main motivation was to apply these results to the study of certain Hilbert scheme degenerations constructed as relative GIT quotients. In the second part of the talk, I will indicate how VGIT can be used to provide a conceptual understanding of the (semi)stable locus in this quotient constructione. </p>
<h3>15.09.2023 - Dennis Eriksson, Chalmers/GU: Determinant of the cohomology and mirror symmetry</h3>
<p>Abstract: In this talk, I will discuss the determinant of cohomology and its (conjectural) relationship to certain curve-counting on Calabi—Yau manifolds. The case in which the Calabi— Yau manifolds are elliptic curves will be discussed in detail, and other examples will be considered. If time permits, I will discuss ongoing work (w. Gerard Freixas) on these topics, surrounding the Grothendieck—Riemann—Roch theorem and geometric properties possibly expected from mirror symmetry considerations.  </p>
<h3>31.08.2023 - Victor Rotger, Universitat Politecnica de Catalunya, Barcelona: Elliptic Stark conjectures</h3>
<p>Abstract: In this lecture I will discuss several variants of a conjecture of Darmon, Lauder and myself. </p>
<p>Given a triple (f, g, h) of modular forms of weights (2, 1, 1), the conjecture formulates a p-adic BSD-type relationship </p>
<p>between an analytic iterated integral and a regulator given by logarithms of global points. I will focus on the particularly intriguing case where the weight one form g gives rise to a point on the eigencurve that<br />fails to be étale over weight space. </p>
<h3>07.06.2023 - Jan Vonk, Leiden University: Around the class number one problem</h3>
<p><strong>Abstract</strong>: I will discuss ongoing work with H. Darmon about singular moduli for real quadratic fields, and how the analytic part of the work of Gross-Zagier on analytic families of Eisenstein series can be fruitfully transposed to a p-adic context, if it is complemented by considerations of p-adic Galois deformations.  </p>
<h3>01.06.2023 - Huayi Chen, Université Paris Cité, Sorbonne Université: Arakelov geometry over an adelic curve</h3>
<p>Abstract: In a series of works in collaboration with Atsushi Moriwaki, we have been able to establish an Arakelov theory on a general countable field. In this talk, I will explain the basic idea of the construction and the results that we could obtain in such a framework. </p>
<h3>24.05.2023 - Mengdi Wang, KTH: Smooth numbers are orthogonal to nilsequences</h3>
<p><strong>Abstract</strong>: We say an integer is $[y',y]$-smooth if all its prime factors are in the interval $[y',y]$. Suppose that $K'\geq1$ is a large integer and $y'=\log^{K'}N$. In joint work with Lilian Matthiesen we prove that $[y',y]$-smooth numbers are orthogonal to nilsequences (generalized polynomial phase functions) as long as $\log^K N\leq y\leq N$ and $K/K'$ is sufficiently large. As an application, when the set of $[y',y]$-smooth numbers is rather dense, we can also count the number of solutions of linear equations in $[y',y]$-smooth numbers.  </p>
<h3>17.05.2023 - Lejla Smajlovic, University of Sarajevo: On some analytic and topological properties of the Ruelle zeta function twisted by a unitary multiplier system</h3>
<p><strong>Abstract</strong>: We study the Ruelle zeta function associated to cofinite hyperbolic Riemann surfaces with ramification points twisted by a unitary multiplier system of arbitrary real weight 2k. Using the properties of the zeta-regularized determinants we derive a new form of a functional equation for this function and compute explicitly the first term in the Laurent or Taylor series expansion of this function at s=0. When k is an integer, the order of a zero or a pole at s=0 is expressed in terms of topological invariants of the surface, degrees of singularity of the multiplier system at cusps and torsion points and the order of a zero/pole at s=0 of the scattering determinant. When k is non-integral, the order of a zero or a pole depends only on the  order of a zero/pole at s=0 of the scattering determinant.</p>
<p>We develop three applications that will be discussed during the talk. Two are related to the properties of the higher-dimensional Rademeister torsion for cocompact groups and one is related to evaluation of the lead term at s=0  in terms of special values of L-functions, when the underlying Fuchsian group is arithmetic and not cocompact. For example,  we show that the inverse of the higher-dimensional Rademeister torsion for a general Seifert fibered space and any acyclic irreducible representation of SL(n,C) equals the absolute value of the Ruelle zeta function at s = 0 on the cocompact Fuchsian group associated to this Seifert space and twisted by the n dimensional, weight 2k = 1 unitary multiplier system with the action on ramification points induced by this representation.</p>
