August 2022
Public Access Category: All |

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Speaker: Mithun Bhowmik, IISc Bangalore

Time & Date: 4 pm, Monday, 01 August 2022

Venue: Ramanujan Hall

Title: Hardy and Adams Type Inequalities for the Fractional Laplace-Beltrami Operator on Noncompact Symmetric Spaces

Abstract. In this talk, we will discuss Hardy and Adams type inequalities for fractional powers of the Laplace-Beltrami operator on Riemannian symmetric space $X$ of noncompact type. We use solutions to the extension problem in combination with the ground state representation method (of Frank et al) to establish Hardy’s inequality. We will discuss $L^p - L^q$ mapping properties of the extension operator and get an improvement over the corresponding results on Euclidean spaces. This is a joint work with Sanjoy Pusti. Next, we will discuss sharp Adams type inequalities on Sobolev spaces $W^{\alpha,n/\alpha}(X)$ of any fractional order $\alpha < n$ on $X$ with dimension $n$.

- Time:
- 2:00pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
DDT: Tuesday, 2 August, 2:00 – 3:30 pm

Venue : Ramanujan Hall, Department of mathematics.

Title: Okounkov-Vershik approach to the representation theory of symmetric

groups.

Abstract: In this series of talks we will bootstrap the representation

theory of symmetric groups inductively, following the 2005 revision of

Vershik's and Okounkov's seminal paper on the topic.

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!

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. A1A2, CDEEP, Department of Mathematics
- Description:
**Title:**On the tensor product of representations of classical groups**Abstract:**After giving a general introduction to representation theory of GL(n,C) and other classical groups, I will focus attention on Dibyendu Biswas's thesis work around the question on tensor product of representations of GL(n,C) and other classical groups.**Venue:**Room No. A1A2, CDEEP, Department of Mathematics

- Time:
- 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Speaker: Rahul Karki.

Time: Friday, 5 August, 4:30 pm.

Venue: Ramanujan Hall, Mathematics department.

Title: Picard Group and Abel Jacobi Theory on A Finite Graph.

Abstract: A finite graph can be viewed, in many aspects, as a discrete version of a Riemann surface. In this talk, we will see how the notions of the Picard group and Jacobian are defined on a graph and their relations with the chip-firing game on the graph. Later, we will discuss the graph theoretic analog of the Abel-Jacobi map and study some of its properties.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Jyotirmoy Sengupta, TIFR, Mumbai

Title: The sup norm of cusp forms. A guided tour. Abstract: The sup norm of cusp forms, holomorphic and Maass, have been intensively investigated in the recent past. We will describe these results and their connection with other standard problems/conjectures in analytic number theory. Time permitting we will discuss the recent result of Anamby-Das on the sup norm of Jacobi cusp forms. Only a modest background, at the level of M.Sc. 2nd year, will be assumed.

- Time:
- 3:30pm
- Description:
Speaker: Suprajo Das, IIT Bombay

Date: 11 August 2022, 3.30-5.00

Venue: Ramanujan Hall

Title: Numerical aspects of epsilon multiplicity-I

Abstract: Please see the attachment.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
We will have *Sridhar Narayanan* speaking on our RTAG seminar from 2pm to 3:30pm on Tuesday. Here are the necessary details about his 3rd talk: DDT: Tuesday, 16 August, 2:00 – 3:30 pm Venue : Room No 215, Department of mathematics. Title: Okounkov-Vershik approach to the representation theory of symmetric groups. Abstract: In this series of talks we will bootstrap the representation theory of symmetric groups inductively, following the 2005 revision of Vershik's and Okounkov's seminal paper on the topic. 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!

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Speaker: Jeff Adler, American University.

Title: P-adic groups: What and why?

Abstract:

After a review of Pontryagin duality, I will give an introduction to p-adic numbers, emphasizing their role in number theory, and will conclude with a description of part of the Langlands Program, which brings together number theory and harmonic analysis.

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Commutative algebra seminar

===================

Speaker: Suprajo Das, IIT Bombay

Date: Thursday, 18 August, 3.30-5.00 pm

Title: Numerical aspects of the epsilon multiplicity-II

Abstract: In the second talk on this topic we will describe some instances where the length function associated with the epsilon multiplicity is a quasi-polynomial. We will mostly emphasize on the results of Herzog-Trung and Herzog-Puthenpurakal-Verma which together show that the epsilon multiplicity of a monomial ideal in a polynomial ring is a rational number. If time permits we will also discuss some extensions of these results.

- Time:
- 11:30am
- Location:
- Room No 215, Department of Mathematics
- Description:
Speaker: Prashant Arote, IISER Pune.

Title: Harish-Chandra Induction and Jordan Decomposition of Characters

Abstract:

Let G be a connected reductive group defined over a finite field 𝔽q and let

F:G→ G be the corresponding Frobenius morphism.

Let L be a Levi factor of a F-stable parabolic subgroup of G.

Endomorphism algebras of representations parabolically induced from cuspidal representations

of LF were described by Howlett and Lehrer.

In this talk, we show that any such algebra is isomorphic to the twisted endomorphism algebra

of a representation which is parabolically induced from a unipotent cuspidal representation of

Levi subgroup of a finite reductive group.

As an application, we show that for any finite connected reductive group, a Jordan decomposition

can be chosen such that it commutes with Harish-Chandra induction.

This is a joint work with Manish Mishra.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
We will have *Sridhar Narayanan* speaking in our RTAG seminar from 2pm to 3:30pm on Friday. Here are the necessary details for his 4th talk: Time: Friday, 26 August, 2:00 – 3:30 pm. Venue : Room No 215, Department of mathematics. Title: Okounkov-Vershik approach to the representation theory of symmetric groups. Abstract: In this series of talks we will bootstrap the representation theory of symmetric groups inductively, following the 2005 revision of Vershik's and Okounkov's seminal paper on the topic. 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:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Speaker: Suprajo das, IIT Bombay Date and time: 26 August 2022, 3.30pm-5.00 pm Venue: Ramanujan Hall Title: Numerical aspects of Epsilon multiplicity III Abstract: In the third talk on this topic we shall focus on the epsilon multiplicity of ideals in a regular local ring of dimension 3. We will mostly give a survey of the known results and discuss some open questions in this setup.