# Taipei Postdoc Seminar

## June 4 2020 (Wed.) 11:00-12:30 Haewon Yoon (National Center for Theoretical Sciences) Venue: Room 202, Astro-Math. Building Title:Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations

Abstract:

In this talk, we construct an extremizer for the Lieb-Thirring energy inequality using concentration-compactness principle. Moreover, we investigate the properties of the extremizer, such as the system of Euler-Lagrange equations, regularity and summability. As an application, we study a dynamical consequence of a system of nonlinear Schrödinger equations with focusing cubic nonlinearities in three dimension when each wave function is restricted to be orthogonal. Using the critical element of the Lieb-Thirring inequality, we establish a global existence versus finite time blowup dichotomy. This is the joint work with Younghun Hong (Chung-Ang Univ.) and Soonsik Kwon (KAIST).

2016

## 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

### 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: Sheng-Fu Chiu (sfchiu@gate.sinica.edu.tw), Jia-Yuan Dai (jydai@ncts.tw)

Former organisers