Hội thảo hàng năm 2016 (VIASM Annual Meeting 2016)

Chương trình

Tóm tắt các bài giảng:

1. Professor Sir John Ball - University of Oxford

Tiêu đề: The mathematics of liquid crystals

Bản tóm tắt: Liquid crystals are nonlinear fluids whose constituent molecules have orientational, and possibly some positional, order. They are used in a wide range of applications including computer screens, televisions, instrument panels and signage. The lecture will review the main mathematical theories of liquid crystals, and some challenges involved in the description of liquid crystal defects.

2. Professor Ngô Bảo Châu - University of Chicago and VIASM

Tiêu đề: On singularities of arc spaces and non-archimedean local harmonic analysis

Bản tóm tắt:

This is a survey of recent works on singularities of certain arc spaces in connection with local L-factors and orbital integrals.

3. Prof. Dr. Jochen Heinloth - Universität Duisburg-Essen Fakultät für Mathematik

Tiêu đề: Langlands parametrization for function fields (after V. Lafforgue)

Bản tóm tắt:

Vincent Lafforgue gave a beautiful construction of one direction of the Langlands correspondence for function fields for any reductive group. Instead of using the trace formula he introduced geometric arguments inspired by the Satake isomorphism.

In the talk I will try to start by giving some background on the problem and to motivate briefly the geometric ingredients that appear. The main part of the talk will then explain some parts of Lafforgue's construction that also give a new proof for the correspondence for the group GL_n over function fields.

4. Professor Luc Nguyen - University of Oxford

Tiêu đề: Fine blow-up analysis for conformally invariant fully nonlinear elliptic equations

Bản tóm tắt:

The classical Yamabe problem asks to find in a given conformal class a metric of constant scalar curvature and was solved positively through the work of Yamabe, Aubin, Trudinger and Schoen. In fully nonlinear analogues, the scalar curvature is replaced by certain functions of the eigenvalue of the Schouten curvature tensor. I will report on quantitative Liouville theorems and fine blow-up analysis for these problems. Joint work with Yanyan Li.