6:15pm» Anurag Singh, University of Utah- Time:
- 6:15pm
- Description:
- Please note that the talk starts at 6:30pm IST.
Date and Time: 5 June 2020, 6:30 pm IST / 01:00pmGMT / 09:00am EDT
(joining time : 6:15 pm IST - 6:30 pm IST)
Google Meet Link: https://meet.google.com/gkc-hydx-fkn
Speaker: Anurag Singh, University of Utah.
Title: F-rationality of Hankel determinantal rings.
Abstract: We will give a proof that Hankel determinantal rings are
$F$-rational, at least if the characteristic of the residue field is
suitably large. This is joint work with Aldo Conca, Maral
Mostafazadehfard, Matteo Varbaro, and Keiichi Watanabe.
- Time:
- 5:30pm - 6:30pm
- Description:
- 9 June 2020, 5:30 pm IST / 12:00GMT / 08:00am EDT (joining time : 5:15 pm IST - 5:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Srikanth Iyengar, University of Utah - Modular representations of elementary abelian groups and commutative algebra - Part 1
In the first lecture of this series Huneke explained how the work on invariants of groups, due to Hilbert and Noether, lead to some of the modern developments in commutative algebra. In my talks I will discuss a different connection between representation theory of groups and commutative algebra. A starting point for this is the work of Jon Carlson, from the 1980s, on 'rank varieties' for modular representations of abelian groups of the form (ℤ/pℤ)c, where p is some prime number. The group algebra of such an elementary abelian group is a complete intersection ring and Carlson's theory of rank varieties has been extended to apply to all complete intersections. This development was initiated by Avramov and Buchweitz, and is still an area of active research. The aim of my talks is to give an introduction to these ideas, starting with the work of Carlson.
- Time:
- 5:30pm - 6:30pm
- Description:
- Date and Time: 12 June 2020, 5:30 pm IST / 12:00GMT / 08:00am EDT (joining
time : 5:15 pm IST - 5:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Speaker: Srikanth Iyengar, University of Utah.
Title: Modular representations of elementary abelian groups and
commutative algebra - Part 2
Abstract: In the first lecture of this series Huneke explained how the
work on invariants of groups, due to Hilbert and Noether, lead to some of
the modern developments in commutative algebra. In my talks I will discuss
a different connection between representation theory of groups and
commutative algebra. A starting point for this is the work of Jon Carlson,
from the 1980s, on 'rank varieties' for modular representations of abelian
groups of the form (ℤ/pℤ)^c, where p is some prime number. The
group algebra of such an elementary abelian group is a complete
intersection ring and Carlson's theory of rank varieties has been extended
to apply to all complete intersections. This development was initiated by
Avramov and Buchweitz, and is still an area of active research. The aim of
my talks is to give an introduction to these ideas, starting with the work
of Carlson.
- Time:
- 11:00am
- Description:
- Speaker: Debraj Das.
Affiliation: IIT Kanpur.
Title of the talk: Bootstrap Inference in Regression.
Abstract of the talk:
https://drive.google.com/file/d/1DH3CM3_mqVMGlEu90lt9giDP6Qy4XLls/view
Date and Time: Tuesday 16 June 2020, 11.00am.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=me8a0b222c39e84e489a4bf137b3b33d0
Meeting number:
166 274 8342
Password:
X4VgsQCJu44
- Time:
- 3:30pm
- Description:
- 16 June 2020 (Tuesday), 15:30 GMT
Speaker: Nikolaos Tziolas (Cyprus).
Title: Vector fields on canonically polarized surfaces
Abstract: In this talk I will present some results about the geometry of
canonically polarized surfaces defined over a field of positive
characteristic which have a nontrivial global vector field, equivalently
non reduced automorphism scheme, and the implications that the existence
of such surfaces has in the moduli problem of canonically polarized
surfaces.
Zoom link:
https://us02web.zoom.us/j/9918493831?pwd=NzJNWmd5Y2h2eXFqbGpiN3Fva1pYQT09
- Time:
- 6:30pm - 7:30pm
- Description:
- Date and Time: 16 June 2020, 6:30 pm IST - 7:30 pm IST (joining time :
6:15 pm IST - 6:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Speaker: Madhusudan Manjunath, IIT Bombay.
Title: Frobenius numbers.
