<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>

andesod

chrjohv

<h2>Seminars 2023</h2>
<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<br />recent years as a model for the Riemann zeta function on short intervals<br />on the critical line. By now, we have a good understanding of their<br />moments and a decent idea of their extremal behaviour, i.e., almost sure<br />upper and lower bounds. More recently, Soundararajan and Zaman<br />introduced a new model that can be thought of as a simplified function<br />field analogue of random multiplicative functions, and they proved<br />moments bounds for these quantities akin to ones of Harper. In this<br />talk, I will discuss almost sure lower bounds for this quantity and some<br />of the simplifications that can be made in the proof when compared to<br />the random multiplicative setting. I will moreover talk about the<br />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>Coming seminars</h2>
<h3>2023-03-28 at 13:15, MVL14 Alireza Ataei (Uppsala)</h3>
<h4>The Kato square root problem for weighted parabolic operators</h4>
<p>We talk about the Kato square root problem for weighted parabolic equations and the main motivations behind it. The Kato square root problem is one of the major tools for investigating the well-posedness of the boundary value problems (Dirichlet and Neumann) for elliptic and parabolic PDEs. In the talk, we bring up the methods, some recent developments, and open problems in the area.</p>
<h3>2023-04-04 at 13:15, MVL14 Lauren Köhler-Schindler (ETH Zürich)</h3>
<h4>Title to be announced</h4>
<h3>2023-04-18 at 13:15, MVL14 Anna Sakovich (Uppsala)</h3>
<h4>Title to be announced</h4>
<h3>2023-04-25 at 13:15, MVL14 Kevin Brix (Glasgow University)</h3>
<h4>Title to be announced</h4>
<h3>2023-05-02 at 13:15, MVL14 Stein Andreas Bethuelsen (Universitetet i Bergen)</h3>
<h4>Title to be announced</h4>
<h3>2023-05-09 at 13:15, MVL14 Nina Gantert, jubilee professor (Technical University of Munich)</h3>
<h4>Title to be announced</h4>
<h3>2023-05-23 at 13:15, MVL14 Kevin Schnelli (KTH)</h3>
<h4>Title to be announced</h4>

jakobbj

broman

<h2>Previous seminars (most recent on top)</h2>
<h3>2022-03-14 at 13:15, MVL14 Simon Schmidt (Copenhagen)</h3>
<h4>Quantum symmetry vs nonlocal symmetry</h4>
<p>We will introduce the notion of nonlocal symmetry of a graph G, defined as winning quantum correlation for the G-automorphism game that cannot be produced classically. We investigate the differences and similarities between this and the quantum symmetry of the graph G, defined as non-commutativity of the algebra of functions on the quantum automorphism group of G. We show that quantum symmetry is a necessary but not sufficient condition for nonlocal symmetry. In particular, we show that the complete graph on four points does not exhibit nonlocal symmetry. We will also see that the complete graph on five or more points does have nonlocal symmetry. This talk is based on joint work with David Roberson.</p>
<h3>2022-02-28 at 13:15, MVL14 Jasmin Matz (Copenhagen) </h3>
<h4>Analytic torsion for congruence quotients of SL(n,R)</h4>
<p>Abstract: The analytic torsion of a compact Riemannian manifold was introduced by Ray and Singer in the 70s to spectrally study the combinatorial Reidemeister torsion of the manifold. More recently, Bergeron, Venkatesh and others applied this to study torsion in the (co-)homology of cocompact arithmetic lattices in families. This is of number theoretic interest as such torsion classes are (expected to be) related to certain Galois representations. <br /><br />It is thus of interest to try to extend the definition of analytic torsion to non-compact locally symmetric spaces in a suitable way. The rank one (hyperbolic) case has been relatively well understood for a while, but the higher rank case comes with many new analytic difficulties. In this talk, I want to discuss some of the history and motivation for studying torsion, and then talk about some joint work with W. Mueller where we define the notion of analytic torsion for congruence quotients of SL(n,R)/SO(n). </p>
<h3>2023-02-14 Alexei Iantchenko (Malmö)</h3>
<h4>Semiclassical surface-wave imaging and leaking modes in seismology​</h4>
<p>Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. In case of isotropic medium, the surface wave decouples up to principal parts into Love and Rayleigh waves associated to scalar and matrix spectral problems, respectively. Since the mathematical features (such as spectrum, resonances) of these problems can be extracted from the seismograms, we are interested in recovering the Lamé parameters from these data. We generalize spectral methods for Schrödinger operators to the Rayleigh problem, which is essentially not of Schrödinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.</p>
<h3>2023-02-07 Sergey Neshveyev (Oslo) Semigroup</h3>
<h4>C*-algebras and faithful representations of groupoid C*-algebras</h4>
<p>Given a left cancellative monoid, there is a natural definition of its reduced C*-algebra arising from the left regular representation. It is much less clear how to define a full C*-algebra. The problem has over the years attracted attention of a number of mathematicians and by now has been solved for a relatively large class of monoids. One of the approaches is to construct groupoid models for the reduced C*-algebras. The question when such models actually work is part of the more general question of how to determine a faithful family of representations of a reduced groupoid C*-algebra. I'll explain a partial solution of the latter problem and discuss its application to semigroup C*-algebras. (Joint work with Gaute Schwartz.)</p>
<h3>2023-02-03 Urban Larsson (IIT Bombay)</h3>
<h4>Bidding Combinatorial Games</h4>
<p>The motivation of Combinatorial Game Theory (CGT) is recreational games with open information and no chance, such as Chess, Go, Tic-Tac-Toe, Hex, Checkers and many more. The motivation of Classical Game Theory (EGT) is real world economical situations. Tools from CGT are yet rarely (if ever) used in EGT, and vice versa. We discuss a combinatorial game generalization of alternating normal play (last move wins) to bidding normal play, via Discrete Richman Auctions; this is joint work with Prem Kant, Ravi K. Rai and Akshay V. Upasany.</p>
<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>

micbjo

dener

smoritz

<h2>Previous colloquia</h2>
<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>

<p><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">Check the department calendar</a> for the next event. </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>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>

cohend

<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>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>

samuel

Mathematical Sciences

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