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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Date/Time : 21 Mar 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Benoit Perthame, Sorbonne-Universite

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Date/Time : 14 Mar 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Yan Yan Li, Rutgers University

In this talk we give derivative estimates for solutions of divergence form elliptic equations with piecewise smooth coefficients. The equations arise from the study of composite material. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.

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