Title: Gotzmann's regularity and persistence theorem - III
Abstract: Gotzmann's regularity theorem establishes a bound on
Castelnuovo-Mumford regularity using a binomial representation (the
Macaulay representation) of the Hilbert polynomial of a standard graded
algebra. Gotzmann's persistence theorem shows that once the Hilbert
function of a homogeneous ideal achieves minimal growth then it grows
minimally for ever. We start with a proof of Eisenbud-Goto's theorem to
establish regularity in terms of graded Betti numbers. Then we discuss
Gotzmann's theorems in the language of commutative algebra.
Speaker: Udit Mavinkurve
Title: An Introduction to K-theory
Abstract: Topological K-theory was one of the first instances of a
generalized cohomology theory being used to successfully resolve classical
problems involving very concrete objects like vector fields and division
algebras. In this talk, we will briefly review some properties of vector
bundles, introduce the complex K groups, and discuss some of their
properties - including the all-important Bott periodicity theorem.
Homotopy theory Seminar (Lecture 5)
Speaker: Rekha Santhanam
Time & Date: 3:30 PM 7th November
We will give proofs of Cellular approximation and then discuss fibrations
and Blaker-Massey Homotopy Excision thorem.
4:00pm
5:00pm
6:00pm
Time:
10:00am-11:25am
Location:
Ramanujan Hall
Description:
Title: Gotzmann's regularity and persistence theorem - III
Abstract: Gotzmann's regularity theorem establishes a bound on
Castelnuovo-Mumford regularity using a binomial representation (the
Macaulay representation) of the Hilbert polynomial of a standard graded
algebra. Gotzmann's persistence theorem shows that once the Hilbert
function of a homogeneous ideal achieves minimal growth then it grows
minimally for ever. We start with a proof of Eisenbud-Goto's theorem to
establish regularity in terms of graded Betti numbers. Then we discuss
Gotzmann's theorems in the language of commutative algebra.
Time:
10:00am-11:00am
Location:
Room 215
Description:
Speaker: Udit Mavinkurve
Title: An Introduction to K-theory
Abstract: Topological K-theory was one of the first instances of a
generalized cohomology theory being used to successfully resolve classical
problems involving very concrete objects like vector fields and division
algebras. In this talk, we will briefly review some properties of vector
bundles, introduce the complex K groups, and discuss some of their
properties - including the all-important Bott periodicity theorem.
Time:
3:30pm
Location:
Room 215, Department of Mathematics
Description:
Homotopy theory Seminar (Lecture 5)
Speaker: Rekha Santhanam
Time & Date: 3:30 PM 7th November
We will give proofs of Cellular approximation and then discuss fibrations
and Blaker-Massey Homotopy Excision thorem.