Speaker(s): Han Le (University of Michigan)

]]>The equivariant complex cobordism spectrum MU_G, where G is a compact Lie (or just finite) group, are highly interesting and central objects in equivariant stable homotopy theory. In this talk, I will give an explicit computation, in terms of generators and relations, of the coefficient ring of MU_G, in the case where G is a cyclic group whose order is a power of a prime. In particular, I will discuss certain divisibility conditions that arise in the structure of such coefficient rings. Speaker(s): Po Hu (Wayne State University)

]]>In my talk I will introduce a tridiagonal random matrix models related to the classical Gaussian β-ensemble

in the high temperature regime, i.e. when the size N of the matrix tends to infinity with the constraint that

βN=2α constant, α>0. I will show how to explicitly compute the mean density of states and the mean

spectral measure for this ensemble. Finally, I will apply this result to compute the mean density of states for

the periodic Toda lattice in thermal equilibrium.

This talk is based on my recent preprint “On the mean Density of States of some matrices related to the

beta ensembles and an application to the Toda lattice”, arXiv preprint:2008.04604, and partly on a joint

work with T.Grava, A. Maspero, and A. Ponno “Adiabatic invariants for the FPUT and Toda chain in the

thermodynamic limit”, Communications in Mathematical Physics, 380 (2020), pp. 811–851. DOI:

10.1007/s00220-020-03866-2. Speaker(s): Guido Mazzuca (SISSA)

Speaker(s): Xin Zhang (University of Michgan)

]]>Speaker(s): Alex Kapiamba (U(M))

]]>The Robinson-Schensted-Knuth correspondence gives a very concrete algorithm for converting a permutation into a pair of Young Tableaux, from which we can extract the longest increasing subsequence of the original permutation. Fulton and Viennot's Geometric construction gives a different algorithm for producing these Young Tableaux, without so many intermediate steps. Along the way, it converts longest increasing subsequence(s) into disjoint longest paths in N^2 (the positive integer lattice). We will go over this alternative algorithm, enjoy some of its symmetries, and (time permitting) discuss how we might recover these longest disjoint paths. Speaker(s): Scott Neville

]]>Speaker(s): Yueqiao Wu (University of Michigan)

]]>In this talk we consider the propagation of waves transmitted by ambient noise sources.

We discuss a generalized Helmholtz-Kirchhoff identity that derives from Green's identity and Sommerfeld radiation condition. The inspection of this identity makes it possible to design passive imaging methods, i.e., imaging methods using only passive receiver arrays and ambient noise illumination. More surprisingly, it is also possible to design an original passive communication scheme between two passive arrays that uses only ambient noise illumination. The passive transmitter array does not transmit anything but it is a tunable metamaterial surface that can modulate its scattering properties and encode a message in the modulation.

Zoom Link: Join Zoom Meeting:

https://umich.zoom.us/j/94723461309

Meeting ID: 947 2346 1309

Passcode: 618309 Speaker(s): Josselin Garnier (Ecole Polytechnique, France.)

We introduce refined unramified cohomology. This notion allows us to give in arbitrary degree a cohomological interpretation of the failure of integral Hodge- or Tate-type conjectures, of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion classes with trivial transcendental Abel—Jaocbi invariant. Our approach simplifies and generalizes to cycles of arbitrary codimension previous results of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma that concerned cycles of codimension two or three. We give several applications that indicate how this approach can be used to study algebraic cycles in concrete examples. Speaker(s): Stefan Schreieder (Leibniz University Hannover)

]]>The talk is concerned with the Wasserstein metric and contains three parts. Motivated by the model-independent pricing of exotic options that is formulated in terms of the martingale optimal transport, we provide in the first part a computational method as well as its convergence rate using the Wasserstein metric. In the second part, we consider an optimization problem originating from an optimal urban planning problem, where the objective function is given by a parameterized semi-discrete Wasserstein distance. It appears that this optimization problem shares the common formulatation with the so-called Wasserstein GAN (Generative Adversarial Network). In contrast to the gradient methods, we adopt Lloyd's algorithm to solve this optimization problem and investigate its convergence. The last part is based on a recent work that is related to two variants: sliced Wasserstein metric and max-sliced Wasserstein metric. We prove that the max-sliced Wasserstein metric (of order 1) is strongly equivalent to the Wasserstein metric, while the sliced Wasserstein metric does not share this nice property. Speaker(s): Gaoyue Guo (UM)

]]>In this talk, I discuss the general question of how to obstruct and construct group actions on manifolds. I will focus on large groups like Homeo(M) and Diff(M) about how they can act on another manifold N. The main result is an orbit classification theorem, which fully classifies possible orbits. I will also talk about some low dimensional applications and open questions. This is a joint work with Kathryn Mann. Speaker(s): Lei Chen (Caltech)

]]>Speaker(s): Katie Waddle (University of Michigan)

]]>Speaker(s): Andrew Snowden (UM)

]]>Speaker(s): Jose Esparza Lozano

]]>https://arxiv.org/pdf/2003.13206.pdf by Paolo Cascini, Sho Ejiri, Janos Kollar, and Lei Zhang Speaker(s): Devlin Mallory

]]>Speaker(s): Alana Huszar (University of Michigan)

]]>Speaker(s): Katja Vassilev (University of Michigan)

]]>Speaker(s): Peter Haine (MIT)

]]>The Gaussian beta-ensemble (GbetaE) is a 1-parameter generalization of the Gaussian orthogonal/unitary/symplectic ensembles which retains some integrable structure. Using this ensemble, in Ramirez, Rider and Virag constructed a limiting point process, the Airy-beta point process, which is the weak limit of the point process of eigenvalues in a neighborhood of the spectral edge. They constructed a limiting Sturm—Liouville problem, the stochastic Airy equation with Dirichlet boundary conditions, and they proved convergence of a discrete operator with spectra given by GbetaE to this limit.

