March 2022
Public Access Category: All |

- Time:
- 2:30pm - 3:45pm
- Description:
- Reading Seminar

Thursday, 3rd March · 2:30 – 3:45 pm

Google Meet joining info

Video call link: https://meet.google.com/auv-mwkn-ixh

Title: Modular representations of Algebraic groups,

Abstract:

We have studied the Borel-Weil-Bott theorem and Kempf vanishing theorem. Using Serre duality and Borel-Weil-Bott we will first discuss the irreducibility of the Weyl modules over a field of characteristics 0. Then moving to the prime characteristic field and we will briefly discuss the Steinberg Tensor product theorem. Finally we will wrap up the talk by browsing through some later developments and recent trends.

Here is the link to the notes of all the talks.

https://drive.google.com/file/d/1PNqfriaSWV4QbLAC9xcYuwPAu9xhjP6m/view?usp=sharing

So far the main references have been Jantzen's book ``Representation theory of Algebraic Groups'' and a note by Andersen ``Modular representation of Algebraic groups and Relations to Quantum groups''.

For this talk besides the previous references I would also like to point out the following two articles which discuss a few recent big developments in representation theory of reductive groups in prime characteristics and geometric representation theory.

1. Lectures on Geometry and modular representation theory of algebraic groups by Joshua Ciappara and Geordie Williamson

https://arxiv.org/pdf/2004.14791.pdf

2. Modular representations and reflection subgroups by Geordie Williamson

https://arxiv.org/pdf/2001.04569.pdf

- Time:
- 7:30pm
- Description:
- Speaker: Joseph Gubeladze, San Francisco State University, USA.

Date/Time: 4 March 2022, 7:30pm IST/ 2:00pm GMT / 9:00am ET (joining time

7:15pm IST).

Gmeet link: meet.google.com/xcw-ukrb-rtw

Title: Normal polytopes and ellispoids.

Abstract: Lattice polytopes are the combinatorial backbone of toric

varieties. Many important properties of these varieties admit purely

combinatorial description in terms of the underlying polytopes. These

include normality and projective normality. On the other hand, there are

geometric properties of polytopes of integer programming/discrete

optimization origin, which can be used to deduce the aforementioned

combinatorial properties: existence of unimodular triangulations or

unimodular covers. In this talk we present the following recent results:

(1) unimodular simplices in a lattice 3-polytope cover a neighborhood of

the boundary if and only if the polytope is very ample, (2) the convex

hull of lattice points in every ellipsoid in R^3 has a unimodular cover,

and (3) for every d at least 5, there are ellipsoids in R^d, such that the

convex hulls of the lattice points in these ellipsoids are not even

normal. Part (3) answers a question of Bruns, Michalek, and the speaker.

For more information and links to previous seminars, visit the website of

VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 2:30pm - 3:45pm
- Description:
- This week we will have Sudarshan Gurjar speaking on the `Representation theory and Algebraic Geometry' reading seminar group. Note that this will be an on campus meeting and not an online meet.

Here are the details:

DDT: Thursday, 10th March, 2:30 – 3:45 pm

Venue : Ramanujan Hall, Department of mathematics.

Title : Introduction to Lie group representations

Abstract: In the first of the two talks that I will give, I will introduce representations of Lie groups and prove a few basic properties of them. This will prepare ground for the Peter Weyl theorem to be discussed in the second lecture.

We have now a dedicated website where one can find the notes and resources from the past meets and announcements of the upcoming meetings:

https://sites.google.com/view/rtag/

- Time:
- 11:30am - 12:30pm
- Description:
- Date : March 11, Friday

Time : 11:30-12:30

Link : https://meet.google.com/bmi-aoav-tgi?authuser=0

Title: Asymptotic behaviour of certain length functions.

Abstract: The notion of epsilon multiplicity was originally defined by B.

Ulrich and J. Validashti as a limsup and they used it to detect integral

dependence of modules. It is important to know if the limsup can be

replaced by a limit. In this talk we shall see that the relative epsilon

multiplicity of reduced standard graded algebras over an excellent local

ring exists as a limit. However, the associated length function can be

quite complicated. We explore certain situations when the symbolic (multi)

Rees algebra is finitely generated. In such cases, the associated

(multigraded) length function exhibits polynomial-like behaviour.

- Time:
- 6:30pm
- Description:
- Speaker: Craig Huneke, University of Virginia, USA.

Date/Time: 11 March 2022, 6:30pm IST/ 1:00pm GMT / 8:00am ET (joining time

6:15pm IST).

Gmeet link:meet.google.com/pgp-fbva-kzb

Title: Torsion in Commutative Algebra.

Abstract: This talk will be a somewhat historical one, concerning three

problems dealing with the idea of torsion. The three problems are those on

symbolic powers, the Huneke-Wiegand conjecture, and Berger's conjecture.

Besides talking about my own memories, we will focus on torsion in tensor

products.

For more information and links to previous seminars, visit the website of

VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 4:15pm
- Location:
- VMCC, Lecture Hall No: 33, Third Floor
- Description:
- Location: VMCC, Lecture Hall No: 33, Third Floor

Date: 16 March 2022

Time: 4:15 PM

Speaker: Prof. Jugal K. Verma, Department of Mathematics

Recipient of Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences

Title: Multivariate Polynomial Equations and Mixed Volumes of Newton Polytopes

- Time:
- 2:30pm - 3:45pm
- Description:
- DDT: Thursday, 17th March, 2:30 – 3:45 pm

Venue : Ramanujan Hall, Department of mathematics.

