- Time:
- 3:00pm - 4:00pm
- Description:
- Speaker: Aniruddha Samanta

Title/Abstract: Attached

Date/time: Tuesday, February 1 2022, 3 pm - 4 pm

Google meet link: To join the video meeting, click this link:

https://meet.google.com/qty-joci-rdh

Otherwise, to join by phone, dial +1 929-251-5508 and enter this

PIN: 364 520 942#

- Time:
- 11:30am
- Description:
- Speaker: Rakesh Jana: Indian Institute of Technology Guwahati

Title/Abstract: Attached

Date/time: Wednesday, February 2 2022, 11.30 am - 12.30 pm

Google meet link: To join the video meeting, click this link:

https://meet.google.com/qty-joci-rdh

Otherwise, to join by phone, dial +1 929-251-5508 and enter this

PIN: 364 520 942#

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

Thursday, 3 February · 2:30 – 3:30 pm

Google Meet joining info

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

The first speaker is Sarjick Bakshi. He will give two/three talks on the

following topics.

Title: Modular representations of Algebraic groups,

Abstract:

We will discuss a few important and classical theorems in the

representation theory of reductive algebraic groups like the

Borel-Weil-Bott theorem, Kempf's vanishing theorem. The main reference

would be Jantzen's book ``Representation theory of Algebraic Groups'' and a

note by Andersen ``Modular representation of Algebraic groups and Relations

to Quantum groups''.

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

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

Speaker: Luc Hillairet (Institut Denis Poisson, University of Orleans,France)

Time: 3 February 2022, Thursday, 6 pm

Title: Variations on Concentration

Abstract: Studying the concentration of eigenfunctions of Schrodinger or

Laplace-type operators is a well known problem of semiclassical analysis.

Useful tools for the latter include semiclassical measures, WKB expansion.

After recalling some classical results of this theory we will focus on

less classical ones that are related to the study of analytic

eigenbranches or eigenvalue spacing problems. Based on joint work with C.

Judge and J. Marzuola.

Zoom Meeting link:

https://zoom.us/j/95913414820?pwd=WWxRWFp3Y1IzTlRiUWNENyt6bVFNQT09

Meeting ID: 959 1341 4820

Passcode: 832222

- Time:
- 6:30pm
- Description:
- Speaker: *Adam Van Tuyl, McMaster University, Canada*Date/Time: *4* February 2022*,

6:30pm IST/ 1:00pm GMT / 8:00am ET *(joining time 6:15pm IST)

Gmeet link: meet.google.com/vcc-aywh-xgx

Title: Toric ideals of graphs and some of their homological invariants

Abstract: The study of toric ideals of graphs lies in the intersection of

commutative algebra, algebraic geometry, and combinatorics. Formally, if $G

= (V,E)$ is a finite simple graph with edge set $E =\{e_1,\ldots,e_s\}$ and

vertex set $V = \{x_1,\ldots,x_n\},$ then the toric ideal of $G$ is the

kernel of the ring homomorphism $\varphi:k[e_1,\ldots,e_s] \rightarrow

k[x_1,\ldots,x_n]$ where $\varphi(e_i) = x_jx_k$ if the edge $e_i =

\{x_j,x_k\}$. Ideally, one would like to understand how the homological

invariants (e.g. graded Betti numbers) of $I_G$ are related to the graph

$G$. In this talk I will survey some results connected to this theme, with

an emphasis on the Castelnuovo-Mumford regularity of these ideals.

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 - 3:30pm
- Description:
- Reading Seminar

Thursday, 10 February · 2:30 – 3:30 pm

Google Meet joining info

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

The speaker is Sarjick Bakshi. He will give the second talk on the

following topics.

Title: Modular representations of Algebraic groups,

Abstract:

We will discuss a few important and classical theorems in the

representation theory of reductive algebraic groups like the

Borel-Weil-Bott theorem, Kempf's vanishing theorem. The main reference

would be Jantzen's book ``Representation theory of Algebraic Groups'' and a

note by Andersen ``Modular representation of Algebraic groups and Relations

to Quantum groups''.

- Time:
- 5:30pm
- Description:
- Speaker: Shunsuke Takagi, University of Tokyo, Japan.

