Date/Time : 31 Jan 2024 14:00
Venue : S17 #06-11 (SR6)
Speaker : Han Qing, University of Notre Dame

A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this talk, we study whether these metrics have negative Ricci curvatures. We present two classes of results. First, we prove that the Ricci curvature is indeed negative for the complete conformal metrics on convex domains. Second, we demonstrate the Ricci curvature splits in sign if a component of the boundary of the domain is close to a lower dimensional set.

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Date/Time : 29 Jan 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Jimmy He, Massachusetts Institute of Technology

Random growth models in 1+1 dimension capture the behavior of interfaces evolving in the presence of noise. These models are expected to exhibit universal behavior, but we are still far from proving such results even in relatively simple models. A key development which has led to recent progress is the discovery of exact formulas for certain models with rich algebraic structure, leading to asymptotic results. I will survey some of these results, with a focus on models where a single boundary wall is present, as well as applications to rates of convergence for a Markov chain.

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Date/Time : 26 Jan 2024 15:00
Venue : S17 #06-11 (SR6)
Speaker : Tong Zhang, East China Normal University

It is known by Chen-Chen-Jiang that every complex smooth threefold X of general type with p_g(X) >= 11 satisfies the Noether inequality Vol(X) >= 4/3 p_g(X) – 10/3. If X attains the equality, it is said to be on the Noether line. In this talk, I will discuss the explicit structure of threefolds on the Noether line, and talk about what we know so far about their moduli space. This is a joint work in progress with S. Coughlan, Y. Hu, and R. Pignatelli.

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Date/Time : 25 Jan 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Yifeng Liu, IASM, Zhejiang University

In this talk, I will formulate the anticyclotomic Iwasawa main conjecture for Rankin-Selberg products of automorphic representations of hermitian type, and state our results. I will then explain the main ingredients of the proof: an Ihara type lemma, Abel-Jacobi image of basic locus, and a bipartite Euler system over the Iwasawa algebra. This is a joint work with Yichao Tian and Liang Xiao.

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Date/Time : 25 Jan 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Sungwoon Kim, Jeju National University

Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper, we relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group actions on geodesic metric spaces. This generalization is substantial enough to encompass actions of certain nonhyperbolic groups, such as actions of uniform lattices in semisimple Lie groups on flag manifolds. At the same time, our notion is sufficiently robust, and we prove that meandering-hyperbolic actions are still structurally stable. We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions. This is a joint work with Jaejeong Lee and Misha Kapovich.

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Date/Time : 25 Jan 2024 15:00
Venue : S16-06-118, Seminar Room
Speaker : Zhou Fan, Yale University

In statistical and probabilistic models, “mean-field” behavior arises when the aggregate effect of many variables is well-approximated by an average or effective field. Ideas from the analysis of mean-field models in statistical physics have been influential in our understanding of various problems of high-dimensional statistics in recent years. In this talk, I will argue that statistical applications can conversely drive the basic study of mean-field phenomena.

As a motivating example, I will discuss an application of high-dimensional mean-field theory to a nonparametric empirical Bayes procedure for PCA. I will then describe several developments of the theory beyond i.i.d. models, including extensions of Approximate Message Passing algorithms and analyses of spin glass models where the couplings matrices are orthogonally invariant in law.

Joint work w/ Yufan Li, Subhabrata Sen, Chang Su, Tianhao Wang, Yihong Wu, Xinyi Zhong.

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Date/Time : 24 Jan 2024 15:00
Venue : S17 #05-12 (SR4)
Speaker : Ziqing Xiang, Southern University of Science and Technology

We introduce a new notion called the quantum wreath product, which produces an algebra $B \wr_Q H(d)$ from a given associative algebra $B$, a positive integer $d$, and a choice $Q = (R, S, \rho, \sigma)$ of parameters. Important examples include many variants of the Hecke algebras, such as the Ariki-Koike algebras, the affine Hecke algebras and their degenerate version, Wan-Wang’s wreath Hecke algebras, Rosso-Savage’s (affine) Frobenius Hecke algebras, Kleshchev-Muth’s affine zigzag algebras, and the Hu algebra that quantizes the wreath product $\Sigma_m \wr \Sigma_2$ between symmetric groups. We will discuss the bases of quantum wreath product algebras, and some of their representations. This is joint work with Daniel Nakano and Chun-Ju Lai.

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Date/Time : 24 Jan 2024 15:00
Venue : S17 #06-11 (SR6)
Speaker : Wang Kelei, Wuhan University

Since the seminal work of Alt-Caffarelli in 1981, the one phase free boundary problem has been studied by many people. To study the regularity and singularity of free boundaries, blow up analysis is a standard method. It turns out for this free boundary problem, the nondegeneracy condition is crucial for the application of this method. Although this condition holds for energy minimizers, it’s not true for general solutions. In this talk, I will discuss a proof of the nondegeneracy for stable solutions. This is based on a joint work with N. Kamburov.

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Date/Time : 24 Jan 2024 17:00
Venue : S17 #04-05 (SR2)
Speaker : Arturo Rodríguez Fanlo, Hebrew University of Jerusalem

In this talk I will present a new (first-order) logic that mixes positive logic (where negation is not allowed) and local logic (where quantifiers are bounded). We will discuss several basic notions of model theory for this logic such as compactness, positive closedness (existential closedness), completeness (irreducibility), type spaces and retractors (saturated models).

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