Date/Time : 17 Apr 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Zeng Fanhai, National University of Singapore

Date/Time:17 Apr 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Zeng Fanhai, National University of Singapore Fast time-stepping method for fractional integral and derivative operators We develop two fast time-stepping methods with linear complexity to calculate the discrete convolution for the approximation of the fractional integral and derivative operators. The effectiveness of the fast methods are verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model. Add to calendar: 

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Date/Time : 17 Apr 2019 17:00
Venue : S17 #04-06 SR1
Speaker : Liu Tianyu,

Date/Time:17 Apr 2019 17:00 Venue: S17 #04-06 SR1 Speaker: Liu Tianyu Arithmetic algorithm of surreal numbers The surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers. A surreal number is sometimes defined as a function from an initial segment of the ordinals into the set $(+,-)$, usually leads to an infinite sign sequence. It can also be expressed uniquely in a normal form, as $\sum_{i<\alpha} \omega^{a_i}r_i$. In this talk I will present some algorithms for addition, multiplication and division on the real field. Besides, we will cover the normal form and sign sequence of surreal numbers, which will be crucial for arithmetic algorithm of surreal numbers of length $>\omega$. Add to calendar: 

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Date/Time : 15 Apr 2019 17:00
Venue : S17 #06-11
Speaker : Lin Wayne, Lu Jianlong, Lim Zhan Feng, An X, National University of Singapore

Date/Time:15 Apr 2019 17:00 Venue: S17 #06-11 Speaker: Lin Wayne, Lu Jianlong, Lim Zhan Feng, An X, National University of Singapore Black Hole Quartet We will present four 15-minute introductory talks on black holes: i) An introduction to black hole (by Lin Wayne) ii) Frozen star paradox (by Lu Jianlong) iii) Gravitational collapse under spherical symmetry (by Lim Zhan Feng) iv) What’s inside a black hole? (by An Xinliang) Add to calendar: 

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Date/Time : 15 Apr 2019 16:00
Venue : S17 #06-11
Speaker : Deng Changsong, Wuhan University

Date/Time:15 Apr 2019 16:00 Venue: S17 #06-11 Speaker: Deng Changsong, Wuhan University Space and Time-Fractional Equations: a Random Time-Change Approach I will talk about a class of non-local equations with fractional operators in time and space from the point of view of the probability theory. In particular, we establish the exact asymptotic formulas for the fundamental solution to the $n$-dimensional fractional heat equations in both time and space. Add to calendar: 

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Date/Time : 11 Apr 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Jiang Meiyue, Peking University

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Date/Time : 10 Apr 2019 14:00
Venue : S17 #05-11 SR5
Speaker : Li Yunzhe, National University of Singapore

Date/Time:10 Apr 2019 14:00 Venue: S17 #05-11 SR5 Speaker: Li Yunzhe, National University of Singapore Uniqueness of billiards coding in polygon The study of mathematical billiards is a rich subject in dynamical systems. It describes the frictionless motion of a mass point in a domain with elastic reflection on the boundary. Among many other variations of mathematical billiards, polygonal billiards concerns the billiard problem in a two dimensional polygonal domain. One particular strategy to study polygonal billiards is to encode the trajectory of a billiard by the sequence of sides of the polygonal domain hit by the billiard along its trajectory. Several questions could be asked regarding this encoding and its relations with the billiard. Especially, we may want to know to what extend this encoding determines the physical trajectory of the billiard in the polygonal domain? In 1993, it has been proven by G. Galperin, T. Krüger and S. Troubetzkoy that for a non periodic trajectory in a simply connected polygon the encoding uniquely determines the physical trajectory. We aims to generalise this result to a wider class of polygons which are not necessarily simply connected but contain a finite number of holes such that the holes have non zero minimal diameter. This result was proven in a research project in 2018 at Aix-Marseille université under the supervision of S. Troubetzkoy. Add to calendar: 

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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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