<p>This work is joint with Jay Jorgenson and Min Lee.</p>
<h3>16.05.2023 - Céline Maistret, University of Bristol: Parity of ranks of abelian surfaces</h3>
<p><strong>Abstract</strong>: Let K be a number field and A/K an abelian surface. By the Mordell-Weil theorem, the group of K-rational points on A is finitely generated and as for elliptic curves, its rank is predicted by the Birch and Swinnerton-Dyer conjecture. A basic consequence of this conjecture is the parity conjecture: the sign of the functional equation of the L-series determines the parity of the rank of A/K.</p>
<p>Assuming finiteness of the Shafarevich-Tate group, we prove the parity conjecture for principally polarized abelian surfaces under suitable local constraints. Using a similar approach, we show that for two elliptic curves E_1 and E_2 over K with isomorphic 2-torsion, the parity conjecture is true for E_1 if and only if it is true for E_2.</p>
<p>In both cases, we prove analogous unconditional results for Selmer groups.</p>
<h3>10.05.2023 - Anders Södergren, Chalmers/GU: Extending the unconditional support in an Iwaniec-Luo-Sarnak family</h3>
<p><strong>Abstract</strong>: Iwaniec, Luo and Sarnak has (partially) confirmed the Katz-Sarnak heuristic (for the one-level density) in several families of classical automorphic L-functions. In this talk, I will discuss how we can use zero-density estimates for Dirichlet L-functions to extend the unconditional part of Iwaniec-Luo-Sarnak’s work in the family of L-functions attached to holomorphic newforms of fixed even weight and prime level tending to infinity. This is joint work with Lucile Devin and Daniel Fiorilli.</p>
<h3>26.04.2023 – Georg Oberdieck, KTH<br />Curve counting on the Enriques surface and Borcherds automorphic form</h3>
<p><strong>Abstract:</strong> An Enriques surface is the quotient of a K3 surface by a fixed point-free involution. Klemm and Marino conjectured a formula which expresses the Gromov-Witten invariants of the local Enriques surface in terms of automorphic forms. In particular, the generating series of Gromov-Witten counts of elliptic curves on the Enriques is predicted to be the Fourier expansion of (a certain power of) Borcherd's automorphic form on the moduli space of Enriques surfaces (a quotient of a Hermitian symmetric domain of type IV). In this talk I will first give an overview over the conjecture and then explain how to prove it.</p>
<h3>19.04.2023 – Paul Nelson, Aarhus University<br />The orbit method, microlocal analysis and applications to L-functions</h3>
<p><strong>Abstract:</strong> L-functions are generalizations of the Riemann zeta function. Their analytic properties control the asymptotic behavior of prime numbers in various refined senses. Conjecturally, every L-function is a "standard L-function" arising from an automorphic form. A problem of recurring interest, with widespread applications, has been to establish nontrivial bounds for L-functions. I will survey some recent results addressing this problem. The proofs involve the analysis of integrals of automorphic forms, approached through the lens of representation theory. I will emphasize the role played by the orbit method, developed in a quantitative form along the lines of microlocal analysis.</p>
<p>The results/methods to be surveyed are the subject of the following papers/preprints:</p>
<p><a href="https://arxiv.org/abs/1805.07750">https://arxiv.org/abs/1805.07750</a></p>
<p><a href="https://arxiv.org/abs/2012.02187">https://arxiv.org/abs/2012.02187</a></p>
<p><a href="https://arxiv.org/abs/2109.15230">https://arxiv.org/abs/2109.15230</a></p>
<h3>05.04.2023 – Claire Burrin, University of Zurich<br />Discrete lattice orbits in the plane</h3>
<p><strong>Abstract:</strong> Consider an orbit Gv, where G is a discrete group of invertible 2-by-2 matrices and v is a vector in the Euclidean plane. Under certain conditions on G and v, this is a discrete set in the plane. Such sets are instrumental to the study of the linear flow on Veech surfaces and in particular we want to understand how such discrete sets are distributed in the plane. I will give examples and explain which features make this problem amenable to tools from number theory and harmonic analysis.</p>
<p>This talk is based on joint works with Chaika, Fairchild, and Nevo, Ruehr, Weiss.</p>
<h3>29.03.2023 – Maxim Gerspach, KTH<br />Almost sure lower bounds for a model problem for multiplicative chaos in number theory</h3>
