Algebraic Groups Seminar

Friday, August 2, 2024, 4 pm

Venue: Ramanujan Hall

Host: Dipendra Prasad

Speaker: Saad.

Affiliation: IIT Bombay, Mumbai.

Title: Nilpotent Conjugacy Classes

Abstract: We continue the analysis of nilpotent conjugacy classes from the
book of Collingwood and McGovern.
 

 Statistics seminar

Title : A selected summary of extreme value theory for discrete random
variables.

Time, Day & Date: 4:00 pm on 5th August 2024

Venue: Ramanujan Hall

Host: Radhendushka Srivastava

Speaker: Prof. Saralees Nadarajah, The University of Mancheste

Commutative Algebra Seminar

Time, Day and Date :  12:30 pm on Tuesday 6 August

Venue : Room 215

Speaker : Tony J. Puthenpurakal

Title : K-theoretic techniques in local algebra

Abstract : We discuss some K-theoretic techniques to prove Serre's
Vanishing conjecture and the total rank conjecture

Algebraic Groups Seminar.

Time, Day & Date: 4.00 pm, Tuesday, August 6, 2024.

Venue: Room 215.

Host: Dipendra Prasad.

Speaker: Akash Yadav.

Title: Nilpotent conjugacy classes

Abstract: We continue the analysis of nilpotent conjugacy classes from the
book of Collingwood and McGovern.

Combinatorics Seminar

Date/Day: 7th August, Wednesday.

Venue/Time: Ramanujan Hall, 11:30 am

Speaker: Dhruv Mubayi, University of Illinois at Chicago

Title: New results on the Erdos Rogers function

Abstract: Given integers 1 < s < t, what is the maximum size of a K_s-free
subgraph that every n vertex K_t-free graph is guaranteed to contain? This
problem was posed by Hajnal,  Erdos and Rogers in the 1960s as a way to
generalize classical graph Ramsey numbers (which corresponds to the case
s=2). We prove almost optimal results in the case t=s+1 using recent
constructions in Ramsey theory. We also consider the problem where we
replace K_s and  K_t by arbitrary graphs H and G and discover several
interesting new phenomena.  This is joint work with Jacques Verstraete.

Colloquium talk

Title : Billiards in Rational Prisms

Speaker : Jayadev Athreya, University of Washington

Time, Date and day : 7th August (Wed) at 4:00 pm

Venue : Ramanujan Hall

Host: Ravi Raghunathan

Abstract : This talk describes joint work-in-progress with Bedaride, Hooper,
and Hubert. Motivated by the study of billiards in polyhedra, we study
linear flows in a family of singular flat 3-manifolds which we call
translation prisms. Using ideas of Furstenberg and Veech, we connect
results about weak mixing properties of flows on translation surfaces to
ergodic properties of linear flows on translation prisms, and use this to
obtain several results about unique ergodicity of these prism flows.
Furthermore, we construct explicit eigenfunctions for translation flows in
psuedo-Anosov directions with Pisot expansion factors, and use this
construction to build explicit examples of non-ergodic prism flows, and
for
non-ergodic billiard flows in a right prism over a regular 7-gon.

Algebraic Groups Seminar.

Time, Day & Date: 10.00 am, Friday, August 9, 2024.

Venue: Ramanujan Hall.

Host: Shripad M. Garge.

Speaker: Dibyendu Biswas.

Title: Borel subgroups in reductive groups

Abstract: We continue studying Chapter 8 (Reductive Groups) of Springer's
book on Linear Algebraic Groups.
 

1.  Spectral Theory of Automorphic Forms on MONDAYS 11:30am -- 1:00pm

Date, Time, Venue: Every Monday starting 12th August,11:30am-1:00pm,Room 215

Hosts : Keshav Aggarwal and Kummari Mallesham

Abstract : Attached.

https://www.math.iitb.ac.in/~seminar/nt/AnNT_seminar_2024_Fall_revised.pdf

Speaker: Ojas Sahasrabudhe (Department of Mathematics, IIT Bombay)

Date, Time, Venue : 2:30 p.m. on Monday, August 12, Ramanujan Hall

Title: Continued Fractions and Diophantine Approximations
 

Commutative algebra seminar:

