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.
Time:
11:00am
Location:
Ramanujan Hall
Description:
Combinatorics Seminar
Title: Eigenvalues and eigenvectors of the perfect matching
association scheme. (Part II)
Abstract:
We revisit the Bose-Mesner algebra of the perfect matching association
scheme (aka the Hecke algebra of the Gelfand pair (S_2n, H_n), where
H_n is the hyperoctahedral group).
Our main results are:
(1) An algorithm to compute the eigenvalues from symmetric group
characters by solving linear equations.
(2) Universal formulas, as content evaluations of symmetric functions,
for the eigenvalues of fixed orbitals (generalizing a result of
Diaconis and Holmes).
(3) An inductive construction of the eigenvectors (generalizing a
result of Godsil and Meagher).
Time:
11:30am
Description:
Speaker: Prof.Cherif Amrouche, Mathematics, Universite de Pau,France.
Title: L^p -Theory for the Stokes and Navier-Stokes Equations with Different
Boundary Conditions.