Date/Time: 11 February 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining

time 5:15pm IST).

Gmeet link: meet.google.com/ytj-rdzc-tay

Title: Kodaira vanishing for thickenings of globally $F$-regular varieties.

Abstract: Blickle-Bhatt-Lyubeznik-Singh-Zhang proved that if $X$ is a

projective variety over a field $k$ of characteristic zero with isolated

complete intersection singularities, then the Kodaira vanishing theorem

holds for all thickenings of $X$. What if $k$ is of positive

characteristic? Kodaira vanishing can fail in positive characteristic, but

it still holds for Frobenius split varieties. In this talk, I will discuss

Kodaira vanishing for thickenings of globally $F$-regular varieties, a

special class of Frobenius split varieties. This talk is based on joint

work with Kenta Sato.

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:
- Reading Seminar

Thursday, 17 February · 2:30 – 3:45 pm

Google Meet joining info

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

The speaker is Sarjick Bakshi. He will give the 3rd talk on the

following topics.

Title: Modular representations of Algebraic groups,

Abstract:

We will discuss a few important and classical theorems in the

representation theory of reductive algebraic groups like the

Borel-Weil-Bott theorem, Kempf's vanishing theorem. The main reference

would be Jantzen's book ``Representation theory of Algebraic Groups'' and a

note by Andersen ``Modular representation of Algebraic groups and Relations

to Quantum groups''.

- Time:
- 4:00pm
- Description:
- Geometric Analysis seminar series.

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

Speaker: Bruno Premoselli (Université Libre de Bruxelles, Belgium)

Time: February 17, Thursday, 4 pm (Indian Standard Time)

Title: A priori estimates for sign-changing solutions of critical elliptic

equations of Schrodinger-Yamabe type

Abstract: In this talk we consider sign-changing solutions of critical

Yamabe-Schrodinger type equations of second order. Unlike their positive

counterpart these solutions have no direct physical or geometrical

meaning, but have been shown to arise in geometrical contexts. They appear

for instance as extremals for higher eigenvalues minimisation problems in

a given conformal class. We describe in this talk the structure of

bubbling sign changing solutions for these equations and provide a

detailed asymptotic description, in strong spaces, of the blow-up. As a

consequence we prove some precompactness results for the set of

energy-bounded solutions of these equations. Some of these results have

been obtained in collaboration with J. Vétois (McGill University).

Google Meet joining info:

Video call link: https://meet.google.com/ptb-uyyu-zas

Or dial: (US) +1 484-841-8292 PIN: 147 605 745#

- Time:
- 5:30pm
- Description:
- Speaker: Liran Shaul, Charles University, Prague.

Date/Time: 18 February 2022, 5:30pm IST/ 12:00pm GMT / 7:00am ET (joining

time 5:15pm IST).

Gmeet link: meet.google.com/osq-afmn-san

Title: Special classes of rings in derived commutative algebra.

Abstract: The classes of regular, Gorenstein and Cohen-Macaulay rings are

among the most important classes of rings in commutative algebra and

algebraic geometry. In this talk we recall the definitions and basic

properties of these classes, and then explain how to generalize each of

them to derived commutative algebra, in the context of commutative

differential graded algebras. We further explain how each of these

generalizations arise naturallyin various algebraic geometry contexts and

discuss some applications.

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:
- Reading Seminar

Thursday, 24 February · 2:30 – 3:45 pm

Google Meet joining info

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

Website

The speaker is Sarjick Bakshi. He will give the 4th talk on the following topics.

Title: Modular representations of Algebraic groups,

Abstract:

We will discuss a few important and classical theorems in the representation theory of reductive algebraic groups like the Borel-Weil-Bott theorem, Kempf's vanishing theorem. The main reference would be Jantzen's book ``Representation theory of Algebraic Groups'' and a note by Andersen ``Modular representation of Algebraic groups and Relations to Quantum groups''.

- Time:
- 5:30pm
- Description:
- Analysis seminar series.