Time, Day, Date, Venue :  12:30 pm, Tuesday 13 August, Room 215

Speaker: Aryaman Maithani

Affiliation: University of Utah

Host. A. Hariharan

Title: Invariant Theory of Commutative Rings

Abstract: Abstract: Given a group G acting on a ring R, we consider R^G,
the subring of elements fixed by G. It's a natural question to ask what
"good" properties of R are inherited by R^G. Some of these questions were
considered by Hilbert and Noether, and were a motivation to study
noetherian rings. We will discuss some of these results.
This talk should be accessible to someone who's done a first course in
module theory

3. Name of the Seminar: Analysis Seminar

Time, Day and Date: 2:30 p.m., Tuesday, 13 August 2024.

Venue: Ramanujan hall

Host: Anandavardhanan

Speaker: Debanjan Nandi

Affiliation: IISc Bangalore

Title: Martin boundaries of groups hyperbolic to nilpotent subgroups

Abstract: The Martin boundary of a simple random walk on a finitely
generated group hyperbolic relative to nilpotent subgroups is not known in
general. For any such group one can however construct a 'natural' class of
random walks whose Martin boundary (probability-theoretic object) is
homeomorphic to the Bowditch boundary of the group (geometric object), and
the existence of such random walks characterizes these groups among
relatively hyperbolic groups. This is the main result I will discuss.

In the talk I plan to emphasize on giving an overview of this problem,
relations to more classical objects like the Brownian motion in manifolds
of negative curvature, and spend some time recalling the definitions of the
above class of groups, and the Martin boundary as a probabilistic and
potential-theoretic notion. I would also like to talk about further
questions that naturally arise, if time permits.

Time, Day & Date: 4 pm, Tuesday, August 13, 2024

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Dibyendu Biswas.

Title: Borel subgroups in reductive groups - II

Abstract: We study the construction of Borel subgroups in reductive groups through the root groups corresponding to the simple roots corresponding to B. 

4. Representation theory of Automorphic forms- Part 1 (Tate's Thesis)

Date, Time, Venue: Wednesday 14th August, 11:30am - 1:00pm, Room 215

Abstract: Attached.
https://www.math.iitb.ac.in/~seminar/nt/AnNT_seminar_2024_Fall_revised.pdf

Annual Progress Seminar

Wednesday, 14 August 2024, 3:30-4:30pm

Venue: Room 105, Department of Mathematics

Host: Ananthnarayan H.

Speaker: Omkar Javadekar

Affiliation: IIT Bombay

Title: Linear quotients of connected ideals of graphs and some results
on purity of extremal rays of Betti cones.

Colloquium :

Speaker: Keshav Aggarwal, IIT Bombay

Date, Time, Venue : 14th August, 4:00 pm in Ramnujan Hall

Title: Subconvexity bound problem for L-functions

Abstract: Study of L-functions is one of the central themes of modern
number theory. The problem of bounding growth rate of L-functions is
classical and goes back to Weyl (1916), who proved the first non-trivial
result for the Riemann zeta function. This is known as the subconvexity
bound problem and has various applications, apart from being of
independent interest. We will talk about the history of the problem, give
some applications, and present some classical analytic tools like the
circle method used to study the problem.

Name of the Seminar: Pre-synopsis Seminar 

Time, Day and Date: 3:30 p.m., Friday, 16 August 2024.

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

Venue: Ramanujan hall

Host: Anandavardhanan

Speaker: Saad Qadri 

Affiliation: IIT Bombay 
Title: Ext branching laws for the general linear group

Abstract: We study Ext branching laws for Arthur type representations of the p-adic general linear group. We give a precise condition predicting Ext non-vanishing in some cases.

Time, Day & Date: 4 pm, Friday, August 16, 2024

Venue: Room 215

Host: Dipendra Prasad.

Speaker: Deep Makadiya

Title: Nilpotent conjugacy classes

Abstract: We continue the analysis of nilpotent conjugacy classes from the book of Collingwood and McGovern. 

