Tue, October 31, 2017
Public Access Category: All |
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- Time:
- 9:30am-10:25am
- Location:
- Ramanujan Hall
- Description:
- Speaker: Sudeshna Roy
Title: Gotzmann's regularity and persistence theorem - II
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:
- 10:30am-11:25am
- Location:
- Ramanujan Hall
- Description:
- Speaker: Provanjan Mallick
Title : Asymptotic prime divisors - III
Abstract : Consider a Noetherian ring R and an ideal I of R. Ratliff asked
a question that what happens to Ass(R/I^n) as n gets large ? He was able
to answer that question for the integral closure of I. Meanwhile Brodmann
answered the original question, and proved that the set Ass(R/I^n)
stabilizes for large n.
We will discuss the proof of stability of Ass(R/I^n). We will also
give an example to show that the sequence is not monotone. The aim of
this series of talks to present the first chapter of S. McAdam,
Asymptotic prime divisors, Lecture Notes in Mathematics 1023,
Springer-Verlag, Berlin, 1983.
- Time:
- 3:30pm
- Location:
- Room 216
- Description:
- Speaker: Rekha Santhanam
We will talk about relative homotopy groups, long exact sequence in
homotopy and cellular approximation theorem.