Date/Time : 10 Apr 2019 17:00
Venue : S17 #04-06 SR1
Speaker : Gao Ziyuan, National University of Singapore

Date/Time:10 Apr 2019 17:00 Venue: S17 #04-06 SR1 Speaker: Gao Ziyuan, National University of Singapore Finitely distinguishable erasing pattern languages with bounded variable frequency A pattern is a nonempty string made up of symbols from two disjoint sets, an alphabet $\Sigma$ of constant symbols and a countably infinite set $X$ of variables. The erasing pattern language $L(\pi)$ generated by a pattern $\pi$ is the set of all words over $\Sigma$ obtained by replacing all the variables of $\pi$ with arbitrary words over $\Sigma$, with the proviso that identical variables be replaced with the same string. In particular, patterns allow for repetitions of variable substrings, a feature known as backreferencing in programming languages. A distinguishing set for any pattern $\pi$ w.r.t. a class $\Pi$ of patterns containing $\pi$ is a set $D$ of words over $\Sigma$ that distinguishes $\pi$ from every other pattern $\tau$ in $\Pi$ with $L(\tau) \neq L(\pi)$ (i.e., $D \cap L(\pi) \neq D \cap L(\tau)$ whenever $L(\tau) \neq L(\pi)$). Two basic types of counting problems will be discussed: first, given any pattern $\pi$ belonging to a class $\Pi$ of patterns, does $\pi$ have a finite distinguishing set w.r.t. $\Pi$; second, what is the minimum size of a distinguishing set for $\pi$ w.r.t. $\Pi$? The latter quantity gives a measure of the information complexity of $\pi$ w.r.t. $\Pi$, and it is known as the (classical) teaching dimension of $\pi$ w.r.t. $\Pi$ in computational learning theory. We also consider the problem of determining, for any given strict partial order $\prec$ on $\Pi$ (up to equivalence of patterns) and any pattern $\pi$ belonging to $\Pi$, the minimum size of a distinguishing set for $\pi$ w.r.t. the subclass of all $\tau$ in $\Pi$ such that $\tau \not\prec \pi$; this quantity is known as the preference-based teaching dimension of $\pi$ w.r.t. $(\Pi,\prec)$. We study how the classical and preference-based teaching dimensions of patterns w.r.t. various “naturally” defined classes of patterns and strict partial orders depend on the alphabet size and the maximum number of variable repetitions in any single pattern belonging to the class. Add to calendar: 

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Date/Time : 10 Apr 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Wang Dong , National University of Singapore

Date/Time:10 Apr 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Wang Dong, National University of Singapore Phase transition related to Lyapunov exponents in the model of product of complex Ginibre matrices In this talk we consider the product of M independent complex Ginibre matrices, each of size N x N. The singular values of the product random matrix as M goes to infinity, under proper scaling, are Lyapunov exponents of a toy dynamical system model. In this talk we consider the model as (1) M goes to infinity and N is fixed, (2) N goes to infinity and M is fixed, or (3) M, N both goes to infinity, and find the behaviour of the largest singular eigenvalues. We observe a phase transition as M/N is O(1). Add to calendar: 

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Date/Time : 04 Apr 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Subhroshekhar Ghosh, National University of Singapore

Date/Time:04 Apr 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Subhroshekhar Ghosh, National University of Singapore Two manifestations of rigidity in point sets : forbidden regions and maximal degeneracy A point process is said to be “rigid” if its local observables are completely determined (as deterministic functions of) the point configuration outside a local neighbourhood. For example, it has been shown in earlier work that, in the Ginibre ensemble (a.k.a. the 2D Coulomb gas at inverse temperature beta=2), the point configuration outside any bounded domain determines, almost surely, the number of points in the domain. In this talk, we will explore two recent manifestations of such rigidity phenomena. For the zeros of the planar Gaussian analytic function, we show that outside every large “hole”, there is a “forbidden region” which contains a vanishing density of points. This should be seen in contrast with the corresponding situation for classically understood models (e.g. random matrix ensembles), where no such effects are known to occur. In the second part of the talk, we will consider “stealthy” hyperuniform systems, which are systems whose structure function (i.e., the Fourier transform of the two-point correlation) vanishes near the origin. We show that such systems exhibit “maximal degeneracy”, namely the points outside a bounded domain determine, almost surely, the entire point configuration inside the domain. En route, we establish a conjecture of Zhang, Stillinger and Torquato that such systems have (deterministically) bounded holes. Based on joint works with Joel Lebowitz and Alon Nishry. Add to calendar: 

