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 : 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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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 : 01 Sep 2022 15:00
Venue : S17 #04-04 (SR3)
Speaker : Nhat Minh Doan, Vietnam Academy of Science and Technology

Abstract:  We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two results. As a first application, we show how to deduce a theorem of Thurston which states, in particular for closed hyperbolic surfaces, that if a simple length spectrum “dominates” another, then in fact the two surfaces are isometric. As a second application, we show how to find upper bounds on the number of pairs of pants of bounded length that only depend on the boundary length and the topology of the surface. This is joint work with Hugo Parlier and Ser Peow Tan.

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Date/Time : 01 Sep 2022 10:00
Venue : via Zoom
Speaker : Dr. Pallavi Basu, Indian School of Business

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: In large-scale multiple hypothesis testing problems, the false discovery exceedance (FDX) provides a desirable alternative to the widely used false discovery rate (FDR) when the false discovery proportion (FDP) is highly variable. We develop an empirical Bayes approach to control the FDX. We show that, for independent hypotheses from a two-group model and dependent hypotheses from a Gaussian model fulfilling the exchangeability condition, an oracle decision rule based on ranking and thresholding the local false discovery rate (lfdr) is optimal in the sense that the power is maximized subject to the FDX constraint. We propose a data-driven FDX procedure that uses carefully designed computational shortcuts to emulate the oracle rule. We investigate the empirical performance of the proposed method using both simulated and real data and study the merits of FDX control through an application for identifying abnormal stock trading strategies. This is a joint work with Luella Fu, Alessio Saretto, and Wenguang Sun.

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Date/Time : 31 Aug 2022 16:00
Venue : via Zoom
Speaker : Li Lei, Shanghai Jiao Tong University

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https://nus-sg.zoom.us/j/89214687255?pwd=VmxLYjE3MzJkTFYwdlpXa0swdWxNUT09

Meeting ID: 892 1468 7255
Passcode: 871914

Abstract:  I will give a brief introduction to our recent works regarding the applications of interacting particle systems in scientific computing. In the first part, I will talk about several algorithms we proposed for sampling and solving PDEs using interacting particle systems, which can be efficiently implemented with the random batch approximation. In particular, the random batch Monte Carlo method, the random batch Ewald method and a particle method for PNP equation will be talked about. The second part goes to the fluctuation suppression and enhancement phenomena in interacting particle systems, which may give some evidence why sampling based on particle systems may be preferred sometimes.

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Date/Time : 31 Aug 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Lim Jeck, California Institute of Technology

Abstract:  We show that if $L_1$ and $L_2$ are linear transformations from $Z^d$ to $Z^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $Z^d$,

$$|L_1 A+L_2 A|\geq (|\det(L_1)|^{1/d}+|\det(L_2)|^{1/d})^d |A|- o(|A|).$$

This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and $L_2$. As an application, we prove a lower bound for $|A + \lambda \cdot A|$ when $A$ is a finite set of real numbers and $\lambda$ is an algebraic number.

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Date/Time : 31 Aug 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Yang Yue, National University of Singapore

Abstract: A pair (a,b) of nonzero r.e. Turing degrees is called a strong minimal pair iff the recursive Turing degree is the only common lower bound and if every nonzero Turing degree bounded by a has with b a join greater or equal a. We show that such strong minimal pairs do not exist.

Joint work with Cai Mingzhong, Liu Yiqun, Liu Yong and Peng Cheng

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Date/Time : 26 Aug 2022 09:00
Venue : via Zoom
Speaker : Jinyoung Park, Stanford University

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https://nus-sg.zoom.us/j/84821387838?pwd=QnRaVGtNVFBscWNreG4yVjJ2WGM3QT09

Meeting ID: 848 2138 7838
Passcode: 969669

Abstract: Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its “expectation-threshold,” which is a natural (and often easy to calculate) lower bound on the threshold. In this talk, I will present recent progress on this topic. Based on joint work with Huy Tuan Pham.

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