Dimension bound for doubly badly approximable affine forms by Seonhee Lim

PROGRAM

SMOOTH AND HOMOGENEOUS DYNAMICS

ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana

DATE: 23 September 2019 to 04 October 2019

VENUE: Ramanujan Lecture Hall, ICTS Bangalore

Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to gather top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics.

During the program, The ICTS Distinguished lecture will be delivered by Prof. Marcelo Viana.

Minicourse Lecturers

Week 1:

1. Sylvain Crovisier, Paris Sud, France
2. Stefano Luzzatto, ICTP

Week 2:

1. mitry Kleinbock, Brandeis University​
2. Elon Lindenstrauss, Hebrew University of Jerusalem
3. Amos Nevo, Technion, Haifa
4. Both weeks will feature research talks by leading mathematicians as well as mini courses. A number of slots will be available in the program for younger participants to present their research and a poster session will also be organized.

The program is jointly organised and supported by ICTP and IMPA.

0:00:00 Dimension bound for doubly badly approximable affine forms
0:00:46 Homogeneous Dynamics
0:01:07 Dirichlet theorem
0:02:28 Inhomogeneous Dynamics
0:04:43 Bugeaud, Harrap, Kristensen, Velani (2010)
0:21:54 Idea of proof (LSS)
0:27:59 Observations
0:31:00 Remarks
0:32:45 Best approximation
0:43:18 Remark