Date/Time : 30 Nov 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Yuval Peres, Microsoft Research

Date/Time:30 Nov 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Yuval Peres, Microsoft Research Search games and Kakeya sets I’ll describe a search game with a surprising geometric connection. A hunter and a rabbit move on an n-vertex graph without seeing each other until they meet. At each step, the hunter moves to a neighboring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. We show that an optimal rabbit strategy for the cycle yields a Kakeya set: a plane set of zero area that contains a unit segment in every direction. Kakeya sets have been studied intensively in harmonic analysis since their discovery by Besicovitch (1919); their connection to search games is new and yields insights in both directions. (Based on joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler, and on earlier work by Adler et al (2003).) Add to calendar: 

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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 : 23 Nov 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Pang Chin How, Jeffrey, National University of Singapore

I will talk about my work on designing a distributed optimization algorithm based on dual ascent (or Dykstra’s splitting) that is asynchronous, decentralized, and has deterministic convergence. We also discuss the extension to the case of directed unreliable edges, and on using majorizations so that one can use subgradients approximations or outer approximations of constraint sets to simplify subproblems to be solved. We also studying convergence rates. I will then describe how I had started working on this area after noticing a heuristic for improving the convergence of the method of alternating projections.

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Date/Time : 12 Nov 2018 16:00
Venue : S17 #04-06 SR1
Speaker : Dilip Raghavan, National University of Singapore

I will summarize some of my work on three connected topics in set theory. The work on cardinal invariants covers both countable and uncountable cardinals, and it includes both ZFC theorems and consistency results. The work on special subsets of real numbers concentrates on techniques for constructing ultrafilters and almost disjoint families. The work on partition calculus includes results in both structural Ramsey theory and partition relations at uncountable ordinals. I will provide the necessary background to understand these results.

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Date/Time : 07 Nov 2018 16:00
Venue : S17 #05-12 SR4
Speaker : An Xinliang, National University of Singapore

Date/Time:07 Nov 2018 16:00 Venue: S17 #05-12 SR4 Speaker: An Xinliang, National University of Singapore Formation of Singularity in General Relativity III Besides black holes, can other types of singularities form in gravitational collapse? What does the singularity look like? Will the singular information be censored in universe? In this talk, I will address above questions. Add to calendar: 

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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 : 24 Oct 2018 16:00
Venue : S17 #05-12 SR4
Speaker : An Xinliang, National University of Singapore

Date/Time:24 Oct 2018 16:00 Venue: S17 #05-12 SR4 Speaker: An Xinliang, National University of Singapore Formation of Singularity in General Relativity I I will present three introductory talks on a mathematical approach to studying singularity formation in general relativity. In the first talk, basic concepts and theorems of space time geometry will be discussed. PhD students in 1st and 2nd years are welcome to attend. Add to calendar: 

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Date/Time : 18 Oct 2018 16:00
Venue : S17 #05-12 SR4
Speaker : An Xinliang, National University of Singapore

Date/Time:31 Oct 2018 16:00 Venue: S17 #05-12 SR4 Speaker: An Xinliang, National University of Singapore Formation of Singularity in General Relativity II In this talk, I will address an interesting physical question: can a black hole form dynamically in the vacuum? Without the help of matter, we will show that focusing of gravitational waves could lead to black hole formation. Add to calendar: 

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Date/Time : 16 Aug 2018 14:00
Venue : S17 #04-05 SR2
Speaker : Dong Chaoping, Shanghai Normal University

Date/Time:16 Aug 2019 14:00 Venue: S17 #04-05 SR2 Speaker: Dong Chaoping, Shanghai Normal University Dirac cohomology: Towards the classification We will recall necessary math ingredients related to the notion of Dirac cohomology, such as Parthasarathy’s Dirac operator inequality, PRV-component, spin module, the unitarily small convex hull, and the spin norm. Then we will discuss some recent progress towards the classification of irreducible unitary representations with non-vanishing Dirac cohomology. In particular, we will mention a few questions. Add to calendar: 

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