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Tuesday, October 24, 2017
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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 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.


[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, Springer-Verlag, Berlin, 1983.

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