Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Train tracks and automorphisms of free groups
Speaker: Amartya Muthal, TIFR, Mumbai
Date: April 2, 2024
Time: 15:30:00 Hours
Venue: A-369
Abstract: On a surface $S$, a measured train track is a combinatorial tool that allows us to assign coordinates to isotopy classes of essential simple closed curves. This allows us to see the action of a diffeomorphism on curves in terms of linear algebra on train tracks. In the context of free group automorphisms, this takes the form of finding an efficient representative of an automorphism as a nice homotopy equivalence of graphs, called a train track map. In this talk, I will introduce the idea of train track maps and show how a generalisation of it, called relative train track maps, was used to prove Scott's conjecture: Fixed subgroups of automorphisms of $F_n$ have rank at most $n$.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Cohomological flatness in dimension 0
Speaker: Yogish Holla, TIFR, Mumbai
Date: April 2, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In this lecture we will study the notion of Cohomological flatness in dimension 0 and give sufficient conditions numerically for it over discrete valuation rings following the results of Offer Gabber and Rémi Lodh (arXiv: 2403.01831v1 [math.AG] 4 March 2024), generalising a classical result of Raynaud.
Title of Talk: Train tracks and automorphisms of free groups
Speaker: Amartya Muthal, TIFR, Mumbai
Date: April 2, 2024
Time: 15:30:00 Hours
Venue: A-369
Abstract: On a surface $S$, a measured train track is a combinatorial tool that allows us to assign coordinates to isotopy classes of essential simple closed curves. This allows us to see the action of a diffeomorphism on curves in terms of linear algebra on train tracks. In the context of free group automorphisms, this takes the form of finding an efficient representative of an automorphism as a nice homotopy equivalence of graphs, called a train track map. In this talk, I will introduce the idea of train track maps and show how a generalisation of it, called relative train track maps, was used to prove Scott's conjecture: Fixed subgroups of automorphisms of $F_n$ have rank at most $n$.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Cohomological flatness in dimension 0
Speaker: Yogish Holla, TIFR, Mumbai
Date: April 2, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In this lecture we will study the notion of Cohomological flatness in dimension 0 and give sufficient conditions numerically for it over discrete valuation rings following the results of Offer Gabber and Rémi Lodh (arXiv: 2403.01831v1 [math.AG] 4 March 2024), generalising a classical result of Raynaud.