


Commutative algebra seminar
Date: Tuesday, 13 September 2022
Time: 3.305.00 pm
Venue: Ramanujan Hall
Speaker: J. K. Verma
Title: Noetherian symbolic Rees algebrasIII
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 twodimensional 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 settheoretic complete intersections.
Mathematics Colloquium Date and time: 14 September 2022 at 4 pm Venue: Ramanujan Hall (Room 213, II Floor) Title: Boundary nullcontrollability of 1d linearized compressible NavierStokes 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 NavierStokes 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 nullcontrollability 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 parabolichyperbolic moments problem and a parabolic hyperbolic joint Inghamtype 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
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
padic groups. Here we will discuss the Hecke algebra attached to
BushnellKutzko 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!