Abstract: For a natural number $k$, the $k$-th (generalised) Frobenius
number of relatively prime natural numbers $(a_1, \dots, a_n)$ is the
largest natural number that cannot be written as a non-negative integral
combination of $(a_1, \dots, a_n)$ in $k$ distinct ways. We study the
$k$-th Frobenius number from a commutative algebraic perspective. We
interpret the $k$-th Frobenius number in terms of the Castelnuovo-Mumford
regularity of certain modules associated to $(a_1, \dots, a_n)$. We study
these modules in detail and using this study, show that the sequence of
generalised Frobenius numbers form a finite difference progression, i.e. a
sequence whose set of successive differences form a finite set. This talk
is based on a joint work with Ben Smith.
- Time:
- 2:00pm
- Description:
- 18 June 2020 (Thursday), 14:00 GMT
Speaker: Claire Voisin (Paris, France)
Title: Triangle varieties and surface decomposition of hyper-Kahler manifolds
Abstract: In recent years, new constructions of complete families of
polarized hyper-Kahler manifolds have been found starting from Fano
geometry. These hyper-Kahler manifolds also appear as general deformations
of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will introduce
the notion of surface decomposition for a variety X with a nontrivial
Hodge structure on degree 2 cohomology. I will show that this notion is
restrictive topologically, as it implies Beauville-Fujiki type relations.
I will also show the existence of such a surface decomposition for the
general hyper-Kahler manifolds mentioned above. This has interesting
consequences on Beauville's conjecture on the Chow ring of hyper-Kahler
manifolds.
Zoom link:
https://us02web.zoom.us/j/9918493831?pwd=NzJNWmd5Y2h2eXFqbGpiN3Fva1pYQT09
- Time:
- 6:00pm
- Description:
- Speaker: Vivek Mukundan (Unversity of Virginia, USA)
Day and Time: 6:00 p.m. (18:00 hours), Thursday, June 18, 2020
Title: Two themes on Rees Algebra of Ideals.
Abstract: The talk discusses two problems, namely, the Implicitization
problem and the stable Harbourne problem which uses Rees Algebra of ideals
in an essential way. Implicitization problem seeks the equations defining
the closed image of certain rational map. The rational map is defined by a
height two perfect ideals satisfying certain conditions. This translates
to finding the equations defining the special fiber ring.
The second problem relates to finding optimal solution to the containment
problem. The containment problem is about finding the best values of n and
b such that I^{(b)}\subseteq I^n. We discuss the Harbourne conjecture and
various aspects of the containment problem. We then introduce the stable
Harbourne problem and prove classes of ideals giving credence to it.
Videoconferencing will be via webex.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=m982006e853c9c6d003858b79e7767d37
Meeting number: 166 383 6958
Password: pK39MPtDfe3
- Time:
- 6:30pm - 7:30pm
- Description:
- Date and Time: 19 June 2020, 6:30 pm IST - 7:30 pm IST (joining time :
6:15 pm IST - 6:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Speaker: Madhav Nori, University of Chicago.
Title: Intersection multiplicities.
Abstract: Bezout's theorem states that projective curves of degrees a and
b meet in ab points if ''counted properly''. The correct number to count
at a point of intersection is the intersection-multiplicity defined in
Serre's book ''Local Algebra and Intersection-Multiplicity''. The talk,
meant for graduate students, will be an introduction to the subject. The
definitions will be looked at from various angles. This will be followed
by a report on the progress towards Serre's conjectures.
- 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.
- Time:
- 11:30am
- Description:
- Speaker: Mihir Seth (TIFR, Mumbai)
Title: Non-admissible irreducible representations of GL_2(Q_{p^2}) in
characteristic p.
Time, Day and Date: 11:30 a.m., Monday, June 29
Abstract: Every smooth irreducible representation of a reductive p-adic
group over an algebraically closed field of characteristic 0 is
admissible. This is no longer true for representations over characteristic
p fields. In this talk, I will speak about the joint work with E. Ghate in
which we construct non-admissible smooth irreducible representations of
GL_2(Q_{p^2}) over any characteristic p field. The construction uses the
formalism of diagrams of Breuil-Paskunas and is based on the similar work
of Daniel Le.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=mf053554c22896926d0d1c67abe03dde9
Meeting number:
166 186 9677
Password:
58tMdhDXSW3
- Time:
- 5:30pm - 6:30pm
- Description:
- Date and Time: 30 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: Manoj Kummini, Chennai Mathematical Institute
Title: Big Cohen-Macaulay algebras - Part 1.
Abstract: In the first talk, we will look at some applications of big
Cohen-Macaulay algebras. In the second we will give an outline of the
proof by Huneke and Lyubeznik that the absolute integral closure of a
noetherian local domain that is a homomorphic image of a Gorenstein local
ring is a (big) Cohen-Macaulay algebra over it.