<p><strong>Abstract:</strong> Random multiplicative functions have received a lot of attention in recent years as a model for the Riemann zeta function on short intervals on the critical line. By now, we have a good understanding of their moments and a decent idea of their extremal behaviour, i.e., almost sure upper and lower bounds. More recently, Soundararajan and Zaman introduced a new model that can be thought of as a simplified function field analogue of random multiplicative functions, and they proved moments bounds for these quantities akin to ones of Harper. In this talk, I will discuss almost sure lower bounds for this quantity and some of the simplifications that can be made in the proof when compared to the random multiplicative setting. I will moreover talk about the optimality of these bounds.</p>
<h3>27.03.2023 - Seungki Kim, University of Cincinnati<br />The Siegel/Rogers integral formula and its extensions</h3>
<p><strong>Abstract:</strong> Abstract: Counting points of a random lattice -- a random element of SL(n,Z) \ SL(n,R) with respect to its natural probability measure -- has become a popular topic in recent years. The integral formulas of Siegel and Rogers, which translate an integral of counting functions over random lattices to an integral over a Euclidean space, are essential tools for such a task. In this talk, I will discuss several known approaches to proving formulas of this kind, and introduce some recent results.</p>
<h3>22.03.2023 - Jacques Benatar, University of Helsinki<br />Polynomials with multiplicative coefficients, and related questions</h3>
<p><strong>Abstract:</strong> I will discuss some recent work, joint with Alon Nishry and Brad Rodgers, concerning the distribution of Dirichlet and trigonometric polynomials generated by multiplicative coefficients f(n). In the first part of the talk we will explore some old and new results for deterministic sequences f(n) (Möbius, Legendre symbol,...), stopping along our journey to marvel at a variety of wild and thorny conjectures. The second half of the talk will be devoted to Steinhaus random multiplicative coefficients f(n) = X(n). These considerations give rise to a couple of intriguing arithmetic problems.</p>
<h3>15.03.2023 - Tobias Magnusson, Chalmers/GU<br />Scalar-valued depth two Eichler-Shimura integrals of Cusp Forms</h3>
<p><strong>Abstract: </strong>In this talk, I will introduce a scalar-valued Eichler-Shimura integral of depth two, and show that it is a component of a vector-valued modular form of a certain extension type. I will also show that the existence of this extension type provides an alternative proof of an orthogonality relation satisfied by period polynomials that is originally due to Pasol and Popa. I will emphasize throughout the relation of this research to existing research on higher order modular forms, Eichler cohomology, and iterated Eichler-Shimura integrals.</p>
<p>The talk is based on joint work with Martin Raum, and in particular the paper "Scalar-valued depth two Eichler-Shimura Integrals of Cusp Forms" (arXiv:2209.00488).</p>
<h3>01.03.2023 - Mykola Pochekai <br />How to compute Hodge-Deligne diamonds of limiting Hodge structures?</h3>
<p><strong>Abstract:</strong> In the talk, I will review the theory of limiting Hodge structures and its applications in the study of degenerations of Kähler manifolds. Specifically, I will compute the Hodge-Deligne diamond of limiting Hodge structures for a very concrete example: the degeneration of the Hodge structures of the family that arises as the mirror dual family to the general intersection of two cubics. Additionally, I will present the applications of these computations to Mirror Symmetry.</p>
<h3>22.02.2023 - Olav Richter, University of North Texas<br />Congruences of Hurwitz class numbers</h3>
<p><strong>Abstract: </strong>I will report on recent joint work with Olivia Beckwith and Martin Raum, and I will explain how automorphic forms can be used to study congruences of Hurwitz class numbers. The talk will be for non-experts and should also be accessible to graduate students interested in algebra and number theory.</p>
<h3>09.02.2023 - Magdalena Larfors, Uppsala University<br />Calabi-Yau metrics and machine learning </h3>

<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>
<h3>2023-10-03 at 13:15, MV:L14 Alexandru Aleman<br />(Lund)</h3>
<h4>Cyclicity in weighted Besov spaces</h4>
<p>If H is a reproducing kernel Hilbert space and Mult(H) denotes the space of pointwise multipliers of that space, we say that f ∈ H is cyclic if Mult(H) is dense in H. The first important example of cyclic functions are the so called outer functions which emerge from Beurling’s famous theorem about invariant subspaces of the unilateral shift operator on the Hardy space H2. Later, the work of Korenblum, Brown and Shields revealed that in smaller spaces of analytic functions in the disc, cyclicity of an outer function also depends on the size of its zero-set on the boundary. In general, a complete characterization of such functions is lacking, but the area is rich with deep results. Much less is known in the setting of spaces of functions on the unit ball in several complex variables and as is to expect, the situation is quite complicated. For example, there are polynomials without zeros in the ball which are not cyclic in the standard Drury-Arveson space.</p>
