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.

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

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!