제 3회 정수론 Festival

날짜: 2014. 2. 22(토)

장소: KAIST 자연과학동 1501호

스케줄:

11:00 ~ 11:50 선해상 교수 (충북대)

Continued fraction and distribution of modular symbols

12:00 ~ 14:00 점심

14:00 ~ 14:50 정준혁 박사 (KAIST)

Lindelöf hypothesis on average for triple product L-functions and its application

15:00 ~ 15:50 최영주 교수 (포항공대)

Schubert Eisenstein Series

16:00 ~ 16:50 명성 교수 (인하대)

Overview of Bloch-Kato conjecture

17:30 ~ 20:00 만찬 (호텔리베라 르소매 ; 리베라 호텔 지하 1층)

초 록

Speaker : 선해상

Title : Continued fraction and distribution of modular symbols

Abstract : We begin the talk by introducing the problem of distribution of modular symbols in the homology group of modular curves X_0(N). After the introduction, we present how to relate the problem to a study on the denominators of convergents of continued fractions. This is a research in progress and numerical evidences related to this problem are also to be presented.

Speaker : 정준혁

Title: Lindelof Hypothesis on average for triple product L-functions and its application

Abstract: I'll first discuss how one can relate shifted convolution sums of Fourier coefficients of Maass forms to the special values of L-functions. Then I'll sketch proof of an average statement for Lindelof Hypothesis using Kuznetsov trace formula. This has applications in Quantitative Quantum Ergodicity and various L^p restriction estimates of Maass-Hecke cusp forms. In the end, I'll present a stronger lower bound for the number of nodal domains than that is given in Ghosh-Sarnak-Reznikov's recent paper, for almost all Maass Hecke cusp forms.

Speaker : 최영주

Titile: SCHUBERT EISENSTEIN SERIES

Abstract: We introduce Schubert Eisenstein series as sums like usual Eisenstein series but with the summation restricted to elements of a particular Schubert cell, indexed by an element of the Weyl group. They are generally not fully automorphic, but still have functional equations. We explain some results and methods for [eqn: GL _{3}] which was done jointly with D. Bump and further progress.

Speaker : 명성

Title: Overview of Bloch-Kato conjecture
Abstract: In this talk, we briefly explain the motivic Bloch-Kato conjecture and its proof by Voevodsky and Rost. Bloch-Kato conjecture is a generalization of the Milnor's conjecture which was proved earlier by Voevodsky.