July 20, 2020 - July 24, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Sujoy Chakraborty
Time: Monday 20th July 4 to 5pm (joining time 3.50pm)
Google Meet Link: https://meet.google.com/ubd-taca-nio
Title: Moduli of Parabolic bundles over a curve and its first rational
Chow group
Abstract: In this talk, we will aim to study the rational Chow group of
1-cycles for the moduli of semistable Parabolic bundles of fixed rank,
determinant and weight over a curve. Chow groups are interesting and
important objects to study for various reasons. Unfortunately, not much is
known about the Chow groups for various moduli space of semistable vector
bundles of a fixed rank and determinant over a curve. We will first
discuss the notions related to Parabolic bundles and their moduli, and
study the effect on Chow group of 1-cycles as we vary the generic weight.
As a consequence, we can get an explicit description of the Chow group of
1-cycles in a particular case of rank 2 Parabolic bundles, extending an
earlier result of I. Choe and J. Hwang.
- Time:
- 6:30pm-7:30pm
- Description:
- Date and Time: Tuesday 21 July 6.30 pm-7.30 pm
Google Meet Link: https://meet.google.com/gkc-hydx-fkn
Speaker: Melvin Hochster, University of Michigan.
Title: Tight Closure, lim Cohen-Macaulay sequences, the content of local
cohomology, and related open questions - Part 1.
Abstract: The talks will give multiple characterizations of tight closure,
discuss some of its applications, indicate connections with the existence
of big and small Cohen-Macaulay algebras and modules, as well as variant
notions, and also explain connections with the theory of content. There
will be some discussion of the many open questions in the area, including
the very long-standing problem of proving that Serre intersection
multiplicities have the behavior one expects.
- Time:
- 11:00am-12:00pm
- Description:
- Title of the Thesis: Operator theory on two domains related to
$\mu$-synthesis
Abstract: We shall discuss Nagy-Foias type operator theory for operators
associated with two domains
related to $\mu$-synthesis, namely the tetrablock and the symmetrized
polydisc.
Date and Time: July 24, 2020, Friday from 11 am - 12 noon
WebEx Link Details:
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=m99f0f4c8b20a85a7ed79974d06f07269
Meeting number:
166 634 3026
Password:
CWvrJia7E24
All are cordially invited to participate.
- Time:
- 6:30pm-7:30pm
- Description:
- Date and Time: Friday 24 July 6.30pm - 7.30pm.
Google meet link: https://meet.google.com/epm-ddze-asm
Speaker: Hai Long Dao, The University of Kansas.
Title: Reflexive modules over curve singularities
Abstract: A finitely generated module $M$ over a commutative ring $R$ is
called reflexive if the natural map from $M$ to $M^{**} = Hom(Hom(M,R),
R)$ is an isomorphism. In understanding reflexive modules, the case of
dimension one is crucial. If $R$ is Gorenstein, then any maximal
Cohen-Macaulay module is reflexive, but in general, it is quite hard to
understand reflexive modules even over well-studied one-dimensional
singularities. In this work, joint with Sarasij Maitra and Prashanth
Sridhar, we will address this problem and give some partial answers.