Taipei Postdoc Seminar


Upcoming Talk


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.




Previous Talks


2016

Sep.14, Jyun-Ao Lin (AS) On the number of commuting matrices and Kac polynomials
Sep.21, Chih-Wei Chen (NCTS) The Ricci flow - a chronological survey
Sep.29, Hiep Dang (NCTS) Identities involving (doubly) symmetric polynomials and integrals over Grassmannians
Oct.5, Haitao Wang (AS) Wave structures in Bolzmann and Landau equations
Oct.12, Kazuya Kawasetsu (AS) Uniqueness of a class of holomorphic vertex operator algebras of central charge 24

Oct.19, Edward Ho (NCTS) Blob-Based Super-Resolution Image Reconstruction
Oct.26, Yu-Yen Chien (NCTS) An Introduction to Hyperbolic Groups
Nov.2, Atsushi Yamamori (AS) An How to compute Bergman kernel functions
Nov.9, Chan-Liang Chung (AS) Sum formulas of multiple zeta values with arguments are multiple of a positive integer
Nov.16, Jui-En Chang (NTU) The bounds of Hausdorff measure of nodal sets
Nov.23, Nadim Rustom (NCTS) A Promenade Along Modern Algebraic Number Theory
Dec.7, Manas Kar (NCTS) Inverse parameter identification problems for p-Laplace equation
Dec.14, Liao He (AS) Enumeration of convex polytope
Dec.21, Tse-Chung Yang (AS) Counting isoclasses superspecial abelian surfaces over finite fields


2017

Jan.4, Gyeongha Hwang (NCTS) Deterministic and probabilistic analysis of nonlinear dispersive equation
Feb.22, Tomohiro Uchiyama(NCTS) Complete reducibility, geometric invariant theory, and spherical buildings
Mar.1, Yusuke Shimabukuro (AS) Stochastic six vertex model
Mar.15, Yongjie Wang (NCTS) Central Extensions of Matrix Lie Superalgebras
Mar.22, Chien-Hao Huang (NCTS) To collapse or not to collapse, that is the question.
Mar.29, Saud Hussein (AS) Sieve methods in analytic number theory.
Apr.12, Guokuan Shao (AS) Equidistribution of zeros of random holomorphic sections
Apr.19, Tien-Tsan Shieh (NCTS) Ground State Patterns and Phase Transition of Spin-1 Bose-Einstein Condensates via Γ-Convergence Theory
Apr.26, Chi-Kwong Fok (NCTS) Representation stability and moduli spaces
May 3, Yasuhiro Terakado (As) The determinant and the discriminant of a complete intersection of even dimension
May 10, Wan-Yu Tsai (AS) A brief introduction to nilpotent orbits and the orbit philosophy
May 17, Yang-Kai Lue (NCTS) The stability of self-shrinkers of mean curvature flow
May 24, Jia-Rui Fei (NCTS) The recreation I did for the past five years
May 31, Hsiao-Fan Liu (As) An introductory on discrete versions of Painlevé equations
Jun. 7, Taiji Marugame (AS) Construction of global CR invariants via Cheng-Yau metric
Jun. 14, Chih-Whi Chen (NCTS) Affine periplectic Brauer algbera
Jun. 28, Catalin Carstea (NCTS) Uniqueness for the inverse boundary value problem of anisotropic elasticity with piecewise constant coefficients
--
Sep. 6, Hsieh-Yung Lin (Universitaet Bonn) Some pieces of frontiers between symplectic, Kahler, and algebraic geometry
Sep. 20, Hiep Dang (NCTS) SQuantum cohomology of the Lagrangian Grassmannian
Oct. 11, Hung-Yu Yeh (AS) Effective action from $M$-theory on twisted connected sum $G_2$-manifolds
Oct. 25, Nobuo Sato (NCTS) Confluence relations for the multiple zeta values
Nov. 22, Sheng-Fu Chiu (AS) Categorification and Contact Non-squeezing.
Dec. 06, Peng-Jie Wong (PIMS) Group theory and the Artin holomorphy conjecture
Dec. 20, Guanghui Jin (NCTS) Remarks on Chern-Simons gauged O(3) sigma model in one space dimension


