Speaker(s): David Schwein (University of Michigan)

]]>When studying dynamical systems, one is often interested in proving strong chaotic properties about a dynamical system like ergodicity, and mixing. Ergodicity, being the weaker property, is usually easier to prove. However, under certain conditions, we can upgrade ergodicity to mixing using a seemingly unrelated result from representation theory, the Howe-Moore theorem. In this talk, we will see how this is done, and also give a proof of the Howe-Moore theorem. Speaker(s): Sayantan Khan (University of Michigan)

]]>In this talk, I will present the tame automorphisms group preserving an affine quadric threefold. The main focus of my talk is the understanding of the degree sequences induced by the elements of this group. Precisely, I will explain how one can apply some ideas from

geometric group theory in combination with valuative techniques to show that the values of the dynamical degrees of these tame automorphisms admit a spectral gap. Finally I will apply these techniques to characterize when the degree exponents of a random walk on this particular group are strictly positive. Speaker(s): Nguyen-Bac Dang (Stony Brook University)

4-dimensional N=2 supersymmetric quantum field theories provide many interesting results in mathematical physics. Among them, the Seiberg-Witten theory can be used to compute some topological invariants, and the AGT relation sets up a connection between 4d quantum field theories and 2d conformal field theories. It was found by Nekrasov that the Seiberg-Witten theory can be solved using localization in the so-called Omega background. Using some recently developed techniques, we can generalize the previous works to 4d N=1 supersymmetric theories by localizing them on some backgrounds equivalent to the Omega background. This new result can be used to establish the AGT relation in some previously unknown cases (N=2 non-Lagrangian theories, N=1 theories, etc.), and may lead to some novel topological invariants in lower dimensions. In this talk, we will discuss these aspects of 4d N=2 and N=1 quantum field theories. Speaker(s): Jun Nian (UM)

]]>How do you find a maximum matching on a bipartite graph? What about if the edges are weighted? In the first case, we can connect the problem to a question of max flow in networks. In the weighted case, the exact connection to networks is lost, and new methods must be employed . We'll go through the Ford-Fulkerson algorithm for unweighted bipartite graphs, and the Hungarian method for weighted bipartite graphs. I'll discuss the complexity of the algorithms in both cases and other methods that improve the complexity. Speaker(s): Alana Huszar (University of Michigan)

]]>Speaker(s): Dan Burns (UM)

]]>A discussion session of our Learning Community on Inclusive Teaching. Speaker(s): Discussion

]]>In this talk we will introduce the Iwasawa decomposition of real semisimple Lie groups. The topics that we are going to discuss include: the Cartan decomposition of real semisimple Lie groups, the restricted root space decomposition and the Iwasawa decomposition. If time permits we will discuss some uniqueness properties of the Iwasawa decomposition. Speaker(s): Yuping Ruan (University of Michigan)

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The notion of topological entropy, arising from information theory,

is a fundamental tool to understand the complexity of a dynamical system.

When the dynamical system varies in a family, the natural

question arises of how the entropy changes with the parameter.

In the last decade, W. Thurston introduced these ideas in the

context of complex dynamics by defining the "core entropy" of

a quadratic polynomials as the entropy of a certain

forward-invariant set of the Julia set (the Hubbard tree).

As we shall see, the core entropy is a purely topological / combinatorial

quantity which nonetheless captures the richness of the fractal structure

of the Mandelbrot set. In particular, we will relate

the variation of such a function to the geometry of the Mandelbrot set.

We will also prove that the core entropy on the space of polynomials

of a given degree varies continuously, answering a question of Thurston. Speaker(s): Giulio Tiozzo (University of Toronto)

This talk considers model-free bounds for multi-asset option prices in a setting where the marginals are known and the dependence structure is partially known. We will first present methods to sharpen the classical FrÃ©chet-Hoeffding bounds on copulas using additional information on the dependence structure, and discuss their application in option pricing, portfolio Value-at-Risk and the detection of arbitrage. Then, we will consider model-free hedging of multi-asset option prices in the presence of additional information on the dependence structure. An extension of the classical optimal transport superhedging duality will allow us to provide new insights in model-free hedging, and show (non) sharpness of the improved FrÃ©chet-Hoeffding bounds. Speaker(s): Antonis Papapantaleon (National Technical University of Athens)

