Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Graph homomorphisms, some cohomology and the word problem
Speaker: Nishant Chandgotia, TIFR-CAM
Date: May 21, 2024
Time: 11:00:00 Hours
Venue: A-369
Abstract: When can a given subset S be tiled by rectangular tiles in Z^2? This is an old question and for answering it Conway and Lagarias introduced certain groups which are now known as the Conway-Lagarias group (1990). Together with some analytic conditions, Thurston noticed that these questions can be answered completely in certain situations. This later formed the basis for understanding what uniformly random tiling of regions looked like (for instance in the results from Cohn, Kenyon and Propp from 2001). In 1995, Klaus Schmidt realised that this was related to a certain cohomology of dynamical systems and initiated its formal study. We will talk about such questions in the context of graph homomorphisms on the Z^d lattice and see how it relates to the word problem of finitely presented groups. The talk should be accessible to a general audience.
Title of Talk: Graph homomorphisms, some cohomology and the word problem
Speaker: Nishant Chandgotia, TIFR-CAM
Date: May 21, 2024
Time: 11:00:00 Hours
Venue: A-369
Abstract: When can a given subset S be tiled by rectangular tiles in Z^2? This is an old question and for answering it Conway and Lagarias introduced certain groups which are now known as the Conway-Lagarias group (1990). Together with some analytic conditions, Thurston noticed that these questions can be answered completely in certain situations. This later formed the basis for understanding what uniformly random tiling of regions looked like (for instance in the results from Cohn, Kenyon and Propp from 2001). In 1995, Klaus Schmidt realised that this was related to a certain cohomology of dynamical systems and initiated its formal study. We will talk about such questions in the context of graph homomorphisms on the Z^d lattice and see how it relates to the word problem of finitely presented groups. The talk should be accessible to a general audience.