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

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

Speaker: Prof. Agnid Banerjee, TIFR-CAM

Date and time: 2 September 4-5 pm

Venue: Ramanujan Hall

Title: Space like a strong unique continuation for some fractional parabolic equations

Abstract: I will talk about some recent work on space like a strong unique continuation for fractional heat type equations. This is based on a joint work with Vedansh Arya, Donatella Danielli and Nicola Garofalo. I will also try to report on some subsequent works of mine on this subject which are also in part joint with Venky Krishnan and Soumen Senapati.

Note: The colloquium is addressed to a general audience.

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

Tuesday, 30 August 2022, 4.00 pm--5.30 pm

Venue: Ramanujan Hall

Speaker: J. K. Verma

Title: Fibers of blowing ups, symbolic Rees algebras, and set-theoretic complete intersections

Abstract: In this series of three talks, I will present classical results of Cowsik-Nori about fibers of blowing ups, criteria for Noetherian property of symbolic Rees algebras, due to Huneke, Goto-Nishida, and its relation with set-theoretic complete intersections. If time permits, I will show some concrete examples of set-theoretic complete intersection ideals in polynomial rings such as monomial space curves, Fermat ideals, and certain ideals of hyperplane arrangements.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium****Venue:**Ramanujan Hall, Mathematics Department, Room 214**Date and time:**Wednesday, 7 September 2022 at 4 pm**Speaker:**Dr. Akashdeep Dey, Princeton University**Title:**A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

Abstract: Min-max theory for the area functional was developed by Almgren

and Pitts to construct closed minimal hypersurfaces in arbitrary closed

Riemannian manifolds. There is an alternate PDE-based approach to the

construction of minimal hypersurfaces. This approach is based on the study

of the limiting behavior of solutions to the Allen-Cahn equation. In my

talk, I will briefly describe the Almgren-Pitts min-max theory and the

Allen-Cahn's min-max theory and discuss the question of to what extent these

two theories agree.**Note: The Mathematics Colloquia are accessible to the general audience.**

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium Speaker: Prof. Ravi Raghunathan Date: Friday, 9 September 2022 Duration: 4.00-5.00 pm Venue: Ramanujan Hall, Mathematics Department, Room 214 Title: Sphere packing, the Uncertainty Principle, $E_8$ and Fourier interpolation on the real line Abstract: The talk will focus on two theorems of M. Viazovska who was awarded the Fields medal in Helsinki earlier this year. The first theorem resolved the problem of sphere packing in eight dimensions, while the closely related second theorem (proved jointly with D. Radchenko) establishes a new "Fourier interpolation" result for even Schwartz functions on the real line. The first half of the talk should be completely accessible to anyone with a first course in linear algebra and multivariable calculus (MA 109, MA 111, MA 106), and thus to most undergraduate students at IIT. The second half will require some familiarity with basic complex analysis (MA 205).

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

Date: Tuesday, 13 September 2022

Time: 3.30-5.00 pm

Venue: Ramanujan Hall

Speaker: J. K. Verma

Title: Noetherian symbolic Rees algebras-III

Abstract: We shall give examples of ideals whose symbolic Rees algebra is Noetherian. These are the

(1) ideals of space curves of multiplicity 3,

(2) ideals of a finite set of points in projective space,

(3) height one prime ideals in two-dimensional normal local domains.

We shall also discuss necessary and sufficient conditions for the symbolic Rees algebra of a prime ideal to be Noetherian in terms of set-theoretic complete intersections.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium Date and time: 14 September 2022 at 4 pm Venue: Ramanujan Hall (Room 213, II Floor) Title: Boundary null-controllability of 1d linearized compressible Navier-Stokes System by one control force. Speaker: Shirshendu Chowdhury, Department of Mathematics and Statistics, IISER Kolkata, Abstract: In the first part of the talk, we introduce the concept of controllability of Differential Equations. Then we give some examples in finite (ODE) and infinite dimensional(PDE) contexts. We recall the controllability results of the Transport and Heat equation. In the second part of the talk, we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state $(Q_0, V_0 ) $, with $Q_ 0 > 0, V 0 >0 $. It is a Coupled system of transport and heat type equations. We study the boundary null-controllability of this linearized system in the interval $(0,1)$ when a Dirichlet control function is acting either only on the density or only on the velocity component at one end of the interval. We obtain null controllability using one boundary control in the space ${H}^s_{per}(0,1)\times L^2(0,1)$ for any $s>\frac{1}{2}$ provided the time $T>1$, where ${H}_{per}^s(0,1)$ denotes the Sobolev space of periodic functions. The proof is based on spectral analysis and on solving a mixed parabolic-hyperbolic moments problem and a parabolic hyperbolic joint Ingham-type inequality. This is a recent joint work (https://arxiv.org/abs/2204.02375 [1], 2022) with Kuntal Bhandari, Rajib Dutta and Jiten Kumbhakar. Note: Mathematics Colloquia are accessible to the general audience Links: ------ [1] https://arxiv.org/abs/2204.02375

- Time:
- 2:00pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Dear all,

We will have *Basudev Pattanayak* speaking in our RTAG seminar from 2pm to

3:30pm on Thursday.

Here are the necessary details for his talk:

Time: Thursday, 15 September, 2:00 – 3:30 pm.

Venue : Ramanujan Hall, Department of mathematics.

Title: A Visit to the Local Langlands Conjecture

Abstract: In this series of talks, we first recall some important results

of class field theory. Then we will discuss the representation theory of

p-adic groups. Here we will discuss the Hecke algebra attached to

Bushnell-Kutzko types. With little basic setup, later we will state the

local Langlands Conjecture and its enhancement. For some special cases, we

will discuss their proofs.

