September 25, 2017 - September 29, 2017
Public Access Category: All |
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- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Free Resolutions of Monomial Ideals.
Speaker: Prof. Madhusudan Manjunath
Abstract: We'll study free resolutions of monomial ideals via the notion
of a labelled simplicial complex. We derive a criterion due to Bayer,
Peeva and Sturmels for a labelled simplicial complex to define a free
resolution.
As consequences, we show that the Koszul complex is exact and prove the
Hilbert syzygy theorem.
- Time:
- 9:30am-10:25am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Linear resolutions of monomial ideals - I
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: Huneke-Itoh Intersection Theorem and its Consequences - II
Abstract: Huneke and Itoh independently proved a celebrated result on
integral closure of powers of an ideal generated by a regular sequence. As
a consequence of this theorem, one can find the Hilbert-Samuel polynomial
of the integral closure filtration of I if the normal reduction number is
at most 2. We prove Hong and Ulrich's version of the intersection theorem.
- Time:
- 2:30pm-5:30pm
- Location:
- Room 113, Department of Mathematics
- Description:
- Speaker: Nagarjuna Chary
Title: Local Fields
Abstract: We will cover the material in Chapter 2 in Cassels and Frohlich.