Lecture series on algebraic stacks
Time: Monday, 9th Oct, 11.30 am

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Venue: Ramanujan Hall
Host: Sudarshan Gurjar

Speaker: Nitin Nitsure

Affiliation: TIFR, Mumbai (Retd)

Title: Algebraic Stacks
Abstract: In this talk, we will look at equivalent definitions of algebraic stacks, together with various examples. The main reference for the talk is Chapter 4 of the book Champes Algebriques by Laumon and Moret-Bailly.

Topology and Related Topics Seminar

Tuesday, 10  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
Abstract: The goal of this series of talks is to show that the integral cohomology ring of a moment angle complex associated with the simplicial complex $K$ is isomorphic to the tor algebra of $K$. In the first talk, we will present various constructions of moment angle complexes and prove that those associated with simplicial spheres form topological manifolds.

 IPDF Candidate Statistics Seminar
 Tuesday, 10th October, 5:30 pm
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 Venue: Online. Details can be obtained from the host
 Host: Sanjeev Sabnis

 Speaker: Neeraj Poonia
 Affiliation: IIT Mandi
 

Title: Temperature modeling using a new statistical distribution derived from the Clayton copula

Abstract: Due to global warming, temperature is getting elevated around the world which further leads to deglaciation in mountainous regions and disturbs the overall climate dynamics. The Northwest Himalayan region has many glaciers and rising temperatures in this region can cause flood in rivers which is destructive to economic activities. In this talk, I will discuss the newly constructed bivariate exponentiated Teissier distribution using the Clayton copula. Further, some statistical properties along with the parameter estimation techniques will be discussed. In this work, the maximum likelihood estimation and inference function of margin procedures for parameter estimation are compared through a simulation study for the proposed model. Finally, to show the applicability of the proposed model, the bivariate exponentiated Teissier distribution is used for modeling the temperature data over 525 grids of the Northwest Himalayan region, and some interesting patterns are observed.    

Mathematics Colloquium

Wednesday, 11 October, 4 pm

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Venue: Ramanujan Hall

Host: Murali K. Srinivasan

Speaker: Subhajit Ghosh

Affiliation: Bar-Ilan University, Ramat-Gan, Israel

TITLE: Aldous-type spectral gap results for the complete monomial group

ABSTRACT: Let G be a finite group. We consider a connected graph such that the edges and vertices are equipped with independent Poisson clocks  (alarm clocks that ring at time distributed as the exponential distribution).  Also, there are lamps with configurations indexed by the elements of G and lamplighters at the vertices of the graph.  The lamplighters at a pair of neighboring vertices exchange their position whenever the associated edge rings.  The lamplighter at a vertex updates the lamp configuration whenever the vertex rings.  The process can be viewed as a continuous-time random walk on the complete monomial group G wreath S(n) (symmetric group).   If the configuration of a lamp is x, then it changes to g.x with a non-negative rate alpha(g).  We assume that the rates are symmetric, and the elements g in G with positive alpha(g) generate G.  We show that the spectral gap of the process is the same as that of the continuous-time lamplighter random walk (i.e., the process with a single lamplighter) on the graph.  This is an analog of the Aldous' spectral gap conjecture for the complete monomial group of degree n over G.

Statistics seminar

Wednesday 11th Oct, 5-6 pm

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Venue: Ramanujan Hall

Host: Siuli Mokhopadhyay

Speaker: Prof. Manisha Pal

Affiliation: St. Xavier's University, Kolkata

Title: EXACT INFERENCE IN A MULTINOMIAL DISTRIBUTION

Abstract: Sequential sampling plans for unbiased estimation of the Bernoulli parameter 'p' have been studied for almost 70 years. Thereafter, there have been some studies for unbiasedly estimating functions of p. An extension of the idea to parametric function estimation in a trinomial distribution has been considered briefly. In this paper we address the problem of finding unbiased estimators of the parameters p and q in a tetranomial distribution, where the cell probabilities are p2, q2, r2, and 2(pq + pr + qr), satisfying p, q, r > 0, p + q + r = 1. Some illustrative examples have been cited to demonstrate the underlying concepts and the computational procedure.

Lecture series on Hodge Theory

Thursday, 12 Oct. 11.30-1.00

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Venue: Ramanujan Hall

Host: Sudarshan Gurjar

Title: Kahler condition and its consequences
Abstract: These are part of an ongoing series of lectures on the basics of Hodge theory. We will discuss the Kahler condition, and its consequences (Kahler identities, etc.).

Topology and Related Topics Seminar

Thursday, 12  October  2023, 2:30 pm

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Venue: 215

Host: Rekha Santhanam

Speaker:  Omkar Javadekar

Affiliation: IIT Bombay

Title: A review of derived category and related topics 

Abstract: In this talk, we will see the construction of localization of a category with respect to an arbitrary class of morphisms, and define the derived category using localization. We will sketch the proof of the fact that the homotopy and derived categories are triangulated. Along the way, we will also try to revise the example of projective model structure on the category Ch(R) of chain complexes of modules over a ring R. We will then define the notion of support for objects of the derived category D(R), and end by stating the theorem of Hopkins-Neeman for small R-complexes.

Commutative Algebra Seminar

Thursday, 12 Oct. 3.30-5.00 pm

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Venue: Room 215

Host: Tony Puthenpurakal

Speaker: J. K. Verma, IIT Bombay

Title: Introduction to local cohomology

Abstract: I will discuss various ways of computing local cohomology modules and describe their basic properties needed for the proof of Grothendieck-Serre formula for the Hilbert function of a graded module over a graded algebra.

Analysis Seminar

Thursday, 12th 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 second talk of the series. We will finish our discussion on Hausdorff-Young inequality.

IPDF Candidate seminar on PDE

Friday, 13 Oct. 2.30—3.30

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Venue: Online meeting

Details can be obtained from the

Host: Neela Nataraj

Speaker: Raman Kumar

Affiliation: IIT Guwahati

Title: High order weak Galerkin finite element methods for H(curl) and H(curl, div)-elliptic problems.

Abstract: Weak Galerkin finite element methods (WG-FEMs) for H(curl) and H(curl, div)-elliptic problems will be discussed in this presentation. The WG method as applied to curl-curl and grad-div problems uses two operators: discrete weak curl and discrete weak divergence, with appropriately defined stabilizations that enforce a weak continuity of the approximating functions. This WG method is highly flexible by allowing the use of discontinuous approximating functions on the arbitrary shape of Polyhedra and, at the same time, is parameter-free. The optimal order of convergence is established for the WG approximations in discrete H1 norm and L2 norm. In fact, theoretical convergence analysis holds under low regularity requirements of the analytical solution. Results of numerical experiments that corroborate the theoretical results are also presented.