8:00am 


9:00am 
[9:30am] Sudeshna Roy
 Description:
 Title: Gotzmann's regularity and persistence theorem
Abstract: Gotzmann's regularity theorem establishes a bound on
CastelnuovoMumford 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 EisenbudGoto's theorem to
establish regularity in terms of graded Betti numbers. Then we discuss
Gotzmann's theorems in the language of commutative algebra.
[10:30am] Provanjan Mallick
 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,
SpringerVerlag, Berlin, 1983.


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