2018

Apr. 18, Chao Zhang (AS) The Kuga-Satake Constructions and Newton Stratifications on Orthogonal Shimura Varieties
May 2, Kian Chuan Ong (NCTS) Finite Difference Method for Numerical Simulation of Incompressible Fluid Flow
May 16, Kei Yuen Chan (University of Georgia) Branching rules for reductive groups
May 30, Chia-Yu Hsieh (NCTS) A Poisson-Nernst-Planck Model with Singular Permanent Charges
--
Sep. 20, Hsuan-Yi Liao (Penn. State University) Formality Theorem for Differential Graded Manifolds
Oct. 11, Chien-Hsun Wang (NCTS) Kuranishi structures of the moduli spaces of J-holomorphic curves
Oct. 17, Ryo Sato (AS) On Zhu's algebra of N=2 vertex operator superalgebras
Oct. 24, Hao Qi (AS) Maximum d-degenerate subgraph of a planar graph
Oct. 25, Chien-Hsun Wang (NCTS) Introduction of the wrapped Fukaya category
Oct. 30, Zhibin Du (AS) Combinatorial properties of real symmetric matrices related to the multiplicity of eigenvalues
Nov. 7, Kyung-youn Kim (AS) Estimates of heat kernel for symmetric Markov processes.
Nov. 15, Chien-Hsun Wang (NCTS) Generation of the Fukaya category
Nov. 28, Yao Cheng (AS) Special Value Formulae for the Twisted Triple Product and Applications
Nov. 29, Chien-Hsun Wang (NCTS) Generation of the Fukaya category II
Dec. 13, Sheng-Fu Chiu (AS) Introduction to wrapped microlocal sheavesWrapped Microlocal Sheaves


2019

Jan. 3, Sheng-Fu Chiu (AS) Wrapped Microlocal Sheaves II
Jan. 4, Sheng-Fu Chiu (AS) Wrapped Microlocal Sheaves III
Jan. 18, Yi-ning Hsiao (University of Geneva) The E-polynomials of a stratification of the Hilbert scheme of points.
May 15, Sasha Minets (IST Austria) Cohomological Hall algebras and sheaves on surfaces
--
Sep. 18, Bingying Lu (AS) Riemann-Hilbert problem and Painlevé-I equation
Oct. 2, Yuki Chino (NCTS) Stochastic processes in random media
Oct. 16, Shih-Yu Chen (AS) On The Algebraicity of The Symmetric Sixth Power L -functions of Elliptic Modular Forms
Oct. 23, Junsik Bae (NCTS) Solitary waves of the Euler-Poisson system
Oct. 30, You Hung Hsu (NCTS) Shifted q=0 affine algebras.
Nov. 6, Bharathwaj Palvannan (NCTS) Codimension two cycles in Iwasawa theory
Nov. 13, Bochen Liu (NCTS) Interplay between analysis and combinatorics: distance, tiling, and exponential basis
Nov. 20, Chen Hao (Universität Göttingen) Triply Periodic Minimal Surfaces, my recent adventures
Nov. 27, Sanghyuck Moon (NCTS) Variational methods for an elliptic equation and system
Dec. 4, Arasteh Rad (NCTS) Langlands Program and Manifestations of Shtukas
Dec. 11, Yoshihiro Sugimoto (NCTS) Symplectic topology and Hamiltonian dynamics
Dec. 25, David Wen (NCTS) Birational Models of Elliptic Fibrations and Beyond


