Name of speaker: Aditya Dwivedi, IIT Bombay
Host: Sanjoy Pusti
Date: 3rd May, 4-5 PM
Place: Ramanujan Hall

Title : Classification of irreducible representation of the unitary group U(n)

Abstract: In this talk we will classify all irreducible unitary representations of the unitary group, using the formulation of highest weight of a representation. We will also find out the dimension and characters of all of those representations.

MSc Reading Project, 
Talk 1:

Title: Waring’s problem

Speaker: Mahadeb Mandal, M.Sc. Mathematics.

 Date: May 06, 2024

Time: 11 am

Venue : Ramanujan Hall

Abstract: This seminar delves into the historical context of Waring's
problem, presents asymptotic formulas, and examines key properties of
singular series.

MSc Reading Project,
Talk 2:
Title: Rational points on elliptic curves

Speaker: Andan Dhar, MSc mathematics

Date : May 06, 2024

Time: 12 pm

Venue: Ramanujan Hall

Abstract: We will discuss proof of Mordell's theorem on rational points on
elliptic curves using height function & basic group theory.

Algebraic Groups seminar (Host: Dipendra Prasad)

Monday and Friday at 4 pm in room # 105.

Monday's talk by Deep Makadiya will be the last talk on Steinberg's paper.

The talk on Friday by Dibyendu/Chayan will be on what is called  ``Borel-Siebenthal" theory,
which determines all maximal subgroups of maximal rank of a reductive group.

Algebraic Groups Seminar

Tuesday, May 7, 2024, 4 pm
====================

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Saad

Affiliation: IIT Bombay, Mumbai

Title: Weyl groups

Abstract: We start the 7th chapter of Springer's book with the study of the Weyl group of a connected linear group.

Algebraic Groups seminar (Host: Dipendra Prasad)

Monday and Friday at 4 pm in room # 105.

Monday's talk by Deep Makadiya will be the last talk on Steinberg's paper.

The talk on Friday by Dibyendu/Chayan will be on what is called  ``Borel-Siebenthal" theory,
which determines all maximal subgroups of maximal rank of a reductive group.

Speaker: Vamsi Pingali (Department of Mathematics, IISc.)

Time, Day and Date: 11:30 a.m., Tuesday, May 14

Venue: Ramanujan Hall (2nd floor, Department of Mathematics)

Title: Gravitating vortices and cosmic strings

Abstract: The gravitating vortex (GV) equations on a compact Riemann surface arise as a dimensional reduction of the Kaehler-Yang-Mills equations. A special case of the GV equations includes the equations governing the (as of now, hypothetical) cosmic strings. I shall describe existence, uniqueness, and algebro-geometric obstructions to existence to these equations. This talk is based on joint work with M. Garcia-Fernandez, L. Alvarez-Consul, O. Garcia-Prada, and Chengjian Yao.

Algebraic Groups Seminar

Tuesday, May 14, 2024, 4 pm
====================

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Saad

Affiliation: IIT Bombay, Mumbai

Title: Semi-simple groups of rank one

Abstract: We prove that a connected, semi-simple group of rank one is
isomorphic to SL(2) or PSL(2).

PhD Defense of Brahadeesh Sankarnarayanan
Title - Some Problems in Combinatorics: Excursions in Graph Colorings and
Extremal Set Theory
Date - 16 May, Thursday
Time - 1130 AM
Venue - Ramanujan Hall
Weblink - https://meet.google.com/wvq-uobf-zib

Special Mathematics Colloquium
Speaker: Prof. R. Parimala
Title: `A Hasse principle for projective homogeneous spaces’
Date and time : Friday 17 May 2024 11:30 to 12:30 hrs
Venue : Ramanujan Hall

Algebraic Groups seminar (Host: Dipendra Prasad)

Friday at 4 pm in room # 105.

Deep Makadia  will speak  on what is called  the ``Borel-Siebenthal" theory,
which determines all maximal subgroups of maximal rank of a reductive
group, following a paper of P. Gille.

Day, Date & Time: Tuesday, 21st May 2024 at 11:30 AM

Speaker: Dr. Puspendu Pradhan, IISER Pune

Title: PGL(2,q)-orbits of lines of PG(3,q) and binary quartic forms

Venue: Google Meet: https://meet.google.com/hac-ugpk-kyn

Abstract: Attached.

Algebraic Groups Seminar

Tuesday, May 14, 2024, 4 pm
====================

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Saad

Affiliation: IIT Bombay, Mumbai

Title: Semi-simple groups of rank one

Abstract: We prove that a connected, semi-simple group of rank one is
isomorphic to SL(2) or PSL(2).

Title : Covariance Identities and Variance Bounds for Infinitely Divisible
Distributions and Their Applications.

