Date/Time : 06 Mar 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Georgios Daskalopoulos, Brown University

Loosely speaking, Holomorphic rigidity of Teichmueller space states that the action of mapping class group uniquely determines the Teichmueller space as a complex manifold. I will sketch the main ideas involved in proving such result. The method of proof is through harmonic maps and fits into the framework of geometric superrigidity. In addition, I may discuss a harmonic maps proof of both the high rank and the rank one superrigidity of the mapping class group proved via other methods by Farb-Masur and Yeung.

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Date/Time : 13 Feb 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Yu Shih Hsien, National University of Singapore

A novel approach by combinations of classical mathematical analysis, probabilistic argument, and modern PDE together to give the fundamental solution of a heat equation with a bounded variation heat conductivity with a sharp 2nd order derivatives estimates.

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Date/Time : 16 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Frank den Hollander, Leiden University, The Netherlands

Search algorithms on networks are important tools for the organization of large data sets. A key example is Google PageRank, which assigns a numerical weight to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of measuring its relative importance within the set. The weighting is achieved by exploration. The mixing time of a random walk on a random graph is the time it needs to approach its stationary distribution (also called equilibrium distribution). The characterisation of the mixing time has been the subject of intensive study. Many real-world networks are dynamic in nature. It is therefore natural to study random walks on dynamic random graphs. In this talk we focus on a random graph with rescribed degrees. We investigate what happens to the mixing time of the random walk when at each unit of time a certain fraction of the edges is randomly rewired. We identify three regimes in the limit as the graph becomes large: fast, moderate, slow dynamics. These regimes exhibit surprising behaviour. The talk is aimed at a general mathematics audience. No prior knowledge of probability theory or graph theory is required.

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Date/Time : 09 Jan 2019 14:30
Venue : S17 #04-06 SR1
Speaker : Ngo Bao Chau, The University of Chicago and Vietnam Institute for Advanced Study in Mathematics

Back to 2000, Braverman and Kazhdan formulate a program aiming at generalizing the Godement-Jacquet construction of principal L-function. We will recall their program with more precision and some modest progress.

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Date/Time : 02 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Xu Jinchao, Penn State University

In this talk, I will discuss some mathematical relationships between deep neural networks, finite element and multigrid methods.

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Date/Time : 12 Dec 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Alan Reid, Rice University

A consequence of Mostow-Prasad rigidity is that the trace-field of an orientable finite volume hyperbolic 3-manifold M is a number field. In addition, there is a quaternion algebra over this number field that is a natural invariant associated to M. This talk will review this background, and survey recent advances in trying to understand the trace-field and this quaternion algebra, especially in the setting of Dehn surgery on a hyperbolic knot.

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Date/Time : 29 Nov 2018 16:00
Venue : S17 #04-06 SR1
Speaker : Yuval Peres, Microsoft Research

Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ? “Fairly” means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition—with exactly equal areas, no matter how the points are distributed. (See the cover of the AMS Notices at http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf or the PNAS article http://www.pnas.org/content/early/2018/09/06/1720804115 ). Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching of n uniform blue points to n uniform red points on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984). I will emphasize open problems on the diameters of the basins and the behavior of greedy matching schemes. Joint work with Nina Holden and Alex Zhai.

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Date/Time : 31 Oct 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Francois Labourie, University of Nice – Sophia Antipolis

The general subject of the talk will be to explain techniques helping in building surfaces in spaces. We will first recall how one can build (topologically) surfaces from triangles. Moving to geometry, and after a brief crash course in plane hyperbolic geometry, we will explain how one can describe « hyperbolic » surfaces out of « ideal triangles » in the hyperbolic plane, which themselves correspond to triple of points in the projective line. After having explained these basic constructions, I will explain how one can move to describe triangles associated to Lie group — think of of the group of invertible matrices with complex coefficients –and explain how these constructions, will the help of ideas from Probability Theory, can help to solve our initial problem: building surfaces in spaces known as symmetric spaces. The talk should be accessible to graduate students and I will assume no knowledge of hyperbolic geometry and Lie groups. This is motivated by a recent collaboration with J.Kahn and S. Mozes.

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Date/Time : 16 May 2018 14:00
Venue : IMS Seminar Room, House 3
Speaker : Michael Miksis, Northwestern University

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