2020

Mar. 4, Kazuki Tokimoto (AS) Affinoids in the Lubin-Tate Space at Infinite Level and the Local Langlands Correspondence
Mar. 11, Kwok-Wing Tsoi (NTU) On the Theory of Higher Special Elements for p-adic Representations
Mar. 18, Ziqing Xiang (AS) An invitation to spherical designs
Apr. 8, Ji Guo (AS) An Overview of Some Progress on the Arithmetic of Linear Recurrences and the Complex Analogues
Apr. 15, Jinwan Park (AS) The Regularity Theory for the Double Obstacle Problem
Apr. 22, Andrea Galasso (NCTS) Asymptotics Expansions in Geometry and Quantization
Apr. 29, Chih-Wei Chang (NCTS) Chamber Structures on Mori Dream Spaces
May 06, Jia-Yuan Dai (NCTS) An invitation to pattern formation and feedback controls
May 13, Hang Fu (NCTS) Arithmetic dynamics of rational maps
May 20, Ser-Wei Fu (NCTS) Simple closed curves, foliations, and flat surfaces
May 27, Yen-Liang Kuan (NCTS) The Mordell-Weil theorem for t-modules
June 4, Chien-Hsun Wang (NCTS) Mirror Symmetry and Seiberg Duality
June 10, Yi-Sheng Wang (NCTS) Classification of Knotted Objects
June 17, Haewon Yoon (NCTS) Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations
--
Sep. 23, Wei-Bo Su (AS) An Introduction to Special Lagrangian Submanifolds and Lagrangian Mean Curvature Flow
Sep. 30, Peng-Jie Wong (NCTS) Cyclicity of CM Elliptic Curves Modulo p in Short Intervals
Oct. 7, Yao Cheng (AS) On the newform problem for split $SO_{2n+1}$
Oct. 14, Jesse Madnick (NCTS) Minimal Submanifolds in Exceptional Geometries via the Octonions
Oct. 21, Yuan Shyong Ooi (NTU) Higher Codimension Minimal Surface System
Oct. 28, Chun-Wei Chang (NCTS) Anticipating the Occurrence and Type of Critical Transitions
Nov. 18, Yasuhiro Terakado (AS) Hecke Eigensystems of Automorphic Forms (mod p) of Hodge Type and Algebraic Modular Forms
Dec. 2, Bin Nguyen (Universidade de Lisboa) Positivity of Direct Image Bundles
Dec. 16, Iacopo Brivio (University of California, San Diego) On Algebraic Invariance of Plurigenera
Dec. 30, Sheng-Fu Chiu (AS) Hamiltonian Dynamics and Symplectic Rigidity from the Viewpoint of Triangulated Categories


2021

Jan. 13, You Hung Hsu (NCTS) Exceptional Collections, t-structures and Categorical Action
Mar. 10, Shih-Yu Chen (AS) On Deligne's Conjecture for Symmetric Fourth L-functions of Hilbert Modular Forms
Mar. 24, Wei-Guo Foo (AS) Some Remarks on Second Order Ordinary Differential Equations
Apr. 7, Jun-Wen Peng (University of Rochester) An Embedding of the Arboreal Galois Group for PCF Map
Apr. 21, Yan-Yu Chen (NTU) Global Dynamics on One-dimensional Excitable Media
[Cancellation] May 19, Guan-Ru Yu (Institute of Statistical Science, Academia Sinica) Bijections for Ranked Tree-Child Networks
--
Sep. 29, Yen-An Chen (NCTS) Boundedness of Canonical Models of Foliated Surfaces
Oct. 13, Iacopo Brivio (NCTS) On Deformation Invariance of Plurigenera in Positive and Mixed Characteristic
Oct. 27, Oguz Gezmis (NCTS) On Drinfeld Modules, Drinfeld Modular Forms and Multiple Zeta Values in Positive Characteristic
Nov. 10, Shih-Hsin Chen (NCTS) On Mathematical Analysis of Synchronization for Bidirectionally Coupled Kuramoto Oscillators
Nov. 24, Kuan-Hsiang Wang (NCTS) Ground States for a Linearly Coupled Indefinite Schrödinger System with Steep Potential Well
Dec. 8, Nicolau Sarquis Aiex (NTNU) Index of rotationally symmetric self-shrinkers
Dec. 22, Albert Wood (NTU) Gluing Constructions in Geometric Analysis


2022

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