<p>The purpose of the talk is to present some recent results in this direction and the material is based on joint work with K.M. Perfekt, S. Richter, C. Sundberg and J. Sunkes.</p>
<h3>2023-10-10 at 13:15, MV:L14 Daniel Ueltschi <br />(Warwick, UK)</h3>
<h4>The Kac-Ward solution of the 2D Ising model</h4>
<p>Onsager proposed a closed-form expression for the free energy of the Ising model in 1944. The method of Kac and Ward is particularly elegant and it has recently been made rigorous by Lis and Aizenman-Warzel. I will show how to extend it to the triangular lattice, with coupling constants of arbitrary signs.</p>
<p>This is ongoing work with Georgios Athanasopoulos.</p>
<h3>2023-10-17 at 13:15, MV:L14 Frederik Ravn Klausen<br />(Copenhagen)</h3>
<h4>TBA</h4>
<h3>2023-10-24 at 13:15, MVL14 Nico Michele Schiavone<br />(BCAM, Bilbao)</h3>
<h4>TBA</h4>
<h3>2023-11-07 at 13:15, MVL14 Jacob Stordal Christiansen<br />(Lund)</h3>
<h4>TBA</h4>
<h3>2023-11-14 at 13:15, MV:L14 Marco Fraccaroli<br />(BCAM)</h3>
<h4>TBA</h4>
<h3>2023-11-28 at 13:15, MV:L14 Mia Deijfen</h3>
<h4>TBA</h4>

<h2>Previous seminars (most recent on top)</h2>
<h3>2023-09-26 Andreas Rosén<br />(Chalmers/University of Gothenburg)</h3>
<h4>Dirichlet and Neumann vs. Atiyah-Singer-Patodi</h4>
<p>We prove solvability results for these three types of boundary value problems for second order divergence form elliptic systems on manifolds with Lipschitz boundaries. Coefficients are bounded, accretive and measurable, satisfying a Carleson condition near the boundary, and solvability results are obtained in weighted L_2 norms of boundary data. We show how hard estimates from harmonic analysis are combined with soft estimates from Fredholm theory to prove solvability.</p>
<p>This is joint work with Pascal Auscher and Andrew Morris.</p>
<h3>2023-09-19 Nachi Avram Re'em<br />(Chalmers/University of Gothenburg)</h3>
<h4>α-stable stationary processes</h4>
<p>It is a classical result that mixing properties of Gaussian processes can be discerned through their associated spectral measure. It turns out that a similar phenomenon holds true for α-stable processes. In this talk, I will introduce the spectral representation of α-stable processes and discuss recent results on how it reflects their mixing properties. In contrast to Gaussian processes, in which the spectral measure is available when the indexing group is Abelian, our results in α-stable processes hold to the generality of all amenable groups.</p>
<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>
<p>We study the asymptotics of the k-regular self-similar fragmentation process. For α&gt;0 and an integer k≥2, this is the Markov process (I_t)_{t≥0} in which each It is a union of open subsets of [0,1), and independently each subinterval of It of size u breaks into k equally sized pieces at rate u^α. Let k^{−mt} and k^{−Mt} be the respective sizes of the largest and smallest fragments in I_t. By relating (I_t)_{t≥0} to a branching random walk, we find that there exist explicit deterministic functions g(t) and h(t) such that |mt−g(t)|≤1 and |Mt−h(t)|≤1 for all sufficiently large t. Furthermore, for each n, we study the final time at which fragments of size k^{-n} exist. In particular, by relating our branching random walk to a certain point process, we show that, after suitable rescaling, the laws of these times converge to a Gumbel distribution as n→∞.</p>
<p>Based on joint work with Piotr Dyszewski, Samuel G. G. Johnston, Joscha Prochno and Dominik Schmid</p>
<h3>2023-08-29 Jakob Björnberg (Chalmers/University of Gothenburg)</h3>
<h4>Dimerisation in mirror models and quantum spin chains</h4>
<p>We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous mirror weights. In the terminology of quantum spins, this symmetry-breaking is called "dimerisation". Based on joint works with K. Ryan as well as with P. Muehlbacher, B. Nachtergaele and D. Ueltschi.</p>
<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) </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>

<h2>Previous colloquia</h2>
<h3>2023</h3>
<h4>11/9 Pavel Kurasov, Stockholm</h4>
<p><strong>Crystalline measures and Fourier quasicrystals: from metric graphs to stable polynomials</strong></p>
<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>
<h3>2022</h3>
<h4>24/1 Jan Gerken (Chalmers and University of Gothenburg)</h4>
<p><strong>Geometric deep learning: On the interplay between mathematics and deep neural networks</strong></p>
<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)</h4>
<p><strong>Mathematical works of Hugo Duminil-Copin</strong></p>