Jointly with Gaultier Lambert, we give a construction of a new limiting object, the stochastic Airy function (SAi); we also show this is the limit of the characteristic polynomial of GbetaE in a neighborhood of the edge. It is the solution of the stochastic Airy equation, which is the usual Airy equation perturbed by a multiplicative white noise, with specified asymptotics at time=+infinity. Its zeros are given by the Airy-beta point process, and the mode of convergence we establish provides a new proof that Airy-beta is the limiting point process of eigenvalues of GbetaE. In this talk, we survey what new information we have on the characteristic polynomial; we show from where the stochastic Airy equation arises; we show how SAi is constructed; and we leave some unanswered questions. Speaker(s): Elliot Paquette (McGill University)

Speaker(s): Berkan Yilmaz (University of Michigan)

]]>For historians, the thirties are arguably the most difficult decade of the twentieth century to capture. Crisis and consolidation coexisted. The talk will illustrate this general impression with respect to the international mathematical community and the development of mathematics.

A broad variety of events will be discussed, such as the beginning of the IAS in Princeton, two brilliant ICMs (1932 in Zurich and 1936 in Oslo), a memorable conference in Moscow; the axiomatization of probability, the beginning of Bourbaki, the rewriting of Algebraic Geometry; politically motivated migrations, the fate of international mathematical review journals, etc. etc.

Many of these events have left their mark on mathematics as we know it today.

Zoom Link: https://umich.zoom.us/j/99980730858

Passcode: 201877 Speaker(s): Norbert Schappacher (Université de Strasbourg)

Speaker(s): Alex Kapiamba (U(M))

]]>Speaker(s): Ekaterina Shchetka (University of Michigan)

]]>Let S be the random walk obtained from “coin turning" with some sequence {p_n}n≥2, where {p_n}n≥2 is a given sequence of the probabilities to "turn the coin" at step n. In this paper we investigate the scaling limits of S in the spirit of the classical Donsker invariance, both for the heating and for the cooling dynamics.

We prove invariance principles, albeit with a non-classical scaling, holds for “not too small" sequences. The order const·n−1 (critical cooling regime) being the threshold. At and below this critical order, the scaling behavior is dramatically different from the one above it. The same order is also the critical one for the Weak Law of Large Numbers to hold.

In the critical cooling regime, an interesting process emerges: it is a continuous, piecewise linear, recurrent process, for which the one-dimensional marginals are Beta-distributed. Speaker(s): Zhenhua Wang (UM)

Speaker(s): Laure Flapan (Michigan State University)

]]>Speaker(s): Patricia Klein (University of Minnesota)

]]>In this talk we will present an area of analysis that is concerned with the extent to which a differential operator, and the properties of its solutions, determine the geometry of the domain on which they are considered. We will initially describe the case where the differential operator sees the domain as a homogeneous medium. We will contrast this with several inhomogeneous cases and mention some recent results in that direction. The tools used come from analysis of partial differential equations, harmonic analysis and geometric measure theory.

Zoom Link: https://umich.zoom.us/j/92859023148

Passcode: 831588 Speaker(s): Tatiana Toro (University of Washington)

Speaker(s): Giulio Tiozzo (Toronto)

]]>We compute the Bowley solution of a one-period, mean-variance

Stackelberg game in insurance, in which a buyer and a seller of insurance are the two

players, and they act in a certain order. First, the seller offers the buyer any

(reasonable) indemnity policy in exchange for a premium computed according to the

mean-variance premium principle. Then, the buyer chooses an indemnity policy, given

that premium rule. To optimize the choices of the two players, we work backwards.

Specifically, given any pair of parameters for the mean-variance premium principle, we

compute the optimal insurance indemnity to maximize a mean-variance functional of

the buyer's terminal wealth. Then, we compute the parameters of the mean-variance

premium principle to maximize the seller's expected terminal wealth, given the

foreknowledge of what the buyer will choose when offered that premium principle. This

pair of optimal choices, namely, the optimal indemnity and the optimal parameters of

the premium principle, constitute a Bowley solution of this Stackelberg game. We

illustrate our results via numerical examples. Speaker(s): Jenny Young (UM)

Speaker(s): Nick Wawrykow (UM)

]]>Speaker(s): TBA

]]>Speaker(s): Jesse Capecelatro (University of Michigan)

]]>Speaker(s): TBA

]]>Speaker(s): Daniel Lecoanet (Princeton University)

]]>Speaker(s): Sandor Kovacs (University of Washington)

]]>Speaker(s): TBA

]]>Speaker(s): Burt Totaro (UCLA)

]]>Title: Tame geometry and Hodge Theory

Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendieck period conjecture, this transcendence is severely constrained.

Tame geometry, whose idea was introduced by Grothendieck in the 80s, seems a natural setting for understanding these constraints. Tame geometry, developed by model theorists as o-minimal geometry, has for prototype real semi-algebraic geometry, but is much richer. It studies structures where every definable set has a finite geometric complexity.

The aim of these lectures is to present a number of recent applications of tame geometry to several problems related to Hodge theory and periods. Speaker(s): Bruno Klingler (Humboldt University)

Speaker(s): Huyen Pham (Universite Paris Diderot)

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