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:
**Mathematics Colloquium****Time and Date:**4-5 pm Wednesday, 21 September 2022**Speaker:**Prof. Saikat Mazumdar, IIT Bombay

**Title:**Searching conformally for metrics with constant curvature.

**Abstract:**I will start by surveying the Yamabe problem, which asks to find a (conformal) metric with constant scalar curvature on a compact Riemannian manifold. This amounts to solving a nonlinear PDE involving the Laplacian. The solution to the Yamabe problem highlighted the role played by local and global geometry of the manifold and the unexpected connection to the positive mass theorem of general relativity.I will first discuss the case of compact surfaces, and introduce some tools and techniques from Calculus of Variations, Nonlinear Analysis on Manifolds, and PDEs. In the remaining time, I will discuss the higher-order version of the Yamabe problem: “Given a compact Riemannian manifold, does there exists a conformal metric with constant Q-curvature”?

**Note: The speakers make an effort to make Mathematics Colloquia****accessible to the general audience.**

- Time:
- 2:00pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
We will have *Basudev Pattanayak* speaking in our RTAG seminar from 2pm to 3:30pm on Thursday. Here are the necessary details for his talk: Time: Thursday, 22 September, 2:00 – 3:30 pm. Venue : Ramanujan Hall, Department of mathematics. Title: A Visit to the Local Langlands Conjecture - 2 Abstract: In this series of talks, we first recall some important results of class field theory. Then we will discuss the representation theory of p-adic groups. Here we will discuss the Hecke algebra attached to Bushnell-Kutzko types. With little basic setup, later we will state the local Langlands Conjecture and its enhancement. For some special cases, we will discuss their proofs. 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 215, Department of Mathematics
- Description:
Speaker: P Amrutha, IISER Thiruvananthapuram

Date & Day: September 22, 2022, Thursday Time: 4.00--5.00 pm

Venue: Room 215

Title: On the partitions and multipartitions not divisible by powers of 2

Abstract:

Given a finite group G and a natural number p, an interesting question one can ask is to count

the number of inequivalent irreducible representations of G whose degree is not divisible by p. This

question originated in a paper by I. G. Macdonald for the case of prime numbers. MacDonald’s

paper was a motivation for the McKay conjecture. The announcement of McKay conjecture in 1971

is the origin of a different kind of counting conjectures of finite groups. Extending Macdonald’sresults to all integers is a much harder problem to study. Motivated by a question from chiral rep-

resentations of the wreath products, we will see a generalization of the above question to compositenumbers of the form 2k and a recursive formula for the groups Sn, An, and (Z/rZ)â‰€ Sn. Regardless

of the description of the count, even for the smaller integers, a complete characterization of the

irreducibles with a degree not divisible by a given prime number is still missing in the literature.

We will see such characterization for some special cases at the end and further open problems in

this direction. This is joint work with T. Geetha.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Commutative algebra seminar Tuesday, 27 September 2022 @3.30 pm. Venue: Ramanujan Hall Speaker: Tony Puthenpurakal, IIT Bombay Title: On coefficient ideals-II Abstract: Let (A, m) be a Cohen-Macaulay local ring of dimension d ≥ 2 with infinite residue field and let I be an m-primary ideal. Let For 0 ≤ i ≤ d let Ii be the i th-coefficient ideal of I. Also let Ie = Id denote the Ratliff-Rush closure of A. Let G = GI (A) be the associated graded ring of I. We show that if dim H j G+ (G) ∨ ≤ j−1 for 1 ≤ j ≤ i ≤ d−1 then (I n)d−i = Ifn for all n ≥ 1. In particular if G is generalized Cohen-Macaulay then (I n)1 = Ifn for all n ≥ 1. As a consequence we get that if A is an analytically unramified domain with G generalized Cohen-Macaulay, then the S2-ification of the Rees algebra A[It] is L n≥0 Ifn.

- Time:
- 5:10pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Dear all, Prof. Nitin Nitsure will give a series of lectures on 'Algebraic Stacks and Moduli Theory' starting next week. The draft announcement is attached. The first talk will be introductory and will be accessible to everyone with very minimal knowledge of algebraic geometry. For the benefit of students, this is a very central and important area of algebraic geometry and Prof. Nitsure is a very good lecturer. Do try and attend the first lecture in Ramanujan Hall on Tuesday 27th at 5:10 pm. The first talk will be of 1 hour.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Date 28 September 2022

Time 4-5 pm

Venue: Ramanujan Hall

Speaker: Prof. Eknath Ghate, TIFR, Mumbai

Title: Semi-stable representations as limits of crystalline representations

Abstract: We construct an explicit sequence of crystalline representations

converging to a given irreducible two-dimensional semi-stable

representation of the Galois group of Q_p. The convergence takes place in

the blow-up space of two-dimensional trianguline representations studied

by Colmez and Chenevier. It is connected to a classical formula going back

to Greenberg and Stevens expressing the L-invariant as a logarithmic

derivative.

Our convergence result can be used to compute the reductions of any

irreducible two-dimensional semi-stable representation in terms of the

reductions of certain nearby crystalline representations of exceptional

weight. For instance, using our zig-zag conjecture on the reductions of

crystalline representations of exceptional weights, we recover completely

the work of Breuil-Mezard and Guerberoff-Park on the reductions of

irreducible semi-stable representations of weights at most p+1, at least

on the inertia subgroup. As new cases of the zig-zag conjecture are

proved, we further obtain some new information about the reductions for

small odd weights.

Finally, we use the above ideas to explain away some apparent violations

to local constancy in the weight of the reductions of crystalline

representations of small weight that were noted in our earlier work and

which provided the initial impetus for this work.

This is joint work with Anand Chitrao and Seidai Yasuda.