# Taipei Postdoc Seminar

## May 20 2020 (Wed.) 11:00-12:30 Ser-Wei Fu (National Center for Theoretical Sciences) Venue: Room 202, Astro-Math. Building Title:Simple closed curves, foliations, and flat surfaces

Abstract:

Simple closed curves often serve as the example to connect intuition to theorems. This talk will start from Riemann surfaces and conclude with length rigidity and deformations. The focus will be placed on the intermediate object, the space of measured foliations. The aim of the talk is to present the beautiful intertwined picture involving the mapping class group, Teichmuller theory, holomorphic quadratic differentials, and the dynamics of deformations.

## May 27 2020 (Wed.) 11:00-12:30 Yen-Liang Kuan (National Center for Theoretical Sciences) Venue: Room 202, Astro-Math. Building Title:The Mordell-Weil theorem for t-modules

Abstract:

For each positive characteristic multiple zeta value (defined by Thakur) $\zeta_A(\mathfrak{s})$, Chang-Papanikolas-Yu constructed the $t$-module $E_{\mathfrak{s}}$ defined over $A$ and integral points $\mathbf{v}_{\mathfrak{s}}$, $\mathbf{u}_{\mathfrak{s}} \in E_{\mathfrak{s}}(A)$. They proved that $\zeta_A(\mathfrak{s})$ is Eulerian (resp. zeta-like) if and only if $\mathbf{v}_{\mathfrak{s}}$ is an $\mathbb{F}_q[t]$-torsion point in $E_{\mathfrak{s}}(A)$ (resp. $\mathbf{v}_{\mathfrak{s}}$, $\mathbf{u}_{\mathfrak{s}}$ are $\mathbb{F}_q[t]$-linearly dependent in $E_{\mathfrak{s}}(A)$).
In this talk, we are interested in the structure theory of the $t$-module $E_{\mathfrak{s}}(A)$. Poonen proved an analogue for Drinfeld modules of the Mordell-Weil theorem. We shall generalize his results to the case of specific families of $t$-modules. In particular, we prove that the $t$-module $E_{\mathfrak{s}}(A)$ is the direct sum of its torsion submodule, which is finite, with a free $\mathbb{F}_q[t]$-module of rank $\aleph_0$.

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

### 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