Speaker : Dr. Anugu Sumith Reddy,

          Post Doctoral Fellow, Rice University

Date and Time : Monday, 19th August, 11.00 am- 12.00 noon

Venue: Ramanujan Hall

Title: Ergodic risk sensitive control of diffusions under a general

structural hypothesis

Abstract: In this talk, we present the ergodic (infinite horizon) risk

sensitive control (ERSC) problem for diffusion processes under a general

hypothesis that is 'in between' the conditions of uniform stability and

near-monotonicity. This problem can be studied as a limit of a family of

perturbed ERSC problems with inf-compact running cost. Because of the

exponential nature of the cost function, limiting procedure is

challenging. We discuss how we overcome this challenge. This involves

exploiting a well-known variational representation of exponential

functionals of Brownian motion and applying it to the objective

exponential cost function of the controlled diffusion. This representation

facilitates us to view the risk sensitive cost for any stationary Markov

control as the optimal value of a control problem of an extended diffusion

involving a new auxiliary control where the optimal criterion is to

maximize the associated long-run average cost criterion that is a

difference of the original running cost and an extra term that is

quadratic in the auxiliary control. The main difficulty in using this

approach lies in the fact that tightness of mean empirical measures of

the extended diffusion is not a priori implied by the analogous tightness

property of the original diffusion. We will discuss how to overcome this

by establishing a priori estimates for the extended diffusion associated

with the nearly optimal auxiliary controls. Finally, we present the

relevant results on characterization of optimal va

lue and optimal

controls.

Monday, 19/08:

Description: Tate's Thesis
Date, time, venue: 19/08, 11:30am -- 1pm, Room 215
Hosts: Keshav Agarwal and Mallesham Kummari
Speaker: Keshav Aggarwal
Abstract: We'll discuss the topology of adeles and ideles and prove the
adelic Poisson summation formula.

2. Algebraic Groups seminar

Time, Day & Date: 4 pm, Tuesday, August 20, 2024

Venue: Ramanujan Hall

Host: Shripad M. Garge

Speaker: Dibyendu Biswas.

Title: Borel subgroups in reductive groups - III

Abstract: We study the construction of Borel subgroups in reductive groups
through the root groups corresponding to the simple roots corresponding to
the Borel.
 

Wednesday, 21/08:

Description: Spectral theory of Automorphic forms
Date, time, venue: 21/08, 11:30am -- 1pm, Room 215
Hosts: Keshav Agarwal and Mallesham Kummari
Speaker: Suraj Panigrahy
Abstract: We'll discuss Sections 1.2 -- 1.3 of Iwaniec's Topics in
Classical Automorphic Forms.
 

Speaker : Sai Krishna

Date/Time/Venue : Friday 23rd August 2023, 11-11:45 am, Ramanujan Hall

Title : Exponential maps and their applications

Abstract: Exponential maps of k-domains are a generalization of locally
nilpotent derivations. We will see some results related to exponential
maps and their applications to the characterization of the affine three
space and
the cancellation of the affine plane.

Link to join online : https://meet.google.com/dxk-giid-jyd
 

Description: Tate's thesis
Date, time, venue: 26/08, 11:30am -- 1pm, Room 215
Hosts: Keshav Aggarwal and Mallesham Kummari
Speaker: Akash Yadav, IIT Bombay
Abstract: We will discuss the end of section 1.5, and sections 1.6 and 1.7
from Goldfeld-Hundley Vol 1. Topics are p-adic and adelic Fourier
inversion.

 Partial Differential Equations Seminar:
Speaker: Ramesh Mete (IISc. Bengaluru)
Title: The J and dHYM equations, and corresponding natural flows.
Time, Day and Date: 11:30 a.m., Tuesday, August 27
Venue: Online (Zoom): https://us06web.zoom.us/j/88652942508?pwd=5qyzxKZbRXYOSTwwDDJZpjQah0qcLl.1

Abstract: 

The J-equation and deformed Hermitian-Yang-Mills (dHYM) equation are two important examples of complex Hessian equations which have received considerable attention in last two decades. The J-equation, introduced independently by S.K. Donaldson and X.X. Chen (1999) from different viewpoint, is related to the cscK problem in K\"{a}hler geometry. The dHYM equation, introduced by Leung-Yau-Zaslow (2000), has connection to mirror symmetry in string theory. It is well-known that each equation admits a (unique) smooth solution if and only if certain cone (or sub-solution) condition holds, or equivalently, if and only if a Nakai-Moishezon type criterion holds (which is the so-called "stable" situation). In this talk, we will focus on the existence and uniqueness of (singular) solutions for both equations in the unstable case on compact K\"{a}hler surfaces and higher dimensional K\"{a}hler manifolds with Calabi symmetry using some natural flows. Based on a joint work with Dr. Ved Datar (IISc Bengaluru) and Prof. Jian Song (Rutgers University).

