Seminar on quantum groups and C*-algebras

Monday, 16 October  2023, 11:30 am

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Venue: Ramanujan hall

Host: Saikat Mazumdar

Speaker: Dr. Sutanu Roy
Affiliation: NISER Bhubaneswar

Title: Braided quantum groups and quantum symmetries in the C*-algebraic
framework
Abstract: Compact quantum groups naturally generalize compact groups in 
the realm of noncommutative geometry. They also appear as symmetries of 
various (classical and quantum) spaces. However, while investigating the 
semidirect product of compact quantum groups, a more general concept, 
namely braided compact quantum groups, emerges quite naturally. In this 
talk, I will provide motivation for braided compact quantum groups and 
illustrate them with examples. Following that, I will present recent 
developments in the relationship between braided compact quantum groups 
and quantum symmetries of spaces (of certain types). If time permits, I 
shall mention certain aspects of the general theory of locally compact 
braided quantum groups within the C*-algebraic framework.

Ph.D. defense seminar

Monday, 16th October, 4 pm

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Host: Siuli Mukhopadhyay

Venue: Ramanujan Hall

Speaker: Savita Pareek

Title: On Some Problems in Mixed-effect Models

Topology and Related Topics Seminar

Tuesday, 17  October  2023, 2:30 pm

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Venue: Ramanujan hall

Host: Rekha Santhanam

Speaker: Navnath Daundkar

Affiliation: IIT Bombay

Title: Cohomology of moment angle complexes - II

Abstract: This talk is a continuation of the previous session on 
"Cohomology of moment angle complexes." We will present a cellular 
structure on a moment angle complex associated with a simplicial complex 
$K$ and prove that the corresponding cellular cochain algebra is a 
quotient of the Koszul algebra of the Stanley-Reisner ring of $K$.

Commutative Algebra seminar

Tuesday, 17 Oct. 3.30-4.45 pm

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

Venue: Ramanujan Hall

Host: Tony Puthenpurakal

Speaker: Jugal Verma, IIT Bombay

Title: The Grothendieck-Serre formula for Hilbert functions

Abstract: We will prove the Grothendieck-Serre formula for Hilbert 
functions of finite graded modules over graded Noetherian rings.

Mathematics Colloquium

Wednesday, 18 October, 4-5 pm

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Venue: Ramanujan Hall

Host: Sudhir R Ghorpade

Speaker: Trygve Johnsen,

Affiliation: The Arctic University of Norway

Title: Various types of codes and matroids

Abstract: The talk will be about the general principles of 
error-correcting codes and various ways of defining such codes 
mathematically. We will see how some important properties, but not all 
properties, of the codes, are determined by certain combinatorial 
structures (matroids, q-matroids, etc.) associated with them.

Algebraic geometry seminar

Wednesday, 19th October, 10 am

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: Sourav Das

Affiliation: Chennai Mathematical Institute

Title: Moduli problems on nodal curves

Abstract: In this talk, I will mainly discuss the moduli of Higgs 
bundles on nodal curves. First, I will talk about degenerations and 
briefly overview a few moduli problems on a nodal curve, e.g., Picard, 
moduli of vector bundles. Then, I will discuss a semi-stable 
degeneration of the moduli of Higgs bundles and the extension of 
Hitchin's symplectic form to this degeneration. If time permits, I will 
discuss a few possible applications of this study.

Lecture series on Hodge Theory

Thursday, 12 Oct.

11.30-1.00 and 3.30-4.30 pm

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Kahler condition and its consequences
Abstract: We review the basics of spectral sequences, and then discuss 
the ``Hodge to de Rham'' spectral sequence.

Topology and Related Topics Seminar

Thursday, 19  October  2023, 2:30 pm

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Venue: Room 215

Host: Rekha Santhanam

Speaker: Shuchita Goyal

Affiliation: Krea University

Title: Grid graphs and their independence complexes

Abstract: A matching in a graph G is a collection of disjoint edges. The 
matching complex of a graph G is a simplicial complex whose simplices 
are matchings in G. Lately, grid graphs have been studied for their 
homological and homotopical structures. In this talk, we will focus on 
the grid graphs whose each block is a square. In particular, we will see 
that the matching complexes of 3n grid graphs are homotopy equivalent to 
a wedge of spheres. We will also see the comprehensive list of the 
dimensions of spheres appearing in the wedge.

Lecture series on Hodge Theory

Thursday, 12 Oct.

11.30-1.00 and 3.30-4.30 pm

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

Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Speaker: V. Srinivas, IIT Bombay

Title: Kahler condition and its consequences
Abstract: We review the basics of spectral sequences, and then discuss 
the ``Hodge to de Rham'' spectral sequence.

Analysis and PDE seminar

Thursday, 19th Oct, 5:15 pm - 6:15 pm

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Venue: Ramanujan Hall

Host: Chandan Biswas

Speaker: Chandan Biswas, IIT Bombay

Title: A basic introduction to Fourier restriction estimates

Abstract: This is the third talk of the series. We will finish our 
discussion on Hausdorff-Young inequality,  and start on restrictions on 
the parabola in dimension 2 and the moment curve in higher dimensions.

Lecture series on algebraic stacks
Friday 20 October, 11.30 am

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Venue: Ramanujan Hall
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (Retd)

Title: Examples of Algebraic Stacks
Abstract:  This lecture will present various basic examples and 
non-examples of algebraic stacks. These examples are useful in 
applications, and they also serve to better understand the definitions
 

Mathematics Colloquium

Friday, 20 Oct. 4 pm

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Venue: Ramanujan Hall

Host: Ravi Raghunathan

Speaker: Dinakar Ramakrishnan

Affiliation: California Institute of Technology

Title: Abelian 3-folds of Picard type, and a uniform irreducibility 
result

Abstract: Half a century ago Manin proved a uniform boundedness result 
for the p-power torsion of any non-CM elliptic curve E over a given 
number field k. A few years ago, Cadoret and Tamagawa established a  
similar result for the p-adic representations attached to 1-dimensional 
abelian families. In joint work with M. Dimitrov, we provide the 1st 
evidence in higher dimension, for families of abelian 3-folds 
parametrized by certain Picard modular _surfaces_. The proof also 
involves aspects of  (global and local) representation theory.

Coding Theory Seminar

Friday, 20th Oct.,  5.15 pm

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Venue: Ramanujan Hall

Host: Sudhir Ghorpade

Speaker: Prof. Trygve Johnsen

Affiliation: Arctic University of Norway=

Title: Homological and combinatorial invariants of rank-metric codes

Abstract:  We will look at some similarities and differences between the 
behavior of (traditional) linear codes with the Hamming distance, and 
Gabidulin rank metric codes.  We will study how methods for determining 
the spectra and invariants of traditional codes can, or cannot, be 
"transferred" to studying analogous properties of the rank-metric codes.