Tue, October 17, 2017
Public Access Category: All |
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- Time:
- 9:30am-10:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- 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
- Time:
- 10:30am-11:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.