<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)</h4>
<p><strong>Skeins on Branes</strong></p>
<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></h4>
<p><strong>AI Alignment, Embedded Agency and Decision Theory</strong></p>
<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)</h4>
<p><strong>Harnessing Quantum Entanglement</strong></p>
<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)</h4>
<p><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></p>
<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>

<h2>Upcoming seminars</h2>
<h3>2023-10-05 at 11:00–11:45, MVL14<br />Richard Lärkäng, Chalmers/GU</h3>
<h4>Chern classes of coherent analytic sheaves</h4>

<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 2023</h2>
<p>(Most recent on top.)</p>
<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 Wednesdays 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>2023-10-11 at 13:15, MV:L14<br />Mohammad Asadzadeh, Chalmers &amp; University of Gothenburg<br />On Nitsche approach for a finite element scheme for Maxwell equations</h3>
<p>Abstract: We show improved convergence for a $h-p$, streamline diffusion (SD), Nitsche's scheme for the Vlasov-Maxwell (VM) system. The standard Galerkin for VM equations, as 1st order hyperbolic, suffers from the draw-back of poor convergence. We have improved this convergence rate using:</p>
<p>(i) The SD method that adds artificial diffusion to the system.</p>
<p>(ii) The $h-p$ approach to gain adaptivity feature</p>
<p>(iii) Combined, differentiated, Maxwell equations to render the first order hyperbolic system to a second order hyperbolic equation (not applicable to Vlasov part).</p>
<p>(iv) Add of {\sl symmetry} and {\sl penalty} terms to reach final step of Nitsche's scheme.</p>
<p>Numerical examples are justifying the theory.</p>

<h2>Previous seminars during 2023</h2>
<h3>2023-09-27 at 13:15, MV:L14<br />Ioanna Motschan-Armen, Chalmers &amp; University of Gothenburg<br />Euler-Maruyama approximations of the stochastic heat equation on the sphere</h3>
<p>Abstract: The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated by a spectral method in space and forward and backward Euler– Maruyama schemes in time. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. Optimal strong convergence rates for a given regularity of the initial condition and driving noise are derived for the Euler– Maruyama methods. Besides strong convergence, convergence of the expectation and second moment is shown, where the approximation of the second moment converges with twice the strong rate. Numerical simulations confirm the theoretical results. <br />This is joint work with Annika Lang.</p>
<h3>2023-09-20 <br />Sagy Ephrati, University of Twente<br />Stochastic modeling for coarse computational geophysical fluid dynamics</h3>
<p>Abstract: Stochasticity has been employed systematically in geophysical fluid dynamics (GFD) to model uncertainty. Additionally, fully resolving geophysical flows is computationally expensive due to the large range of scales of motion present in these flows. These computational costs are efficiently mitigated by performing GFD simulations on coarse computational grids and modeling the effects of unresolved scales on resolved scales. On such grids, the uncertainty due to unresolved small-scale motions has to be taken into account as well as the loss of accuracy due to poorly resolved spatial derivatives. In this presentation, we discuss how data assimilation methods can be used to derive data-driven stochastic forcing for coarse computational GFD. We will show that a straightforward algorithm, based on several simplifying assumptions, already leads to qualitatively accurate outcomes at strongly reduced computational costs.</p>
<h3>2023-09-13 <br />Akash Sharma, Chalmers/University of Gothenburg<br />Random walks for approximating boundary value problems</h3>
<p>Abstract: We will present numerical method to simulate reflected stochastic differential equations. We generalize this algorithm to approximately solve linear Robin boundary value problems via their probabilistic representations. In next part of the talk, we will present numerical schemes to simulate confined Langevin dynamics which results in approximate solution of specular boundary value problems. We obtain rate of convergence of these algorithms and verify them with numerical experiments. This is a joint work with Prof. Benedict Leimkuhler (University of Edinburgh) and Prof. Michael V. Tretyakov (University of Nottingham).</p>
<h3>2023-09-06 <br />Yoshio Komori, Kyushu Institute of Technology<br />Split S-ROCK methods for high-dimensional stochastic differential equations</h3>
