2週內演講

Colloquium, 國立中央大學數學系 鄒駿祥助理教授 Thursday, December 15, 16:10—17:00 數學系3174 Title: Inverse Scattering by Corners and Regular of Transmission Eigenfunctions Abstract:This work concerns on the recovery of polygonal shaped scatterers using a single far-field pattern measurement. At the same time, we studied the associ- ated transmission eigenvalue problem and derived the regularity results on the transmission eignefunctions. On the side of inverse problems, we have applied the micro-local analysis and the quantitative unique continuation property. One of our original initiative is to use the singular decomposition of the solutions to elliptic equations near polygonal corners. We finally derived a double logarith- mic type stability estimate to the inverse problem and an H ?older type regularity to the associate transmission eigenfunctions. This a joint work with Prof. Hongyu Liu at City University HK.

Colloquium, University of Vienna 石勝吉博士 Thursday, December 22, 15:10—16:00 數學系3174 Title: On Iwasawa Invariants of Modular forms with Reducible and Non-P-Distinguished Residual Galois Representations Abstract: In this talk, we will first introduce the Iwasawa main conjecture for ordinary modular forms. We will then report a recent joint work with Jun Wang on the p-adic L-functions of p-adic weight one cusp forms f, obtained via the p-stabilization of weight one Eisenstein series E_1(\chi,1). Here \chi is an odd primitive Dirichlet character with \chi(p)=1. As an application, we compute the Iwasawa invariants of ordinary modular forms of weight k>= 2 with the same residual Galois representations as the one of f, which in our setting, is reducible and non-p-distinguished. Combining this with a result of Kato, we prove the Iwasawa main conjecture for these forms.

Colloquium, 中央研究院數學研究所 吳侊儒博士 Thursday, December 22, 16:10—17:00 數學系3174 Title: Holomorphic Vector Bundles, Hermitian Metrics, and Positivity Notions. Abstract: We will introduce holomorphic vector bundles, Hermitian metrics, and Chern curvature. There are various positivity notions about the curvature, and we will focus on Griffiths positivity. Some basic properties will be given and proved. We will also mention some problems that seem still open

Colloquium, The George Washington University 高連庸助理教授 Thursday, December 29, 16:10—17:00 數學系3174 Title: Dynamics, Geometry, and Rigidity Abstract:In this talk, we aim to have a glance at the spark between dynamics and geometry through Thermodynamic Formalism, a dynamical system tool inspired by statistical mechanics. Our discussion will be centered around the question: can one see the geometry of the underlying space through dynamical quantities? Along the way, we will discuss seminal works of Sinai (2014 Abel Prize winner), Margulis (1978 Fields medal- ist), Thurston (1982 Fields medalist), McMullen (1998 Fields medalist), Mirzakhani (2014 Fields medalist), and some of my works about entropy (type) rigidity, Manhattan curves, and pressure metrics on deformation spaces.