# Taipei Postdoc Seminar

## Nov. 16 (Wed.) 14:00-15:00 Rajat Gupta (Institute of Mathematics, Academia Sinica) Venue: Room 515, Cosmology Building (NTU Campus) Title: Koshliakov zeta functions and modular relations

Abstract:
Nikolai Sergeevich Koshliakov was an outstanding Russian mathematician who made phenomenal contributions to number theory and differential equations. In the aftermath of World War II, he was one among the many scientists who were arrested on fab- ricated charges and incarcerated. Under extreme hardships while still in prison, Koshliakov (under a different name ‘N. S. Sergeev’) wrote two manuscripts out of which one was lost. Fortunately the second one was published in 1949 although, to the best of our knowledge, no one studied it until the last year when Prof. Atul Dixit and I started examining it in detail. This manuscript contains a complete theory of two interesting generalizations of the Riemann zeta function having their genesis in heat conduction and is truly a masterpiece! In this talk, we will discuss some of the contents of this manuscript and then proceed to give some new results (modular relations) that we have obtained in this theory. This is joint work with Prof. Atul Dixit.

## Jan. 5, Jun-Wen Peng (NCTS) Rigid Geometry: Berkovich Spaces, Perfectoid Spaces, and their Application on Arithmetic Dynamics Jan. 19, Albert Wood (NTU) Gluing Constructions in Geometric Analysis Feb. 16, Ryota Mikami (AS) Log-concavity and Matroids Mar. 2, Harrison I-Yuan Chen (AS) Traces of convolution categories Mar. 16, Ryotaro Harada (Japan Society for the Promotion of Science) n Some Linear Independence Results for Special Values of Thakur Hypergeometric Functions Apr. 6, Tsung-Wen Yen (NSYU) Investigating and understanding extreme events in the financial market using methods based on “algebraic topology” Apr. 20, Brian Harvie (NCTS) Static manifolds and quasi-local mass in general relativity May 4, Jia-Wei Lin (NYCU) Structure-Preserving Methods for Computing Complex Band Structures of Three Dimensional Photonic Crystals May 18, Seonghyeon Jeong (NCTS) Introduction to the Optimal Transportation Problem and the Monge-Ampere Equation Sep. 28, Nawaz Sultani (AS) Gromov-Witten Invariants of Non-convex Orbifolds Oct. 12, Marco Sutti (NCTS) Computing Geodesics on the Stiefel Manifold Oct. 26, You-Cheng Chou (AS) Quantum K-theory and Gopakumar-Vafa invariants Nov. 16, Rajat Gupta (AS) Koshliakov zeta functions and modular relations

### The Taipei Postdoc Seminar is a weekly seminar that is organized jointly by the Institute of Mathematics of Academia Sinica and the National Center for Theoretical Sciences during the regular academic year. The seminar is held in these two mathematical institutions, with each one of them hosting the event approximately once every two weeks. The National Taiwan University, Academia Sinica, and the NCTS, together employ a significant number of postdoctoral fellows in mathematics from all over the world every year. The diverse scientific and cultural backgrounds of these postdocs create a unique environment of learning, and the goal of the Taipei Postdoc Seminar is to take advantage of this opportunity by bringing together all these postdocs once in a week in an informal-style seminar to enhance discussions and exchange of ideas among the participants. It is our belief that not only will this seminar encourage and eventually lead to more collaboration among mathematicians in Taipei, but it will also give the participants a chance to broaden their own scientific viewpoints. It is our hope that this seminar will greatly enrich the academic experience of the postdoctoral fellows during their stay in Taipei. Organizers: Shih-Hsin Chen (shchen@ncts.ntu.edu.tw), Sz-Sheng Wang (sswangtw@gate.sinica.edu.tw)

Former organisers

## Yu-Yen Chien (NCTS):Sep. 2016~Jun. 2017 Jyun-Ao Lin (AS): Sep. 2016~May 2018 Yang-Kai Lue (NCTS): Sep. 2017~May 2018 Chien-Hsun Wang (NCTS): Sep. 2018~May 2019 Sheng-Fu Chiu (AS): Sep. 2018~June 2020 Jia-Yuan Dai (NCTS): Sep. 2019~June 2020 Wei-Bo Su (AS): Sep. 2020~June 2021 Peng-Jie Wong (NCTS): Sep. 2020~June 2021 Jun-Wen Peng (NCTS): Sep. 2021~June 2022 Yi-Sheng Wang (AS): Sep. 2021~June 2022

Group_Photo_20170628 HERE