Title: Gotzmann's regularity and persistence theorem
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:
Title : Asymptotic prime divisors - II
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:
2:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
The title and abstract of the talk are attached.
Time:
2:30pm
Location:
Ramanujan Hall
Description:
Title: Typical representations for depth-zero representations.
Abstract: We are interested in understanding cuspidal support of smooth
representations of p-adic reductive group via understanding the
restriction of a smooth representation to a maximal compact subgroup. This
is motivated by arithmetic applications via local Langlands
correspondence. We will explain the case of general linear groups and
classical groups.
Time:
3:30pm
Location:
Room 215
Description:
Title: Higgs Bundles
Abstract: We will define the moduli of Higgs bundles and the Hitchin
fibration, which is a morphism from the moduli of Higgs bundles to an
affine space. Then we will describe the general fibre in terms of the
spectral cover.