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Date/Time : 03 Apr 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Sichen Li , NUS and East China Normal University

Date/Time:03 Apr 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Sichen Li, NUS and East China Normal University A note on a smooth projective surface with Picard number 2 We characterize the integral Zariski decomposition of a smooth projective surface with Picard number 2 to partially solve a problem of B. Harbourne, P. Pokora, and H. Tutaj-Gasinska [Electron. Res. Announc. Math. Sci. 22 (2015), 103–108]. Add to calendar: 

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Date/Time : 27 Mar 2019 16:00
Venue : S17 #04-06 SR1
Speaker : Zhao Quan, National University of Singapore

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Date/Time : 20 Mar 2019
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Date/Time : 20 Mar 2019 15:00
Venue : S17 #05-12 SR4
Speaker : Jonathan Mark Scarlett, National University of Singapore

Date/Time:20 Mar 2019 15:00 Venue: S17 #05-12 SR4 Speaker: Jonathan Mark Scarlett, National University of Singapore Robust Submodular Function Maximization In the first part of this talk, I will give a brief introduction to a “diminishing returns” property of set functions known as submodularity, and overview some applications and classical guarantees of greedy optimization methods. In the second part, I will turn to a robust variation of the submodular optimization problem in which some of the selected elements of the set are removed by an adversary, and we want the function value to remain as a high as possible even after these removals. We introduce an algorithm based on applying the greedy subroutine to carefully defined partitions, and provide a theoretical guarantee of attaining a constant-factor approximation of the best value Add to calendar: 

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Date/Time : 20 Mar 2019 15:00
Venue : S17 #06-11
Speaker : John Loftin , Rutgers University-Newark

Date/Time:20 Mar 2019 15:00 Venue: S17 #06-11 Speaker: John Loftin, Rutgers University-Newark Coordinates along neck pinches for moduli of convex real projective structures It is well-known that the boundary of the Deligne-Mumford compactification of the moduli space of hyperbolic structures on a surface of genus at least 2 can be described in terms of Fenchel-Nielsen coordinates for a pants decomposition of the surface for which the necks to be pinched are boundaries of the pants. Along each loop which is pinched, the length parameter goes to zero, while the twist parameter disappears. These coordinates can be used to form orbifold coordinates for the Deligne-Mumford compactification. I will discuss the analogous degenerations for convex real projective structures, and how to extend a version of Goldman’s Fenchel-Nielsen type coordinates to degenerations along necks. This involves some new classes of geometric limits, and involves a version of Goldman’s interior parameters due to Zhang. I will also discuss how this relates to the complex structure on the moduli space as described via cubic differentials. This is based on joint work with Tengren Zhang. Add to calendar: 

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Date/Time : 20 Mar 2019 14:00
Venue : S17 #06-11
Speaker : Huan Zhen , Sun Yat-Sen University

Date/Time:20 Mar 2019 14:00 Venue: S17 #06-11 Speaker: Huan Zhen, Sun Yat-Sen University Quasi-elliptic cohomology Quasi-elliptic cohomology is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most ellipitc cohomology theories. Quasi-elliptic cohomology is closely related to Tate K-theory. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. Moreover, we construct an orthogonal G-spectrum representing quasi-elliptic cohomology. This construction leads to the birth of a new global homotopy theory. Add to calendar: 

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