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

Speaker: Pierre-Damien Thizy (Institut Camille Jordan, Université Claude

Bernard Lyon 1, France)

Time: February 24, Thursday, 5:30 pm

Title: Large blow-up sets for Q-curvature equations

Abstract: On a bounded domain of the Euclidean space $\mathbb{R}^{2m}$,

m>1, Adimurthi, Robert and Struwe pointed out that, even assuming a volume

bound $\int e^{2mu} dx\le C$, some blow-up solutions for prescribed

Q-curvature equations $(-\Delta)^m u= Q e^{2m u}$ without boundary

conditions may blow-up not only at points, but also on the zero set of

some nonpositive nontrivial polyharmonic function. This is in striking

contrast with the two dimensional case (m=1). During this talk, we will

discuss the construction of such solutions which involve (possible

generalizations of) the Walsh-Lebesgue theorem and some issues about

elliptic problems with measure data.

Google Meet joining info

Video call link: https://meet.google.com/efe-orej-zet

Or dial: (US) +1 651-560-3980 PIN: 954 349 109#

- Time:
- 11:30am - 12:30pm
- Description:
- Speaker: Ankit Mishra, IIT Bombay

February 25 (Friday), 11:30-12:30.

Link : https://meet.google.com/jvr-izyy-ngd?authuser=0

Title : Hilbert series of CM local rings with

$e_2=e_1-e+1$ and MCM modules over hypersurface rings.

- Time:
- 2:30pm - 3:30pm
- Description:
- Date: February 25 (Friday), 2.30 - 3.30 pm Link: meet.google.com/pbb-odky-xvs Title: Generalization of Serre Splitting to monoid algebras R[M] Abstract: In the search for an answer to his conjecture, Serre gave a splitting theorem which states that for a commutative noetherian ring R and a projective R-module P of rank r, if r > dim(R), then P admits a splitting with a free direct summand. This result, often aptly referred to as Serre splitting theorem, shrinks the class of projective R-modules one needs to study to projective R-modules of rank < dim(R) + 1. One may thus ask if a similar splitting exists for projective R[M]-modules of rank > dim(R), when M is a submonoid of Z^n. This problem will be addressed in two parts. In the first part, when rank(P) coincides with dim(R[M]), the said splitting will be demonstrated. The second part will tackle the problem when rank(P) dips even further, i.e., dim(R) < rank(P) < dim(R[M])-1. For n > 0, we define classes of monoids M_n such that if M in M_n is seminormal and rank(P) > dim(R[M]) – n, then P admits a splitting. As a consequence, it can be shown that for a projective module P over Segre extensions S_mn over R, splitting is possible when rank(P) > dim(S_mn)-[(m+n-1)/min(m,n)]. We will also discuss the possibilities of splitting under monic inversion.

- Time:
- 4:00pm - 5:00pm
- Description:
- February 25 (Friday), 4:00-5:00.

Link : https://meet.google.com/jvr-izyy-ngd?authuser=0

Title : Effects of perturbation on low energy Laplace eigenfunctions

Abstract : In this talk, we will discuss the effects of perturbation on

certain topological and geometrical properties of the nodal sets/vanishing

sets of Laplace eigenfunctions. Our discussion will be centred around a

well-known conjecture of Payne which states that: the zero set

corresponding to the second Laplace eigenfunction of any bounded planar

domain should intersect the boundary at exact two points. We will look

into certain stability properties of the nodal sets and obtain some

interesting results concerning the conjecture.

- Time:
- 6:30pm
- Description:
- Speaker: K. Sather-Wagstaff, Clemson University, South Carolina.

Date/Time: 25 February 2022, 6:30pm IST/ 1:00pm GMT / 8:00am ET (joining

time 5:15pm IST).

Gmeet link: meet.google.com/rco-ewra-xmh

Title: Monomial Ideals Arising from Graph Domination Problems.

Abstract: Graph domination problems are ubiquitous in graph theory. In the

broadest terms, they ask how one can ‘observe’ an entire graph by

designating a certain list of vertices, following a proscribed list of

rules. An example of this is the vertex covering problem which happens to

describe the irredundant irreducible decomposition of the edge ideal of a

graph. In this talk, we will survey recent work with various collaborators

on other monomial ideal constructions that arise from other graph

domination problems, including one coming from electrical engineering.

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

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