- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Name of speaker: Aditya Dwivedi, IIT Bombay

Host: Sanjoy Pusti

Date: 3rd May, 4-5 PM

Place: Ramanujan HallTitle : 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.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
MSc Reading Project,

Talk 2:

Title: Rational points on elliptic curvesSpeaker: 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.

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Description:
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.

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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).

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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

- Time:
- 11:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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.

- Time:
- 11:30am
- Location:
- Venue: Google Meet: https://meet.google.com/hac-ugpk-kyn
- Description:
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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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).

- Time:
- 11:30am - 12:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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).

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Room No 105, Department of Mathematics
- Description:
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