Time : 11:30 am - 12:15 pm.

Date: May 22, 2024.(Wednesday)

Venue : Ramanujan Hall, Department of Mathematics, IIT Bombay.

Abstract : In this talk, we discuss a general covariance identity for
infinitely divisible distributions (IDD). Using this result, we derive
Cacoullos-type variance bounds for the IDD. Applications to some important
distributions are discussed, in addition to the computation of variance
bounds for certain posterior distributions. As another application, we
discuss the Stein-type identity for the IDD, which involves the Levy
measure. This result in turn is used to derive the Stein-type identity for
the generalized tempered stable distributions and the variance-gamma
distributions (VGD). This approach, especially for the VGD, is new and
simpler, compared to the ones available in the literature. Finally, we
discuss another application of the covariance identity in deriving known
and some new formulas for the weighted premium calculation principles for
the IDD.

Speaker: P.M.S. Sai krishna 

Advisor: Professor Manoj K.  Keshari 

Title: Exponential maps and their applications  

Date: Friday, 24 May 2024 

Time: 11:00 AM 

Venue: Ramanujan Hall

Google Meet link: https://meet.google.com/rsb-tvox-wdx

The Algebraic Groups seminar will meet at 4 pm today in room # 105,

typically for 90-120 minutes with a tea and snacks break at 5:00 pm.

Today we will begin the topic of ``nilpotent matrices" following the book

of Collingwood and McGovern. The aim  of the subject is to classify nilpotent matrices (in the Lie algebra of a Lie group), and to understand their properties. The seminar presupposes no knowledge beyond eigenvalues and eigenvectors of a linear transformation.

The speaker today is Akash Yadava.

Algebraic Groups Seminar

Tuesday, May 28, 2024, 4 pm
====================

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Saad

Affiliation: IIT Bombay, Mumbai

Title: Semi-simple groups of rank one

Abstract: We prove that a connected, semi-simple group of rank one is
isomorphic to SL(2) or PSL(2).

Speaker: Brahadeesh Sankarnarayanan
Day/Date/Time: 29th May, 2024, Wednesday, 11:30 AM
Venue: Ramanujan Hall
Title: Sunflowers, symmetric designs and tournaments
Abstract: For a fraction a/b in (0,1), a family F of subsets of [n] := {1,
..., n} is called a "fractional (a/b)-intersecting family" if, for every
pair of distinct sets A, B in F, we have |A \cap B| = a/b |A| or a/b |B|.
The natural extremal question is: How large can an a/b-intersecting family
over [n] be? This notion was introduced in Balachandran邦athew邦ishra
(Electron. J. Combin. 26 (2019), #P2.40), wherein they showed that |F|<
O(n log n), and they gave constructions of a/b-intersecting families of
size at least O(n). The conjecture (which is still open) is that |F|<O(n)
for any a/b-intersecting family F over [n]. In this talk, I will discuss
some recent progress on this conjecture, and some related questions
concerning ranks of certain matrix ensembles, tournaments, symmetric
designs, and sunflowers.

Wednesday, May 29, 2024, 04.00 pm
====================

Venue: Ramanujan Hall

Host: Sudhir R. Ghorpade

Speaker: Roy Joshua

Affiliation: Ohio State University

Title: An overview of transfer techniques in cohomology theories

Abstract: In this talk I will give an overview of transfer techniques in various
types of cohomology theories. We will begin with a leisurely review of
such techniques from algebraic topology. We will then discuss similar techniques and results in
the cohomology of algebraic varieties. The cohomology theories we consider
will range from singular cohomology of topological spaces to algebraic K-theory
and motivic cohomology.

Date: Friday, 31st May 2024
Time: 4pm to 5pm
Venue: Ramanujan Hall
Speaker: Debaditya Raychaudhury, University of Arizona
Title: Ulrich subvarieties and non-existence of low rank Ulrich bundles on complete intersections
Abstract: We characterize the existence of an Ulrich vector bundle on a variety $X\subset{\bf P}^N$ in terms of the existence of a subvariety satisfying certain conditions. Then we use this fact to prove that $(X,\mathcal{O}_X(a))$ where $X$ is a complete intersection of dimension $n\geq 4$, which if n = 4, is either ${\bf P}^4$ with $a\geq 2$, or very general with $a\geq 1$ and not of type (2), (2, 2), does not carry any Ulrich bundles of rank $r\leq 3$. Work in collaboration with A.F. Lopez.

The seminar of Dipendra Prasad on Algebraic groups will continue on Friday

at 4:00 pm in Room # 105. We turn to classification of nilpotent elements in a 

Semi-simple Lie algebra, called the Bala-Carter theory, following the book 

of Collingwood and McGovern.

Speaker: Deep Makadia