Date/Time : 13 Sep 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

Abstract: This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling

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Date/Time : 09 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Emile Takahiro Okada, National University of Singapore

Abstract: In my talk last year I introduced new methods for computing the wavefront set of depth 0 representations using local wavefront sets. In this series of talks I will begin by briefly recalling the main results from that talk before I go on to outline new results and open questions that have come from these ideas. These will fall into roughly 3 categories: the structure theory of nilpotent orbits, new results on the wavefront set, and finally applications to Arthurs packets.

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Date/Time : 09 Sep 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Anirban Basak, International Centre for Theoretical Sciences

Abstract:  The classical theory of large deviations deals with precise estimates on the probabilities of rare events (e.g. normalized sum of independent and identically distributed random variables exceed its expectation by a constant factor greater than one) involving linear functions of independent random variables. Beyond the linear setting, possibly the simplest non-trivial interesting question is the large deviations of the triangle counts in Erd\H{o}s-R\’enyi graphs. In the past fifteen years there has been a lot of work in this direction. In this talk we will discuss some of them, focusing mainly on the large deviations of (i) regular subgraph counts and (ii) the spectral radius for sparse Erd\H{o}s-R\’enyi graphs.

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Date/Time : 09 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Chen Haoyang, National University of Singapore

Abstract:  We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3$ and $H^2$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. In 2D, we prove the $H^11/4$ and $H^7/4$ ill-posedness for the elastic wave equations and ideal MHD system (also for Euler equations). Compared with the 3D case, the construction of ill-posed profile in 2D is more delicate. This talk is based on joint works with Xinliang An and Silu Yin.

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Date/Time : 08 Sep 2022 15:00
Venue : S17 #04-06 (SR1)
Speaker : Thibaut Vasseur, University of Lille

Abstract:  A periodic Riesz gas is any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential of parameter s. We focus on the non-integrable case d − 1 < s < d, where the point process can be described by canonical DLR equations. Our main result ensures, for any dimension and inverse temperature, the existence of a periodic Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel set is a function of the point configuration outside the set. As a consequence, we show that this particular Riesz gas satisfies a grand-canonical DLR equation and allows a renormalization of the energy of a point inside an infinite configuration. Based on a joint work with D. Dereudre.

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Date/Time : 07 Sep 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Hao Huang, National University of Singapore

Abstract: One of the central themes in Combinatorics is to study whether or when a discrete object can be decomposed into smaller pieces of a given shape. A celebrated theorem of Baranyai states that when k divides n, the family of all k-subsets of an n-element set can be partitioned into perfect matchings. In this talk, I will discuss an extension of Baranyai’s Theorem to the non-uniform setting. Our study shows that for fixed k and sufficiently large n, the family consisting of all subsets of an n-element set of size at most k has such a decomposition if and only if n ≡ 0 or -1 (mod k).

Joint work with Jinye He and Jie Ma (USTC).

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Date/Time : 07 Sep 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Liao Luke,

Abstract:  We construct a computable coloring function such that any Pi^0_3 set with apartness can not be a witness of Hindman theorem for this coloring. And we can modify the coloring function and drop the condition “with apartness”.

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Date/Time : 02 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Balint Virag, University of Toronto

Abstract : In Euclidean geometry, bisectors are perpendicular lines. What happens in a random geometry? Surprisingly, many features are not sensitive to which model we use. There is a universal random geometry and its bisectors help answer some open questions in particle systems.

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Date/Time : 02 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Hengfei Lu, National University of Singapore

Abstract: Let F be a local field of characteristic zero. Let GL(n,F) acts on the space of n by n matrices by conjugation. Let P be a mirabolic subgroup with last row (0,0,…,0,1). Bernstein proved that the P-invariant distributions on n by n matrices space are also GL(n,F)-invariant when F is nonarchimedean. Aizenbud-Gourevitch prove it for the archimedean case. Let H=GL(p,F)xGL(n-p,F) be a subspace of GL(n,F). Chen-Sun prove that (GL(2n,F),GL(n,F)xGL(n,F)) is a Gelfand pair for any good character \chi of H. In a similar way, we can show that (GL(2n+1,F),GL(n,F)xGL(n+1,F)) is also a Gelfand pair for the good character. Furthermore, if F is nonarchimedean, we can prove that the P’\cap H-invariant linear functional on an H-distinguished irreducible smooth admissible representation \pi of GL(2n+1,F) is also H-invariant. Here H=GL(n,F)xGL(n+1,F) and P’ is the mirabolic subgroup of GL(2n+1,F). As one application, we can show that certain L-function has a pole at s=0 is a necessary condition such that a unitary and unramified principal series representation is distinguished by GL(n,F)xGL(n+1,F). At the end, we will talk about the situation when the character on the subgroup GL(n,F)xGL(n+1,F) is nontrivial.

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