Date/Time : 01 Feb 2023 09:00
Venue : via Zoom
Speaker : Yair Shenfeld, MIT

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https://nus-sg.zoom.us/j/82637054452?pwd=ZkpEVllwN3g1YUNYRHIwMXF3TmUzdz09

Meeting ID: 826 3705 4452
Passcode: 332211

It is classical that the ball is the unique shape which minimizes surface area for a given fixed volume. But what if we want to minimize surface area where in addition to fixing the volume we also fix the average width of the shape? This question turns out to be a very special case of long-standing conjectures at the heart of convex geometry. In the first part of the talk I will explain these conjectures and the significant progress that we made towards their resolutions. In the second part of the talk I will explain how these geometric problems can provide information on problems in combinatorics, which led us to the discovery of some surprising results in the theory of partially ordered sets.

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Date/Time : 30 Jan 2023 10:00
Venue : S17 #04-05 (SR2)
Speaker : Eric Chen, Princeton University

In the recent framework proposed by Ben-Zvi–Sakellaridis–Venkatesh, automorphic periods ought to, very roughly speaking, come in Langlands dual pairs. I will give a short introduction of this prediction and motivate the need to consider certain singular automorphic periods. In particular, I will present an example in joint work with Akshay Venkatesh, where we establish duality using a generalization of L-functions.

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Date/Time : 26 Jan 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Zhicheng Wang, University of Soochow

D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets of irreducible admissible representations and the descent method in the local fields case. Recently, they and D. Liu define the arithmetic wavefront set which based on the local Gan-Gross-Prasad conjecture. In this talk, we study the relationship between wavefront sets, descent method and finite Gan-Gross-Prasad problem for finite symplectic groups. We calculate the multiplicity of an irreducible representation in the generalised Gelfand-Graev representation corresponding to finite fields analogies of the arithmetic wavefront sets. In particular, for cuspidal representations, we give certain multiplicity one theorem and show that the finite fields analogy of arithmetic wavefront sets coincides with the wavefront sets in the sense of G.Lusztig and N. Kawanaka.

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Date/Time : 26 Jan 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Matthew M. Lin, National Cheng Kung University

Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk.

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Date/Time : 25 Jan 2023 17:00
Venue : via Zoom
Speaker : Leonardo Mainardi,

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

When the Canonical Ramsey’s Theorem by Erdös and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and McAloon. Taylor proved a “canonical” version of Hindman’s Theorem, analogous to the Canonical Ramsey’s Theorem. We introduce the restriction of Taylor’s Canonical Hindman’s Theorem to a subclass of the regressive functions, the λ-regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of this Regressive Hindman’s Theorem and of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that this same principle reduces the well-ordering-preservation principle for base-ω exponentiation by a uniform reduction.

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Date/Time : 25 Jan 2023 15:30
Venue : S17 #04-05 (SR2)
Speaker : Wang Tianqi, National University of Singapore

Minsky shows that there is an open set of PSL(2,C) characters of a free group F_n, namely the primitive-stable character, which is strictly larger than the convex-cocompact character and on which the action of Out(F_n) is properly discontinuous. In this talk, we introduce the notion of simple Anosov representations of closed surface groups and give an analogue of Minsky’s theorem, that is, the set of simple Anosov representations of the fundamental group of a closed hyperbolic surface into a higher rank Lie group is open in the character variety, which is strictly larger than the set of Anosov representations, with the mapping class group action properly discontinuous. This is joint work with Nicholas Tholozan.

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Date/Time : 20 Jan 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Sergiu Klainerman, Princeton University

The question whether black holes are real can be approached mathematically by addressing basic issues concerning their rigidity, stability and how they form in the first place. I will review these and focus on recent results concerning the nonlinear stability of slowly rotating Kerr black holes.

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Date/Time : 19 Jan 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Chenyan Wu, University of Melbourne

Let $\pi$ be a cuspidal automorphic representation of a classical group or a metaplectic group. We show an exact relation between two invariants associated to $\pi$, one called the lowest occurrence index of $\pi$ which is an invariant arising from theta lifts and the other the location of the maximal positive pole of an Eisenstein series attached to $\pi$ and a character. As an application, We show that certain global Arthur packets cannot contain cuspidal automorphic representations.

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Date/Time : 18 Jan 2023 17:00
Venue : S17 #04-05 (SR2) via Zoom
Speaker : Bakhadyr Khoussainov, University of Auckland

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

We aim to describe the isomorphism types of algorithmically presented structures in the language of the first order logic.

This is one of the key research topics related to the expressive power of the first order logic. The focus is on two classes of structures. The first class is the class of structures for which the positive atomic diagrams are computably enumerable.

We call these structures positive structures. The second class is the class of structures for which the negative atomic diagrams are computably enumerable. We call these structures negative structures. We investigate definability of positive and negative structures by sets of sentences quantified with Existential, Universal, Existential-Universal and Universal-Existential quantifiers using expansions of languages.

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