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Tuesday, October 17, 2017
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8:00am  
9:00am [9:30am]Neeraj Kumar
Description:
Title: Linear resolutions of monomial ideals - IV Abstract: Consider a graded ideal in the polynomial ring in several variables. We shall discuss criterion for the graded ideal and its power to have linear resolution. Then we focus our attention to study linear resolution of monomial ideals. Monomial ideals are the bridge between commutative algebra and the combinatorics. Monomial ideals are also significant because they appear as initial ideals of arbitrary ideals. Since many properties of an initial ideal are inherited by its original ideal, one often adopt this strategy to decipher properties of general ideals. The first talk is meant for covering the preliminary results on resolution and regularity of monomial ideal.The aim of this series of talk is to present the result in arXiv:1709.05055 .


[10:30am]Provanjan Mallick
Description:
Title : Asymptotic prime divisors. 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 talk to present the first chapter of S. McAdam, Asymptotic prime divisors, Lecture Notes in Mathematics 1023, Springer-Verlag, Berlin, 1983.

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