June 22, 2020 - June 26, 2020
Public Access Category: All |
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- Time:
- 3:00pm-4:00pm
- Description:
- Date and Time: Monday, 22 June, 3pm to 4pm IST (joining time: 2.50pm IST)
Google Meet link: meet.google.com/gxv-jqky-vmy
Speaker: Krishna Hanumanthu
Affiliation: Chennai Mathematical Institute, Chennai
Title: Seshadri constants and rationality questions.
Abstract: Seshadri constants are a local measure of positivity of line
bundles and have many interesting applications. An important question is
whether Seshadri constants can be irrational. While the answer is expected
to be yes, currently we do not know any examples of irrational Seshadri
constants. In this talk, we will start with basics on Seshadri constants
and discuss important results and connections to well known questions. We
will then focus on rationality questions and exhibit irrational Seshadri
constants assuming some conjectures are true. The talk will be based on
two joint works, one with B. Harbourne and another with L. Farnik, J.
Huizenga, D. Schmitz and T. Szemberg. I will try to keep most of the talk
accessible to anyone with knowledge of basic algebraic geometry.
- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Dr. Pranabendu Misra (Max Planck Institute for Informatics,
Saarbrucken, Germany)
Date-time: Monday (June 22), 4-5 PM (Webex Meeting details below)
Title: A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments
Abstract
-----------
A Tournament is a directed graph T such that every pair of vertices is
connected by an arc. A Feedback Vertex Set is a set S of vertices in T
such that T−S is acyclic. We consider the Feedback Vertex Set problem
in tournaments, where the input is a tournament T and a weight
function w:V(T)→N and the task is to find a feedback vertex set S in T
minimizing w(S). We give the first polynomial time factor 2
approximation algorithm for this problem. Assuming the Unique Games
conjecture, this is the best possible approximation ratio achievable
in polynomial time.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=md23f92c26686aa030456a9d08390379d
Meeting number:166 483 6041
Password:RKypRMZy888
- Time:
- 5:30pm-6:30pm
- Description:
- Date and Time: 23 June 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)
Google Meet Link: https://meet.google.com/gkc-hydx-fkn
Speaker: Mitra Koley, TIFR Mumbai
Title: $F$-rationality of Rees algebras.
Abstract: In this talk we will discuss $F$-rationality of Rees algebras.
The study in this direction began when Singh gave an example of
$3$-dimensional hypersurface $F$-rational ring whose Rees algebra with
respect to a maximal ideal is Cohen-Macaulay and normal domain but not
$F$-rational. Motivated by this example Hara, Watanabe and Yoshida
investigated various questions regarding $F$-rationality of Rees algebras.
Using the notion of tight integral closure they gave a criterion for
$F$-rationality of Rees algebras of ideals primary to the maximal ideal of
a Cohen-Macaulay local ring. Their paper is of significant interest
because of some conjectures and some open questions. In a joint work with
Manoj Kummini we study these questions and conjectures and answer some of
them.
- Time:
- 11:30am
- Description:
- Speaker: Shaunak Deo (TIFR, Mumbai)
Title: Deformations of Galois representations
Date and Time: Wednesday 24 June, 11.30 am.
Abstract: One of the main themes of deformation theory of Galois
representations is to study families of Galois representations obtained by
interpolating various Galois representations having certain prescribed
properties. In this talk, I will first review some basic facts and results
of deformation theory of Galois representations. Then I will describe the
basic anatomy of theorems comparing various universal deformation rings
with appropriate Hecke algebras (which are popularly known as 'R=T'
theorems in the literature and are important from Number theoretic point
of view). In the second half of the talk, I will describe some of my own
results in which establishing an R=T theorem has played a crucial role.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=mcc2936a602a0981840edc6eaf71cc3bf
Meeting number:
166 269 1333
Password:
CgwEqxNx672
- Time:
- 5:30pm-6:30pm
- Description:
- Date and Time: 26 June 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)
Google Meet Link: https://meet.google.com/gkc-hydx-fkn
Speaker: Arindam Banerjee, RKM Vivekananda Institute, Belur
Title: An introduction to absolute integral closure.
Abstract: In this talk we shall introduce the notion of absolute integral
closure of a domain and mention some of its basic properties. Along with
some other results we shall prove the Newton-Puiseux theorem and the fact
that for a powers series ring A of finitely many variables over a field of
positive characteristic, the absolute integral closure of A is flat over
A.