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理學院專題學術講座∣西湖數論研討班第十五期

来源: 发布時間:2021-05-06 作者:

時間2021年5月13日(周四)9:00-17:00

Time9:00-17:00, Thursday, May 13, 2021

地點:西湖大學雲棲校區4號樓409-411教室

Venue: Room 409-411, Building 4, Yunqi Campus, Westlake University

主持人:西湖大学理学院 赵永强 博士/西湖大学理学院 赵以庚 博士

Host: Dr. Yongqiang Zhao, School of Science, Westlake University/

Dr. Yigeng Zhao, School of Science, Westlake University

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1.??? 時間/Time: 9:00-12:00

主講嘉賓/Speaker:Prof. Hang Liu, Shenzhen University

講座主題/Title:K-theory and Mahler measure

講座摘要/Abstract:

In this talk, we mainly study the K-theory of curves, Beilinson's conjecture and Mahler measure of two-variable polynomials.

We will construct families of curves of arbitrary genus g, together with g independent elements in the kernel of the tame symbol. This gives a lower bound for K2 of these curves as predicted by Beilinson's conjecture.

We introduce and study the Mahler measure of families of genus 2 and 3 curves and its relation with special values of L-functions of elliptic curves. We will explain these relations by considering the pushforward and pullback of certain elements in K2 of curves defined by these polynomials and applying Beilinson's conjecture on K2 of curves.

We study the Mahler measure of certain families of quadratic Q-curves. We try to present a method to prove the relation between these Mahler measures and special values of L-functions of modular forms for some of these curves with small conductor.? ?

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2.??? 時間/Time: 14:00-17:00

主講嘉賓/Speaker:Prof. Bingrong Huang, Shandong University

講座主題/Title:Sup-norms of automorphic forms

講座摘要/Abstract:

In this talk, I will introduce the sup-norm problem for Laplacian eigenfunctions on a Riemann surface. The first breakthrough of the sup-norm problem for Maass forms was achieved by Iwaniec–Sarnak in 1995. I will state related results for both cusp forms and Eisenstein series. I will also present results for dihedral Maass forms, which are distinguished subsequences of Laplacian eigenfunctions on a modular surface.

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講座聯系人/Contact:

理学院 王老师? wangqiuhui@westlake.edu.cn

理学院 杨老师? yanghangli@westlake.edu.cn