Date/Time : 04 Sep 2024 16:30
Venue : S17 #06-11 (SR6)
Speaker : Lin Bo, National University of Singapore

This talk focuses on the development of time-dependent regularized 13-moment equations for general elastic collision models within the linear regime. The detailed derivation demonstrates that these proposed equations exhibit super-Burnett order for small Knudsen numbers and feature a symmetric structure. A novel modification to stable boundary conditions is introduced to remove boundary layers. The effectiveness of the model is validated through numerical simulations of channel flows.

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Date/Time : 04 Sep 2024 15:00
Venue : S17 #05-11 (SR5)
Speaker : Meiyue Jiang, Peking University

In this talk we will first present an elementary treatment of the Brunn-Minkowski inequalities in dimension 2, which include the classical Brunn-Minkowski inequality, the $L^p$ and the log Brunn-Minkowski inequalities due to Lutwak and his collaborators, then we discuss a Brunn-Minkowski type inequality for the functional associated with the dual $L^p$−Minkowski problem. If time permits, a similar inequality for higher dimensional PDEs will be proposed.

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Date/Time : 04 Sep 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jia Jia, Tsinghua University

We build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable pairs on smooth projective curves in detail and present some calculations in low degrees.

This is based on a joint work with Caucher Birkar and Artan Sheshmani.

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Date/Time : 29 Aug 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Zeng Haozhi , Huazhong University of Science and Technology

The Peterson variety is introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. In this talk, we discuss an explicit morphism from the Peterson variety to the Blume toric orbifold. As an application, we calculate the totally nonnegative part of the Peterson variety in Lie type A and give a proof of Rietsch’s conjecture. This is joint work with Hiraku Abe.

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Date/Time : 29 Aug 2024 17:10
Venue : S17 #05-12 (SR4)
Speaker : Ma Jia Jun, Xiamen University and Xiamen University Malaysia

The speaker will share his personal experiences with Lean through this presentation. As undergraduate final year projects at Xiamen University Malaysia Campus, we have successfully formalized key concepts in game theory, including the Second-Price Auction and von Neumann’s Minimax Theorem. In collaboration with students from Xiamen University and the National University of Singapore, we have also made significant progress in formalizing results related to Lie algebras, Coxeter groups, and Kazhdan-Lusztig polynomials. The speaker will reflect on how formalization can deepen our understanding of mathematical concepts and its potential in teaching and research.

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Date/Time : 29 Aug 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Minsung Kim, Centro di Ricerca Matematica Ennio De Giorgi

The deviation of the Birkhoff integral for area-preserving flow on compact surfaces was first studied by Forni. He proved that the deviation spectrum was determined by the Lyapunov exponents of a renormalization cocycle so-called Kontsevitch-Zorich cocycle. This deviation result was later proved again by Bufetov and Frączek-Ulcigrai for translation flows and locally Hamiltonian flows for non-degenerate types. In this talk, we study the spectrum for deviations of Birkhoff integrals for locally Hamiltonian flows beyond the case of Forni where the observable vanishes at the singularities. Our new developments include a better understanding of the asymptotics at singularities (degenerate type) and the appearance of a new deviation spectrum. This is a joint work with Krzysztof Frączek.

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Date/Time : 28 Aug 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Linus Richter, National University of Singapore

I will outline a few connections between various notions of definability (which vary in degree of logical formality), give examples, and describe some open questions at the intersection of logic and classical mathematics.

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Date/Time : 28 Aug 2024 14:00
Venue : S17 #05-12 (SR4)
Speaker : Lim Jeck, California Institute of Technology

We show that if l_1, … , l_k are algebraic numbers, then, for any finite subset A of ℂ,

|A + l_1·A + … + l_k·A| >= H(l_1,…,l_k)|A|-o(|A|),

where H(l_1,…,l_k) is an explicit constant that is best possible. The case k=1 already confirms a conjecture of Krachun and Petrov. Joint work with David Conlon.

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Date/Time : 28 Aug 2024 16:30
Venue : S17 #04-05 (SR2)
Speaker : Zhang Xiaolong, Nanyang Technological University & Hunan Normal University

The Logarithmic Schrödinger Equation (LogSE) exhibits rich dynamics and possesses unique properties compared to the standard Schrödinger equation with cubic nonlinearity. However, the logarithmic nonlinear term $f(u)=uln(∣u∣^2)$ presents significant challenges for both numerical solutions and error analysis, primarily due to low regularity and singularity. In this talk, we will characterize this low regularity within suitable fractional Sobolev spaces and derive the first set of error estimates for the time-splitting Fourier spectral methods with initial data of fractional-order regularity. These results are supported by recent regularity estimates for the LogSE from the PDE community and ample numerical evidence.(Joint work with Prof. Li-Lian Wang, NTU)

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