Inhyeok Choi (KIAS)
Title: Regularity of the escape rate and the asymptotic entropy for negatively curved groups
Abstract: Given a discrete group $G$ with a probability measure $\mu$, one can study the asymptotics of the n-fold convolution of $\mu$. This naturally generalizes classical random walks on the integers. There are two quantities that captures the evolution of the $\mu$-random walk, namely, the escape rate and the asymptotic entropy. By the work of Ledrappier, Mathieu and Gouëzel, these quantities are known to depend analytically on $\mu$ when $G$ is word-hyperbolic. In this talk, I will discuss regularity of these quantities for other groups including mapping class groups and cubical groups. Part of these results was independently observed by Anna Erschler and Joshua Frisch.
Jae-Hwan Choi (KIAS)
Title: Boundedness of Nonlocal Operators with Variable Coefficients in Weighted Lebesgue Spaces
Abstract: In this presentation, we study the boundedness of infinitesimal generators associated with subordinated Brownian motions with variable coefficients in weighted Lebesgue spaces. We assume weak scaling conditions on the principal part of the jump kernels and impose only minimal regularity assumptions on the coefficients. Our approach relies on tools from probabilistic potential theory, which allow us to obtain the key estimates required for the analysis.
Masato Hoshino (Institute of Science Tokyo)
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Yaozhong Hu (University of Alberta)
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Hong Chang Ji (University of Wisconsin–Madison)
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Kunwoo Kim (POSTECH)
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Aro Lee (KAIST)
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Jungkyoung Lee (KIAS)
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Yong-Woo Lee (Seoul National University)
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Yuchen Liao (University of Science and Technology of China)
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Insuk Seo (Seoul National University)
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Kihoon Seong (SLMath)
Title: Sine–Gordon measures, homotopy classes, and topological soliton manifold
Abstract: I will discuss the sine–Gordon QFT, which lies in the same universality class as the Coulomb gas and the XY model, and exhibits the BKT phase transition (Nobel prize 2016). The sine–Gordon action admits infinitely many homotopy classes. For each class, we construct the corresponding Gibbs measure and analyze its behavior in the joint low-temperature and infinite-volume limit.
Surprisingly, even though the action has no energy minimizers in homotopy classes with high topological charge, the Gibbs measure nevertheless concentrates and exhibits Ornstein–Uhlenbeck fluctuations around the multi-soliton manifold, also known as the moduli space. I will then discuss the geometry of this multi-soliton manifold, including how solitons are arranged.
Based on joint work with Hao Shen and Philippe Sosoe.
Yuanyuan Xu (Chinese Academy of Sciences)
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Seoyeon Yang (Princeton University)
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Jaeyun Yi (SLMath)
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