]]>In this talk we will consider a discrete group acting on the circle by orientation-preserving homeomorphisms and review some of the properties of the Euler class associated to this action. In particular, we will be interested in the Euler class associated to the Nielsen action on the circle of the mapping class group of an orientable surface with one marked point. We will describe some partial results, in ongoing work with Solomon Jekel, on the vanishing and non-vanishing behaviour of the powers of this class. Speaker(s): Rita JimÃ©nez Rolland (Universidad Nacional AutÃ³noma de MÃ©xico)

]]>It is well-known that for compact uniformly hyperbolic systems HÃ¶lder potentials have unique equilibrium states. However, it is much less known for non-uniformly hyperbolic systems. In his seminal work, Knieper proved the uniqueness of the measure of maximal entropy for the geodesic flow on compact rank 1 non-positively curved manifolds. A recent breakthrough made by Burns, Climenhaga, Fisher, and Thompson which extended Knieper's result and showed the uniqueness of the equilibrium states for a large class of non-zero potentials. This class includes scalar multiples of the geometric potential and HÃ¶lder potentials without carrying full pressure on the singular set. In this talk, I will discuss a further generalization of these uniqueness results, following the scheme of Burns-Climenhaga-Fisher-Thompson, to equilibrium states for the same class of potentials over geodesic flows on compact rank 1 surfaces without focal points. This work is joint with Dong Chen, Kiho Park.

Speaker(s): Lien-Yung "Nyima" Kao (University of Chicago)

The Great Lakes Section of SIAM (GLSIAM) was formed in 1988 to serve Michigan, Northern Ohio, Northern Indiana, Southern Ontario, and the surrounding areas. It organizes its annual conferences around themes reflecting its membersâ€™ evolving interests within applied mathematics. Topical disciplines have included computer aided design, computational fluid dynamics, numerical solutions of PDEs, complex systems, and mathematical biology. The 2019 meeting will take place in the Department of Mathematics, East Hall, University of Michigan on Saturday, April 27th, 2019.

See conference webpage for more information:

https://mcaim.math.lsa.umich.edu/events/siam-spring-meeting-2019/

Speaker(s): Jan Obloj (Oxford)

]]>The Severi degrees of â„™1Ã—â„™1 can be computed in terms of an

explicit operator on the Fock space F[â„™1]. We will discuss this and

variations on this theme. We will explain how to use this approach to

compute the relative Gromov-Witten theory of other surfaces, such as

Hirzebruch surfaces and EÃ—â„™1. We will also discuss operators for

calculating descendants. Joint with R. Pandharipande. Speaker(s): Yaim Cooper (IAS)

TBA Speaker(s): JÃ¶rn Zimmerling (University of Michigan)

]]>Speaker(s): Sara Lapan (UC Riverside)

]]>Speaker(s): Charlotte Chan (Princeton University)

]]>Speaker(s): Tarek Elgindi (UC San Diego)

]]>Speaker(s): Ioannis Karatzas (Columbia University)

]]>Speaker(s): Ioannis Karatzas (Columbia University)

]]>Speaker(s): Ioannis Karatzas (Columbia University)

]]>Speaker(s): CRLT

]]>Speaker(s): Justin Sirignano (UIUC)

]]>Speaker(s): Michael Lipnowski (McGill University)

]]>Speaker(s): Fall Break

]]>Speaker(s): Sam Payne (University of Texas at Austin)

]]>Speaker(s): Chelsea Walton (University of Illinois)

]]>Speaker(s): Richard Rimanyi (University of North Carolina)

]]>Speaker(s): Richard Rimanyi (University of North Carolina)

]]>Speaker(s): Benoit Pausader (Brown University)

]]>Speaker(s): Vladimir Sverak (University of Minnesota)

]]>Speaker(s): CRLT

]]>Speaker(s): Winter Break

]]>Speaker(s): Laure Saint Raymond (ENS, Lyons)

]]>Speaker(s): Laure Saint Raymond (ENS Lyon, France)

]]>Speaker(s): Bruno Klingler (Humboldt University)

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