<p>Abstract: We propose explicit stochastic Runge--Kutta (RK) methods for high-dimensional It\^{o} stochastic differential equations. By providing a linear error analysis and utilizing a Strang splitting-type approach, we construct them on the basis of orthogonal Runge--Kutta—Chebyshev methods of order 2. Our methods are of weak order 2 and have high computational accuracy for relatively large time-step size, as well as good stability properties. In addition, we take stochastic exponential RK methods of weak order 2 as competitors. It is shown that the proposed methods can be very effective on high-dimensional problems whose drift term has eigenvalues lying near the negative real axis and whose diffusion term does not have very large noise. This is a joint work with Prof. Kevin Burrage.</p>
<h3>2023-08-30 <br />Johan Ulander, Chalmers/University of Gothenburg<br />Boundary-preserving numerical schemes for stochastic (partial) differential equations</h3>
<p>Abstract: In this talk we consider stochastic (partial) differential equations whose solutions remain in some (half-)bounded domain. This includes, for example, models for heat flow whose solutions remain positive. In general, classical numerical schemes do not have the property of remaining in such domain. In this half-way seminar, I present some novel ideas for developing and analysing boundary-preserving numerical schemes for stochastic (partial) differential equations. The presentation is based on joint works with Charles-Edouard Bréhier, David Cohen, and Lluís Quer-Sardanyons.</p>
<h3>2023-06-12<br />Eugen Smolkin, Högskolan i Gävle<br />The method of integral variational relations in the problem of eigenwaves of a plane dielectric layer coated with graphene</h3>
<p>The problem of propagation of electromagnetic waves in a inhomogeneous dielectric layer coated on one side with a layer of graphene, which is considered to be infinitely thin, is considered. The main problem in describing the process of wave propagation in a waveguide structure is to obtain a properties of the propagation constants. Maxwell's equations are solved in the frequency domain. The conjugation conditions contain the conductivity of graphene. In this work, we neglect the nonlinearity of graphene. The results of calculations of propagation constants depending on the parameters of the problem are presented.</p>
<h3>2023-06-07<br />Lluis Quer-Sardanyons, Autonomous University of Barcelona<br />Stochastic PDEs with fractional noise</h3>
<p>In this talk, we consider the stochastic wave and heat equations on the real line and driven by a Gaussian noise which behaves, in the space variable, like a fractional Brownian motion with Hurst index $H\in (0, 1)$. First, we explain how such a noise may be mathematically modeled, and then we define the notion of mild solution to our equations. Secondly, we focus on our main objective: prove that the solution of each of the above equations is continuous in terms of the parameter $H$, with respect to the convergence in law in the space of continuous functions.</p>
<p>This talk is based on a joint work with Luca M. Giordano (Università degli Studi di Milano) and Maria Jolis (UAB).</p>
<h3>2023-05-24<br />Liliane Basso Barichello, Federal University of Rio Grande do Sul<br />On benchmark solutions to the linear Boltzmann equation</h3>
<p>The linear Boltzmann equation is a fundamental model in the study of particle transport. Numerous relevant applications and the high complexity of such a model motivate continued research in this area.</p>
<p>In this talk, we analyze numerical techniques in developing benchmark solutions to the linear Boltzmann equation, with particular interest in thermal radiation and nuclear safety applications. We discuss asymptotic convergence of the spatial and angular discretization for two-dimensional discrete ordinates solutions. We also introduce the convergence analysis of iterative methods to solve a linear system relevant to the same class of applications.</p>

<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>Time for the seminars is always a Monday at 15:15 - 16:15. <br />We meet in hybrid form in MVL15 <a href="https://chalmers.zoom.us/j/63991155899" title="Zoom-link to the seminar.">and in Zoom</a>.</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 autumn 2023</h3>
<h4>30 October – Laura Fainsilber and Linnea Hietala</h4>
<h4>27 November – Karl de Fine Licht, TME</h4>
<h4>18 December – Staffan Frid, Klara Teoretiska Gymnasium, Stockholm</h4>

<h3>Program for spring 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 maj – Irina Pettersson, Chalmers/University of Gothenburg<br />Aktiv inlärning och andra knep</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. </p>
<h3>28.08.2023 - Javier Marmolejo and Sebastian Kilde: Visualizing the spherical well potential: 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>

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