4. Algebraic Groups Seminar:
Speaker: Dibyendu Biswas (IIT Bombay)
Title: Bruhat Decomposition
Time, Day and Date: 4:00 p.m., Tuesday, August 27
Venue: Ramanujan Hall, Department of Mathematics
Abstract:We will study Bruhat decomposition in reductive groups.

Title: Operads and Infinite loop space theory

Time, Day and Date: 11:30 a.m,  Wednesday 28th August.

Venue: Ramanujan hall

Host: Rekha Santhanam

Speaker: Sahin Mandal

Abstract: In this series of talks we will define Operads and discuss their
properties. We will then define Segal's "gamma" space to prove
Barratt-Priddy-Quillen theorem and discuss uniqueness theorem for infinite
loop spaces machines as proven by May and Thomason.
 

Description: Spectral theory of automorphic forms
Date, time, venue: 28/08, 11:30am -- 1pm, Room 215
Hosts: Keshav Aggarwal and Mallesham Kummari
Speaker: Suraj Panigrahy and Aditi Savalia, IIT Bombay
Abstract: We'll discuss sections 1.3 -- 1.4 from Iwaniec's Topics in
classical automorphic forms. Suraj will continue with his presentation and
discuss section 1.3. Aditi will discuss section 1.4 (and 1.5 if time
allows).

Commutative Algebra Seminar:
Speaker: Tony J. Puthenpurakal (IIT Bombay)
Title: K-theoretic methods in local algebra
Time, Day and Date: 12:30 p.m., Tuesday, August 27
Venue: Room 215, Department of Mathematics
Abstract: We continue over studies in k-theory of complexes

Colloquium:

Speaker: Najmuddin Fakhruddin (School of Mathematics, TIFR, Mumbai)

Title: The Hodge theory of the KZ equations and enriched representation rings

Time, Day and Date: 4:00 p.m. on Wednesday, August 28

Venue: Ramanujan Hall

Abstract: The representation ring of a simple Lie algebra over the field of complex numbers is the free abelian group on the isomorphism classes of irreducible representations with the product structure given by decomposing the tensor product of two irreducible representations as a direct sum of irreducible representations (with multiplicities). In recent joint work with Prakash Belkale and Swarnava Mukhopadhyay we have defined certain families of "enriched" representation rings: these are free modules over the integral polynomial ring in one variable on the set of irreducible representations, with a product which specializes to the usual product when the variable of the polynomial ring is set to 1. Furthermore, the enriched "multiplicities" are polynomials with non-negative coefficients. These rings arose in our work on the Hodge theory of the Knizhnik-Zamolodchikov (KZ) equations: these are certain linear partial differential equations associated to a simple Lie algebra, a finite set of irreducible representations and an auxiliary complex number kappa, and were defined in the context of conformal field theory in the 1980s, but various aspects of these equations, in particular their monodromy, have been studied by mathematicians such as Kohno, Drinfeld and many others. Our work builds on the work of Schechtman-Varchenko and Looijenga which led to the proof that these equations for kappa rational are of Gauss-Manin type, i.e., arise from the cohomology of families of algebraic varieties. In my talk I will explain the construction of the enriched representation rings and how they are relevant to computing the ranks of the Hodge filtration on KZ local systems. The general constructions will be made explicit throughout the talk in the concrete case of the Lie algebra sl_2.
 

6. Algebraic Groups Seminar:
Speaker: Dibyendu Biswas (IIT Bombay)
Title: Nilpotent conjugacy class
Time, Day and Date: 4:00 p.m., Friday, August 30
Venue: Room 215, Department of Mathematics

Abstract: We will continue the analysis of nilpotent conjugacy classes using the book by Collingwood and McGovern.