- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on algebraic stacks**

Time: Monday, 9th Oct, 11.30 am=============================

**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.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Tuesday, 10 October 2023, 2:30 pm

**=========================****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.

- Time:
- 5:30pm
- Description:
**IPDF Candidate Statistics Seminar**

Tuesday, 10th October, 5:30 pm

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

**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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Mathematics Colloquium**Wednesday, 11 October, 4 pm

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

**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.

- Time:
- 5:00pm-6:00pm
- Description:
**Statistics seminar**Wednesday

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

**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*p*2,*q*2,*r*2, 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.

- Time:
- 11:30am-1:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Lecture series on Hodge Theory****Thursday, 12 Oct. 11.30-1.00****=====================****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.).

- Time:
- 2:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Topology and Related Topics Seminar**Thursday, 12 October 2023, 2:30 pm

**==========================****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.

- Time:
- 3:30pm-5:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
**Commutative Algebra Seminar**Thursday, 12 Oct. 3.30-5.00 pm

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

**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.

- Time:
- 5:15pm-6:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Analysis Seminar**Thursday, 12th Oct, 5:15 pm - 6:15 pm

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

**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.

- Time:
- 2:30pm-3:30pm
- Description:
**IPDF Candidate seminar on PDE**Friday, 13 Oct. 2.30—3.30

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

**Venue:**Online meetingDetails 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.