Date/Time : 29 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Wang Wei, Sun Yat-Sen University, Guangzhou

Date/Time:29 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou Non-standard models of arithmetic and their standard systems PA is the first order fragment of Peano’s axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems. Add to calendar: 

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Date/Time : 29 Jan 2020 14:00
Venue : S17 #05-11 SR5
Speaker : Zhong Guolei , NUS

Date/Time:29 Jan 2020 14:00 Venue: S17 #05-11 SR5 Speaker: Zhong Guolei, NUS Int-Amplified endomorphisms of compact Kähler spaces Let X be a normal compact Kähler space of dimension n. A surjective endomorphism f of such X is int-amplified if f *ξ – ξ = η for some Kähler classes ξ and η. First, we show that this definition generalizes the notation in the projective setting. Second, we prove that for the cases of X being smooth, a surface or a threefold with mild singularities, if X admits an int-amplified endomorphism with pseudo-effective canonical divisor, then it is a Q-torus. Finally, we consider a normal compact Kähler threefold Y with only terminal singularities and show that, replacing f by a positive power, we can run the minimal model program (MMP) f-equivariantly for such Y and reach either a Q-torus or a Fano (projective) variety of Picard number one. Add to calendar: 

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Date/Time : 29 Jan 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Bao Huanchen, NUS

Date/Time:29 Jan 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Bao Huanchen, NUS Asymptotic Hecke algebras, part 1 We explain Lusztig’s construction of the asymptotic Hecke algebras. Add to calendar: 

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Date/Time : 22 Jan 2020 14:00
Venue : S17 #04-06 SR1
Speaker : Masayasu Mimura, Hiroshima University

Since Alan Turing stated the notion of diffusion-induced instability in 1952, it is well known that reaction-diffusion “open” systems generate various types of spatio-temporal patterns and in fact, some systems have been used as models of biological pattern formation. In response to this flow, reaction-diffusion “open” systems have been investigated in mathematical communities and became one of the main studies of nonlinear PDEs. As compared to these systems, “closed” systems have been gradually less interesting and have gone from the study of reaction-diffusion systems. However, recently, new pattern formation can be observed even in closed systems as the consequence of transient self-organization, I would like to focus on such “closed systems” in this lecture and emphasize that theoretical understanding of such pattern formation is a very important subject in nonlinear mathematics with application to biology.

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Date/Time : 22 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Asger Dag Toernquist, Kobenhavns Universitet

Date/Time:22 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Asger Dag Toernquist, Kobenhavns Universitet Mad, med, mcg and other maximal combinatorial objects This talk is about the descriptive set theory and infinitary combinatorics. In the past 6 years, a number of long-standing problems related to the definability (in the sense of effective descriptive set theory) of so-called maximal almost disjoint (mad) families, maximal eventually different (med) families, and maximal cofinitary groups (mcg) have been solved by an array of authors. I will give an overview of these developments. Almost disjoint families are families of infinite subsets of omega where any two distinct elements of the family intersect finitely; eventually different families are families of functions from omega to omega such that any two distinct functions in the family are eventually different; and cofinitary groups are subgroups of the group of all permutations of omega with the property that all non-identity elements of the group have at most finitely many fixed points. Maximality of such objects in all cases means maximal under inclusion (among such families). A classical result due to Adrian Mathias states that no analytic infinite mad families. A slew of recent results shed light on this classical result by showing that under suitable descriptive set-theoretic regularity assumptions, there are no mad families at all (and this localizes to suitable pointclasses, especially to analytic sets). In a totally unexpected twist, Horowitz and Shelah showed in 2016 that there are Borel med families and mcg, solving a long-standing problem. I will finish the talk by discussing some related, still unsolved problems, especially the following: Is there a maximal (infinite) analytic set of pairwise Turing-incomparable reals? Add to calendar: 

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Date/Time : 22 Jan 2020 16:00
Venue : S17 #05-11 SR5
Speaker : Lucas Lestandi, Nanyang Technological University

Date/Time:22 Jan 2020 16:00 Venue: S17 #05-11 SR5 Speaker: Lucas Lestandi, Nanyang Technological University Breaking the curse of dimensionality : from large data to reduced order models. It is known to every scientist who works with numerical simulation – that increasing complexity in the computing task leads to exploding computing times. This can then be materialized in many ways e.g. very fine meshes, extremely small time steps, multiscale or multiphysics problems and most importantly, large number of dimensions. The last issue (large of dimensions) is often referred as the curse of dimensionality. It is very common in fields as diverse as finance, chemistry or “simple” mechanical engineering optimization problem, parametric studies, etc. In this talk, we will cover some of the essential aspects in building reduced order models that can overcome some of the above difficulties. First, we introduce low rank approximation of high dimensional data. These tools enable both data reduction (by several orders) and yield reduced bases that are used to build the actual reduced order model (ROM). Then we will see how common ROMs are built and the issues that remain to be solve. Finally, we will have a look at the future of ROM, in which deep learning is set to play a large part. Add to calendar: 

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Date/Time : 21 Jan 2020 14:00
Venue : S17 #04-06 SR1
Speaker : Ma Jiajun, Shanghai Jiao Tong University

Date/Time:21 Jan 2020 14:00 Venue: S17 #04-06 SR1 Speaker: Ma Jiajun, Shanghai Jiao Tong University Towards the explicit description of local descent of symplectic supercuspidal representations of GL(2n) Descent is the “inverse” of Langlands functorial lift. The descent of symplectic supercuspidal representations of GL(2n) to SO(2n+1) over p-adic fields was established by Dihua Jiang, Chufeng Nien, and Yujun Qin. In this talk, I will first give an explicit description of the local descent in the depth zero cases. Then I will discuss a conjectural description in the general case. This is ongoing joint work with Dongwen Liu, Chufeng Nien, and Zhicheng Wang. Add to calendar: 

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Date/Time : 21 Jan 2020 09:00
Venue : S17 #04-06 SR1
Speaker : Paul Nelson, ETH Zurich

Date/Time:21 Jan 2020 09:00 Venue: S17 #04-06 SR1 Speaker: Paul Nelson, ETH Zurich Quantum variance of compact arithmetic surfaces I will talk about the quantum variance of Hecke–Maass cusp forms on arithmetic hyperbolic surfaces. In the case of the non-compact modular surface, the asymptotic quantum variance was determined in work of Luo–Sarnak, Zhao and Sarnak–Zhao, using a method specific to that case. I will describe analogous results in the compact case, obtained by a different method based on the theta correspondence. This will involve some discussion of constructing microlocal lifts via convolution operators, identities and asymptotics involving integrals of theta functions, the Rallis inner product formula, and the method of coadjoint orbits. Add to calendar: 

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Date/Time : 21 Jan 2020 15:00
Venue : S17 #04-04 SR3
Speaker : Xu Zhouli, Massachusetts Institute of Technology

Date/Time:21 Jan 2020 15:00 Venue: S17 #04-04 SR3 Speaker: Xu Zhouli, Massachusetts Institute of Technology In and around stable homotopy groups of spheres The computation of stable homotopy groups of spheres is one of the most fundamental problems in topology. Despite its simple definition, it is notoriously hard to compute. It has connections to many areas of mathematics. In this talk, I will discuss a recent breakthrough on this problem, which depends on motivic homotopy theory in a critical way. I will also talk about applications to smooth structures on spheres, and towards the open problem of Kervaire invariant one in dimension 126. This talk is based on several joint work with Bogdan Gheorghe, Daniel Isaksen, and Guozhen Wang. Add to calendar: 

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