Complex Algebraic Surfaces Seminar

Speaker: Ronnie Sebastian (IIT Bombay)

Title: Castelnuovo's Theorem

Time, day and date: 14:00 - 15:30, Friday, November 1

Venue: Room 215

Algebraic Geometry Seminar

Speaker: Bivas Khan (CMI)

Title: Tropical Vector Bundles

Time, day and date: 16:00 - 17:00, Friday, November 1

Venue: Ramanujan Hall

IPDF Talk
Speaker: Dr Praveen Manju (IIT Delhi)
Title: Twisted Derivations of Group Algebras with Coding Theory Applications
Time, day and date: 4:00:00 PM - 6:00:00 PM, Monday, November 4
Venue: Online talk

Commutative Algebra seminar
Speaker: Sayed Sadiqul Islam (IIT Bombay)
Title: D-modules and Bernstein–Sato polynomial of direct summands.
Time, day and date: 12:30:00 PM - 2:00:00 PM, Tuesday, November 5
Venue: Room 215

Talk by PDF
Speaker: Raman Kumar (IIT Bombay)
Title: Hybrid high-order method for the extended Fisher-Kolmogorov and the Fisher-Kolmogorov equations
Time, day and date: 12:00:00 PM - 1:00:00 PM, Wednesday, November 6
Venue: Ramanujan Hall

Colloquium:
Speaker: Umesh Dubey (HRI, Prayagraj)
Title:Tensor triangular geometry and equivariant categories
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, November 6
Venue: Ramanujan Hall

Abstract: P. Balmer introduced tensor triangular geometry to analyze tensor
triangulated categories using methods from algebraic geometry, building
on the work of Benson, Carlson, Hopkins, Neeman, Thomason, and others.
This approach provides a unified framework for exploring various
homological and homotopical algebra aspects through geometric
techniques. Balmer provided a reconstruction of quasi-compact and
quasi-separated schemes from the derived category of perfect complexes.
One of the key questions in this area is the computation of the Balmer
spectrum.

When a group $G$ acts on a (tensor) triangulated category, it is
possible to define an equivariant category that exhibits a (tensor)
triangulated structure in certain cases. In ongoing joint work with
Vivek Mallick, we have studied the tensor triangular geometry of these
equivariant categories.

In this talk, we will discuss some significant results in tensor
triangular geometry and share updates on our work in progress with Vivek
Mallick.

Algebraic groups seminar
Speaker: Shripad M. Garge (IIT Bombay)
Title: Structure constants
Time, day and date: 4:00:00 PM - 6:00:00 PM, Thursday, November 7
Venue: Ramanujan Hall

Algebraic groups seminar
Speaker: Akash Yadav (IIT Bombay)
Title: Nilpotent Conjugacy Classes
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, November 8
Venue: Room 215

1. Number theory seminar
Speaker: Keshav Aggarwal (IIT Bombay)
Title: Tate's thesis learning seminar
Time, day and date: 11:30:00 AM - 1:00:00 PM, Monday, November 11
Venue: Room 215

IPDF seminar
Speaker: Mohan (ISI Delhi)
Title: On Additive complements with special structures
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, November 11
Venue: Online only (https://meet.google.com/csc-tdak-emb)

Presynopsis seminar:

Date and time: Tuesday, 12 November 2024, 12.00 PM

Venue: Ramanujan Hall, Department of Mathematics

Title : Operators associated with various domains in $\mathbb C^n$

Abstract :
We investigate the interplay between complex geometry and operator theory,
focusing on how certain geometric and algebraic objects can be understood
through the operator theory. In particular, we explore a few key concepts
that have gained significant attention in the study of Hilbert space
operators: spectral sets, operators associated with various domains in
$\mathbb C^n$ and distinguished varieties. The domains of our interest are
polyannulus, bidisc, biball, symmetrized bidisc and pentablock.

Speaker: Pankaj Vishe (University of Durham, United Kingdom)
Title: A two dimensional delta method and applications to quadratic forms
Time, Day and Date: 15:00 - 16:00, Wednesday, November 13
Venue: Ramanujan Hall

Abstract: We develop a two dimensional version of the delta symbol method
and apply it to establish quantitative Hasse principle for a smooth pair
of quadrics defined over Q defined over at least 10 variables. This is a
joint work with Junxian Li (UC Davis) and  Simon L. Rydin Myerson
(Warwick).

Speaker: Raghu Pantangi
Venue: Ramanujan Hall
Time: 11:30-12:30 hrs
Date: 14th Nov 2024

Title: Erd\H{o}s-Ko-Rado theorem and its generalizations.

Abstract: Erd\H{o}s-Ko-Rado (EKR) theorem is a classical result in extremal
combinatorics. This celebrated result determines the size and the structure
of the largest possible collections of pairwise intersecting $k$-subsets of a
fixed $n$-set. There have been many generalizations of this result to other
mathematical objects which possess a notion of intersection ( vector spaces,
permutations, perfect matchings, etc.). In this talk, we will discuss some of
these generalizations, with a special focus on permutation groups.

1. Algebraic groups seminar
Speaker: Shripad M Garge (IIT Bombay)
Title: The isomorphism theorem
Time, day and date: 4:00:00 PM - 6:00:00 PM, Monday, November 18
Venue: Ramanujan Hall

2. Algebraic groups seminar
Speaker: Shripad M Garge (IIT Bombay)
Title: Isomorphism theorem
Time, day and date: 4:00:00 PM - 6:00:00 PM, Wednesday, November 20
Venue: Ramanujan Hall

Student name: Saumyajit Das (194099001)

Title: Qualitative and Quantitative Aspects of Degenerate Triangular
Reaction-Diffusion Systems.

Day and date: Thursday the 21 November 2024.