Title : Introduction to Lie group representations

Abstract: In the first of the two talks that I will give, I will introduce representations of Lie groups and prove a few basic properties of them. This will prepare ground for the Peter Weyl theorem to be discussed in the second lecture.

We have now a dedicated website where one can find the notes and resources from the past meets and announcements of the upcoming meetings:

https://sites.google.com/view/rtag/

- Time:
- 5:00pm
- Description:
- Geometric Analysis seminar series.

https://sites.google.com/math.iitb.ac.in/geometric-analysis/home

Speaker: Samir Shukla (IIT Mandi)

Time: March 17, Thursday, 5:00 pm (Indian Standard Time)

Title: Spectral gap bounds for the simplicial Laplacian and an application

to random complexes

Abstract: Let L(G) denotes the Laplacian of a graph G. The second smallest

eigenvalue of L(G) is called the spectral gap. In this talk, we discuss

two spectral gap bounds for the reduced Laplacian of a simplicial complex.

As an application we prove that, if the spectral gap of the Laplacian of

skeleton of a simplicial complex is enough large, then its co-homology

vanishes up to certain dimensions. We also see an application of these

results in certain random complexes. This is a joint work with D.

Yogeshwaran.

Google Meet joining info

Video call link: https://meet.google.com/yah-ckma-wcj

Or dial: (US) +1 914-893-5944 PIN: 646 903 629#

- Time:
- 6:00pm
- Description:
- Geometric Analysis seminar series.

https://sites.google.com/math.iitb.ac.in/geometric-analysis/home

Speaker: Anke Pohl (University of Bremen)

Time: March 24, Thursday, 6:00 pm

Title: Fractal Weyl bounds

Abstract: Resonances of Riemannian manifolds are often studied with tools

of microlocal analysis. I will discuss some recent results on upper

fractal Weyl bounds for certain hyperbolic surfaces of infinite area,

obtained with transfer operator techniques, which are tools complementary

to microlocal analysis. This is joint work with F. Naud and L. Soares.

Google Meet joining info

Video call link: https://meet.google.com/oua-zdfd-oib

Or dial: (US) +1 406-686-2004 PIN: 869 293 958#

- Time:
- 5:30pm
- Description:
- Speaker: Dharm Veer, Chennai Mathematical Institute, India.

Date/Time: 25 March 2022, 5:30pm IST/ 12:00pm GMT / 8:00am ET (joining

time 5:15pm IST).

Gmeet link: meet.google.com/uht-oqmy-awd

Title: On Green-Lazarsfeld property $N_p$ for Hibi rings/

Abstract: Let $L$ be a finite distributive lattice. By Birkhoff's

fundamental structure theorem, $L$ is the ideal lattice of its subposet

$P$ of join-irreducible elements. Write $P=\{p_1,\ldots,p_n\}$ and let

$K[t,z_1,\ldots,z_n]$ be a polynomial ring in $n+1$ variables over a field

$K.$ The {\em Hibi ring} associated with $L$ is the subring of

$K[t,z_1,\ldots,z_n]$ generated by the monomials

$u_{\alpha}=t\prod_{p_i\in \alpha}z_i$ where $\alpha\in L$. In this talk,

we show that a Hibi ring satisfies property $N_4$ if and only if it is a

polynomial ring or it has a linear resolution. We also discuss a few

results about the property $N_p$ of Hibi rings for $p=2$ and 3. For

example, we show that if a Hibi ring satisfies property $N_2$, then its

Segre product with a polynomial ring in finitely many variables also

satisfies property $N_2$.

For more information and links to previous seminars, visit the website of

VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 11:30am
- Description:
- Title : Some Structures on Principal Lie 2-group Bundles over Lie Groupoid

Time: 11:30- 12:30

Venue: Ramanujan Hall

Abstract : There are several equivalent ways to define the notion of

connection on a principal Lie group bundle over a manifold. One such

definition involves the splitting of the so called Atiyah sequence. For a

principal bundle E over M, the Atiyah sequence is a short exact sequence

of vector bundles over the manifold M. Motivated by this idea, we define

the notion of a Atiyah sequence for a principal Lie 2-group bundle over a

Lie groupoid. Using that, we define some geometric structures on principal

Lie 2-group bundles over Lie groupoid.

This talk is based on recently accepted joint work with Saikat Chatterjee

and Aditya Chaudhuri. https://doi.org/10.1016/j.geomphys.2022.104509

First 40 minutes of the talk is expected to be accessible to M.Sc students.

- Time:
- 2:30pm - 3:45pm
- Description:
- Representation theory and Algebraic Geometry'

Speaker: Ankit Rai

DDT: Thursday, 31st March, 2:30 – 3:45 pm

Venue : Ramanujan Hall, Department of mathematics.

Title : Tannakian categories and some applications.

Abstract : There is a classical result of Tannaka which provides a way to

reconstruct compact Lie groups from the category of its finite dimensional

representations. Later, Grothendieck and Saavedra developed the so-called

Tannakian formalism which allows for an extension of the above result in

the context of algebraic groups. In the two talks I shall give a short

introduction to Tannakian formalism and discuss a few applications.

In the two talks I shall give a short introduction to Tannakian formalism

and discuss a few applications.

We have now a dedicated website where one can find the notes and resources

from the past meets and announcements of the upcoming meetings:

https://sites.google.com/view/rtag/

Please join us this Thursday !