Talk_id  Date  Speaker  Title 
26849

Tuesday 9/1 4:00 PM

Dmitry Chelkak, École Normale Supérieure

Bipartite dimer model and minimal surfaces in the Minkowski space
 Dmitry Chelkak, École Normale Supérieure
 Bipartite dimer model and minimal surfaces in the Minkowski space
 09/01/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
We discuss a new approach to the convergence of height fluctuations in the bipartite dimer model considered on big planar graphs. This viewpoint is based upon special embeddings of weighted planar graphs into the complex plane known under the name Coulomb gauges or, equivalently, tembeddings. The longterm motivation comes from trying to understand fluctuations on irregular graphs, notably on random planar maps equipped with the dimer (or, similarly, the critical Ising) model.
When the dimer model is considered on subgraphs of refining lattices, a classical conjecture due to KenyonOkounkov predicts the convergence of fluctuations to the Gaussian Free Field in a certain conformal structure. However, the latter is defined via a latticedependent entropy functional, which makes the analysis of irregular graphs highly problematic. To overcome this difficulty, we introduce a notion of 'perfect tembeddings' of abstract weighted bipartite graphs and develop new discrete complex analysis techniques to handle correlation functions of the dimer model on tembeddings. Though in full generality the existence of perfect embeddings remains an open question, we prove that  at least in some concrete cases  they reveal the relevant conformal structure in a latticeindependent way: as that of a related Lorentzminimal surface in the Minkowski space.
Based upon joint works with Benoît Laslier, Sanjay Ramassamy and Marianna Russkikh.

26855

Tuesday 9/15 4:00 PM

Martin Hairer, Imperial College London

Taming infinities
 Martin Hairer, Imperial College London
 Taming infinities
 09/15/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! What's worse, this doesn't just happen for some exotic theories, but in the standard theories describing some of the most fundamental aspects of nature. Various techniques, usually going under the common name of “renormalisation” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will dip our toes into some of the conceptual and mathematical aspects of these techniques and we will see how they have recently been used in probability theory to study equations whose meaning was not even clear until now.

26856

Tuesday 9/22 4:00 PM

John Lesieutre, Penn State University

Polynomial interpolation is harder than it sounds
 John Lesieutre, Penn State University
 Polynomial interpolation is harder than it sounds
 09/22/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Suppose that $(x_1,y_1),\ldots,(x_r,y_r)$ is a set of points in the plane. Given a degree $d$ and multiplicities $m_i$, does there a nonzero polynomial in two variables of degree at most $d$ which vanishes to order at least $m_i$ at $(x_i,y_i)$? What is the dimension of the space of such polynomials, and how does it vary with the parameters? I will explain some of the basic results and conjectures and show how this problem is connected to some questions of current interest in algebraic geometry.

26869

Tuesday 9/29 4:00 PM

Ruixiang Zhang, IAS

Kakeya type problems and analysis
 Ruixiang Zhang, IAS
 Kakeya type problems and analysis
 09/29/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Informally, Kakeya type problems ask whether tubes with different positions and directions can overlap a lot. One usually expects the answer to be no in an appropriate sense. Thanks to the uncertainty principle, such a quantified nonoverlapping theorem would often see powerful applications in analysis problems that have Fourier aspects. Perhaps the most wellknown Kakeya type problem is the Kakeya conjecture. It remains widely open in $\Bbb{R}^n (n>2)$ as of today. Nevertheless, in the recent few decades people have been able to prove new Kakeya type theorems that led to improvements or complete solutions to analysis problems that appeared out of reach before. I will give an introduction to Kakeya type problems/theorems and analysis problems that see their applications. Potentially reporting some recent progress joint with Du, Guo, Guth, Hickman, Iosevich, Ou, Rogers, Wang and Wilson.

26870

Tuesday 10/6 4:00 PM

Colin McLarty, Case Western Reserve University

Grothendieck's personal idea of a topos as a space
 Colin McLarty, Case Western Reserve University
 Grothendieck's personal idea of a topos as a space
 10/06/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
In 33 hours of tape recordings in 1973 Grothendieck described his view of topos beyond what is in the collective volume Théorie des topos et cohomologie étale (SGA 4). In particular, this shows how Grothendieck got his idea of a "generalized topological space" simultaneously with what became etale cohomology during a 1958 talk by JeanPierre Serre.

26871

Tuesday 10/20 4:00 PM

Alexander Volberg, Michigan State University

Metric properties of Banach spaces, Enflo's problem, Pisier's inequality and quantum random variables
 Alexander Volberg, Michigan State University
 Metric properties of Banach spaces, Enflo's problem, Pisier's inequality and quantum random variables
 10/20/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin (levina@msu.edu)
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure.
In the joint paper with Paata Ivanisvili and Ramon Van Handel we prove that Rademacher type and Enflo type coincide, settling a longstanding open problem in Banach space theory. The proof is based on a novel dimensionfree analogue of Pisier's inequality on the discrete cube, which, in its turn, is based on a certain formula that we used before in improving the constants in the scalar Poincaré inequality on the Hamming cube. I will also show several extensions of Pisier's inequality with ultimate assumptions on a Banach space structure.
Some of our results use approach via quantum random variables.

26912

Tuesday 10/27 4:00 PM

David Rowe, Mainz University

Emmy Noether: Mathematician Extraordinaire
 David Rowe, Mainz University
 Emmy Noether: Mathematician Extraordinaire
 10/27/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin (levina@msu.edu)
Emmy Noether is famous as the “mother of modern algebra,” but her influence extended far beyond algebra alone. This talk, based on my recent book with the title above, will focus on Noether’s broader influence as an international figure in the 1920s. Beyond her immediate circle of students, Noether’s courses drew talented mathematicians from all over the world. Four of the most important were B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky. Noether’s classic papers on ideal theory inspired van der Waerden to recast his research in algebraic geometry. Her lectures on group theory motivated Alexandrov to develop links between point set topology and combinatorial methods. Noether’s vision for a new approach to algebraic number theory gave Hasse the impetus to pursue a line of research that led to the BrauerHasseNoether Theorem, whereas her abstract style clashed with Taussky’s approach to classical class field theory during a difficult time when both were trying to find their footing in a foreign country. Hermann Weyl, her colleague before both fled to the United States in 1933, fully recognized that Noether’s dynamic school was the very heart and soul of the famous Göttingen community.
Two recent books on Emmy Noether:
Emmy Noether – Mathematician Extraordinaire
https://www.springer.com/gp/book/9783030638092
Proving It Her Way: Emmy Noether, a Life in Mathematics
https://www.springer.com/gp/book/9783030628109
