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3:00pm to 4:00pm - RH 306 - Differential Geometry Sean Paul - (University of Wisconsin, Madison) The (spherical) Mahler measure of the X-discriminant Let P be a homogeneous polynomial in N+1 complex variables of degree d. The logarithmic Mahler Measure of P (denoted by m(P) ) is the integral of log|P| over the sphere in C^{N+1} with respect to the usual Hermitian metric and measure on the sphere. Now let X be a smooth variety embedded in CP^N by a high power of an ample line bundle and let $\Delta$ denote a generalized discriminant of X wrt the given embedding , then $\Delta$ is an irreducible homogeneous polynomial in the appropriate space of variables. In this talk I will discuss work in progress whose aim is to find an asymptotic expansion of m(\Delta) in terms of elementary functions of the degree of the embedding. |
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4:00pm to 5:00pm - RH 306 - Differential Geometry Jingyi Chen - (U of British Columbia) Generalizing curve diffusion flow in higher dimension and codimension We introduce a 4th order flow moving Lagrangian submanifolds in a symplectic manifold. The flow evolves within a Hamiltonian isotopy class and is a gradient flow for volume, and it exists uniquely in shorttime and can be extended if the 2nd fundamental form is bounded. |
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3:00pm to 4:00pm - RH 510R - Combinatorics and Probability Pedro Abdalla - (UCI) Introduction to Robust Statistics I Robust Statistics is a classical topic that dates back to the seminal work of Huber in the 1980s. In essence, the main goal of the field is to account for the effect of outliers when performing estimation tasks, such as mean estimation. A recent line of research, inspired by the seminal work of Catoni, has revisited some classical problems in robust statistics from a non-asymptotic perspective. The goal of this short seminar series is to introduce the key ideas related to robust estimation and discuss various notions of robustness, including heavy-tailed distributions and adversarial contamination. The primary example will be the mean estimation problem, and if time permits, I will also cover covariance estimation |
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1:00am to 2:00am - RH 306 - Harmonic Analysis Haoren Xiong - (UCLA) Semiclassical asymptotics for Bergman projections Abstract: In this talk, we discuss the semiclassical asymptotics for Bergman kernels in exponentially weighted spaces of holomorphic functions. We will first review a direct approach to the construction of asymptotic Bergman projections, developed by Deleporte--Hitrik--Sjöstrand in the case of real analytic weights, and Hitrik--Stone in the case of smooth weights. We shall then explore the case of Gevrey weights, which can be thought of as the interpolating case between the real analytic and smooth weights. In the case of Gevrey weights, we show that Bergman kernel can be approximated in certain Gevrey symbol class up to a Gevrey type small error, in the semiclassical limit. We will also introduce some microlocal analysis tools in the Gevrey setting, including Borel's lemma for symbols and complex stationary phase lemma. This talk is based on joint work with Hang Xu. |
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1:00pm to 1:50pm - RH 340N - Algebraic Geometry Donggun Lee - (IBS-CCG (Korea)) Representations on the cohomology of the moduli space of pointed rational curves The moduli space of pointed rational curves has a natural action of the symmetric group permuting the marked points. In this talk, I will present combinatorial and recursive formulas for the induced representation on the cohomology of the moduli space. These formulas are derived from wall crossings of birational models, governed by Hassett’s theory of weighted stable curves and Choi-Kiem’s theory of delta-stability of quasimaps. These results allow us to investigate positivity and log-concavity of the representation. Based on joint works with Jinwon Choi and Young-Hoon Kiem.
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