Time: 11.30 AM

Venue: Ramanujan Hall, Department of Mathematics.
 

3. Number theory seminar
Speaker: Anurag Sahay (Purdue University)
Title: The moments of the Hurwitz zeta function with irrational shifts
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, November 21
Venue: Ramanujan Hall

Title: Smooth structures on PL-manifolds of dimensions between 8 and
10

Date: 22nd November, 2024 (Friday)

Time: 11:30 AM - 12:30 PM

Venue: Ramanujan Hall

Google meet link: https://meet.google.com/rey-ytkn-xhe
 

Speaker: Rajas Sandeep Sompurkar, IISc Bengaluru
Venue: Online, https://meet.google.com/mvz-brfo-pmw
Date: Friday , 22nd November, 2024, Time: 02:30 p.m.
Title: The Momentum Construction Method for Higher Extremal Kähler and Conical Higher cscK
Metrics
Abstract: This talk consists of two parts. In both the parts we study two new notions of canonical
Kähler metrics introduced by Pingali viz. `higher extremal Kähler metric' and `higher constant
scalar curvature Kähler (higher cscK) metric' both of whose definitions are analogous to the
definitions of extremal Kähler metric and constant scalar curvature Kähler (cscK) metric
respectively. On a compact Kähler manifold a higher extremal Kähler metric is one whose top
Chern form equals its volume form multiplied by a smooth function whose gradient is a
holomorphic vector field, while a higher cscK metric is one whose top Chern form is a real constant
multiple of its volume form or equivalently whose top Chern form is harmonic. In both the parts we
consider a special family of minimal ruled surfaces called as `pseudo-Hirzebruch surfaces' which
are the projective completions of holomorphic line bundles of non-zero degrees over Riemann
surfaces of genera greater than or equal to two. These surfaces have got some nice symmetries in
terms of their fibres and their zero and infinity divisors which enable the use of the momentum
construction method of Hwang-Singer (or the Calabi ansatz procedure) for finding explicit
examples of various kinds of canonical metrics on them.
 In the first part of this talk we will see by using the momentum construction method that on a
pseudo-Hirzebruch surface every Kähler class admits a higher extremal Kähler metric which is not
higher cscK. The construction of the required metric boils down to solving an ODE depending on a
parameter on an interval with some boundary conditions, but the ODE is not directly integrable
and requires a very delicate analysis for getting the existence of a solution satisfying all the
boundary conditions. Then by doing a certain set of computations involving the top Bando-Futaki
invariant we will finally conclude from this that higher cscK metrics (momentum-constructed or
otherwise) do not exist in any Kähler class on this Kähler surface.
 In the second part of this talk we will see that if we allow our metrics to develop `conical
singularities' along at least one of the zero and infinity divisors of a pseudo-Hirzebruch surface
then we do get `conical higher cscK metrics' in each Kähler class of the Kähler surface by the
momentum construction method. Even in this case the construction of the required metric boils
down to solving a very similar ODE on the same interval but with different parameters and slightly
different boundary conditions. We can then see that our momentum-constructed metrics are
conical Kähler metrics satisfying the `polyhomogeneous condition' of Jeffres-Mazzeo-Rubinstein,
and we will be able to interpret the conical higher cscK equation globally on the surface in terms of
the currents of integration along its zero and infinity divisors by using Bedford-Taylor theory.

4. Geometry and Topology seminar
Speaker: Ramesh Kasilingam (IITM)
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, November 22
Venue: Ramanujan Hall

Title: Aspherical Manifolds : Historical Insights and Recent Progress in
Topology

Abstract : We report recent progress on various open and interesting
problems related to aspherical manifolds, i.e., connected, closed
manifolds whose universal coverings are contractible. There are many
well-known examples, such as closed Riemannian manifolds with non-positive
sectional curvature, but also very exotic examples such as
closed aspherical manifolds that do not admit a triangulation. We also
discuss important conjectures, including the Borel Conjecture, the
Hopf-Singer Conjecture, and the Farrell-Jones Conjecture.

5. Algebraic groups seminar
Speaker: Shripad M Garge (IIT Bombay)
Title: Isomorphism theorem
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, November 22
Venue: Room 215

Seminar on Cluster algebras
Speaker: Sarjick Bakshi
Title : Title : g-vectors of Plücker coordinates
Time, Day and Date : Monday 25th November, 5:00-6:00 pm
Venue : Room 105

Algebraic Geometry Seminar
Speaker: Umesh Dubey
Title: Title: Derived categories and Semi-orthogonal decompositions
Time, Day and Date: Tuesday 26th November, 2:00-3:00 pm
Venue: Ramanujan Hall

1. Algebraic groups seminar
Speaker: Chayan Karmakar (IIT Bombay)
Title: Nilpotent Conjugacy Classes
Time, day and date: 4:00:00 PM - 6:00:00 PM, Tuesday, November 26
Venue: Room 215

2. Statistics and Probability seminar
Speaker: Subhadra Dasgupta (Ruhr university Bochum)
Title: Efficient Subsampling for Exponential Family Models on Large Datasets
Time, day and date: 3:30:00 PM - 4:30:00 PM, Thursday, November 28
Venue: Ramanujan Hall

3. Algebraic groups seminar
Speaker: Dibyendu Biswas (IIT Bombay)
Title: Nilpotent Conjugacy Classes
Time, day and date: 4:00:00 PM - 6:00:00 PM, Friday, November 29
Venue: Room 215

Speaker: Suman Mukherjee, NISER, Bhubaneshwar

Venue: Google meet: https://meet.google.com/bjb-xdhv-bsq

Date and Time: 29 November 2024, 4 PM

Title: Linear and bilinear multipliers for the Dunkl transform