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.

Add to calendar :

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.

Add to calendar :

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

Join Zoom Meeting
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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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

Join Zoom Meeting
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.

Add to calendar :

Date/Time : 18 Jan 2023 15:30
Venue : S17 #04-05 (SR2)
Speaker : Yap Jit Wu, Harvard University

Let f,g be two rational maps on P^1. Then Baker-Demarco, and independently Yuan-Zhang, showed that either they have exactly the same set of preperiodic points, or only finitely many in common. More recently, Demarco-Krieger-Ye showed the existence of an uniform bound on number of common preperiodic points for the quadratic family z^2 + c and also the Lattes family. In this talk, we will discuss the ideas behind these two results along with some work in progress by the author on related questions.

Add to calendar :

Date/Time : 17 Jan 2023 10:00
Venue : via Zoom
Speaker : Tan Nguyen, University of California, Los Angeles

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

Meeting ID: 826 3705 4452
Passcode: 332211

Designing deep learning models for practical applications, including those in computer vision, natural language processing, and mathematical modeling, is an art that often involves an expensive search over candidate architectures. In this talk, I present novel frameworks to facilitate the process of designing efficient and robust deep learning models with better representation capacity via three principled approaches: optimization, differential equation, and statistical modeling.

From an optimization viewpoint, I develop a gradient descent analogy of the recurrent cell in the recurrent neural network (RNN). I then integrate the momentum used for accelerating gradient dynamics into the recurrent cell, which results in the MomentumRNN. MomentumRNN can alleviate the vanishing gradient problem and accelerate training by choosing the appropriate momentum coefficients (Efficiency).
From a differential equation approach, I present a random walk interpretation of graph neural networks (GNNs), revealing a potentially inevitable over-smoothing phenomenon. Based on this random walk viewpoint of GNNs, I then propose the graph neural diffusion with a source term (GRAND++) that overcomes the over-smoothing issue and achieves better accuracy in low-labeling rate regimes (Robustness).

Using statistical modeling as a tool, I show that the attention in transformer models can be derived from solving a nonparametric kernel regression problem. I then propose the FourierFormer, a new class of transformers in which the softmax kernels are replaced by the novel generalized Fourier integral kernels. The generalized Fourier integral kernels can automatically capture the dependency of the features of data and remove the need to tune the covariance matrix (Representability).

Add to calendar :