Annual progress seminar

Date:  24th August, 2023

Time:  10:00 AM -- 11:00 AM

Venue: Room 215

Host: Manoj Keshari

Speaker: Sai Krishna

Title: An algebraic characterization of the affine three space in 
arbitrary characteristic

Abstract:  We give an algebraic characterization of the affine three 
space over an algebraically closed field of arbitrary characteristic. We 
will look at a possible application of this characterization to 
reformulate the question of whether  certain ring is isomorphic to the 
polynomial ring in three variables over an algebraically closed field of 
positive characteristic.

Annual Progress Seminar

Time:  02:00 PM -- 02:35 PM

Host: Sourav Pal

Speaker: Priyanka Aroda

Title: Contractions and their dilations

Abstract:   A contraction is an operator on a Hilbert space which has norm
atmost 1. We study Sz.-Nagy's dilation theorem which models contractions
as a part of nicer operators on larger spaces. We also discuss a more
direct and explicit construction of a unitary dilation of a contraction,
which is due to Schaffer. We study an analogue to Sz.-Nagy's dilation
theorem, due to Ando, for a pair of commuting contractions.

Topology and Related Topics Seminar 

Thursday, 24 August 2023, 2.30 -3:45  pm

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Venue: Room 215

Host:  Rekha Santhanam

Speaker: Soumya Deb Samanta 

Affiliation: IIT Bombay

Title: An Introduction to Riemannian Manifolds

Abstract: In this talk, I will give a brief introduction to the different aspects of Riemannian geometry: Riemannian metrics,  affine connections, covariant derivatives, geodesics, curvature, Jacobi fields, and variation formulas. This talk will serve as a prelude to my next talk which will involve some topological aspects of Riemannian Manifolds.

 Analysis Seminar

Time:  02:40 PM -- 03:30 PM

Host: Sourav Pal

Speaker: Saikat Roy

Title: Applications of Birkhoff-James orthogonality and its connection
with dilation

Abstract: Birkhoff-James orthogonality is a generalized notion of
orthogonality that
extends the inner product orthogonality to the setting of Banach spaces.
In this talk, we present some of its applications in geometry of Banach
spaces and its relation with norming properties of some subspaces of
Banach space. We also consider operator orthogonality and its connection
with the unitary and isometric dilations. We study the case when unitary
(isometric) dilations of two contractions preserve the orthogonality
relation between the basic contractions.