Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Fenchel-Nielsen Coordinates on the Teichmuller Space of Genus g
Speaker: Amartya Muthal, TIFR
Date: October 7, 2024
Time: 15:15:00 Hours
Venue: A-369
Abstract: A marked surface S of genus g is an orientable surface of genus g along with a specified collection of 2g curves that generate the fundamental group of S. The Teichmuller space of genus g, denoted by T_g, is the space of hyperbolic metrics on marked surfaces of genus g. A hyperbolic surface of genus g can be cut along geodesic curves into simple pieces called "pairs of pants", the resulting decomposition is called the "pants decomposition" of the surface. The hyperbolic structure of the surface is completely determined by the hyperbolic structure of each piece, and the way these pieces are glued together. This gives rise to a global system of coordinates on T_g called Fenchel-Nielsen coordinates. In this talk I'll describe Fenchel-Nielsen coordinates for T_g, and if time permits, I'll discuss the construction of a compactification of T_g due to Thurston.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Modified Derksen invariant
Speaker: Parnashree Ghosh, TIFR, Mumbai
Date: October 7, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let k be a field of characteristic zero. In this talk we will introduce an invariant related to G a -actions on affine varieties over k, namely the modified Derksen invariant. We will prove that when X is a cylinder over an affine variety Y , then there are only three possible structures of this invariant. We will see examples of varieties of each kind. This is based on the following work of Boldyrev, Gaifullin and Shafarevich: Modified Derksen invariant, https://arxiv.org/abs/2312.08421v1.
Title of Talk: Fenchel-Nielsen Coordinates on the Teichmuller Space of Genus g
Speaker: Amartya Muthal, TIFR
Date: October 7, 2024
Time: 15:15:00 Hours
Venue: A-369
Abstract: A marked surface S of genus g is an orientable surface of genus g along with a specified collection of 2g curves that generate the fundamental group of S. The Teichmuller space of genus g, denoted by T_g, is the space of hyperbolic metrics on marked surfaces of genus g. A hyperbolic surface of genus g can be cut along geodesic curves into simple pieces called "pairs of pants", the resulting decomposition is called the "pants decomposition" of the surface. The hyperbolic structure of the surface is completely determined by the hyperbolic structure of each piece, and the way these pieces are glued together. This gives rise to a global system of coordinates on T_g called Fenchel-Nielsen coordinates. In this talk I'll describe Fenchel-Nielsen coordinates for T_g, and if time permits, I'll discuss the construction of a compactification of T_g due to Thurston.
Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: Modified Derksen invariant
Speaker: Parnashree Ghosh, TIFR, Mumbai
Date: October 7, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Let k be a field of characteristic zero. In this talk we will introduce an invariant related to G a -actions on affine varieties over k, namely the modified Derksen invariant. We will prove that when X is a cylinder over an affine variety Y , then there are only three possible structures of this invariant. We will see examples of varieties of each kind. This is based on the following work of Boldyrev, Gaifullin and Shafarevich: Modified Derksen invariant, https://arxiv.org/abs/2312.08421v1.