- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lie theory seminar

Speaker: M. S. Raghunathan

Title: Lie algebra cohomology

Time: 16:00 - 17:00, Monday, October 1

Venue: Ramanujan Hall, Department of Mathematics

Note: This is the first of two lectures. Also please note the change in time.

- Time:
- 5:15pm
- Location:
- Room. 215
- Description:
- Popular talk in Mathematics

Venue: Ramanujan Hall

Time & Date: 5:15 PM on Monday October 1st 2018.

Speaker: Mayukh Mukherjee

Title: An introduction to spectral problems and shape optimization

Abstract: We will start by giving some broad overview of the general

area of inverse spectral theory and the associated area of

so-called shape optimization. Then, we will make an attempt

to give a proof of the classical Faber-Krahn theorem.

MSc students are encouraged to attend.

Please note tea and snack will be available in Room 215 at 5:00 PM

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic geometry seminar

Date& Time: Wednesday, 3rd October at 2.30 pm

Venue: Ramanujan Hall

Speaker: Piotr Pragacz, Polish Academy of Sciences, Warsaw

https://www.impan.pl/~pragacz/

Title: Gysin maps, duality, and Schubert classes

Abstract: We establish a Gysin formula for Kempf-Laksov flag

bundles and prove a duality formula for Grassmann bundles.

We then combine them to study Schubert bundles, their

push-forwards and fundamental classes.

This is a joint work with Lionel Darondeau.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium

Date & Time: 3rd October, Wednesday, at 4pm

Venue: Ramanujan Hall

Speaker: Debanjana Mitra

Title: An application of microlocal analysis to control theory.

Abstract: In the first part of my talk, some preliminaries on microlocal

analysis will be discussed. In the second part of the talk, some

techniques to study the controllability of a system using microlocal

analysis will be explained. As an example of this approach, the lack of

null controllability of viscoelastic flows will be discussed.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room. 215
- Description:
- Commutative algebra seminar

Thursday, 4 October, 2018

Room 215

2.00-3.30

Speaker: J. K. Verma

Title: The Hoskin-Deligne formula for complete ideals in two-dimensional regular local rings.

Abstract: Let I be a complete m-primary ideal in a two dimensional regular local ring R.

The Hoskin-Deligne (HD) formula expresses the length of the Artin local ring R/I in terms of

the m-adic order of the transforms of I in various local quadratic transforms of R.

It uses a structure theorem of Zariski and Abhyankar about two dimensional regular

local rings which birationally dominate R. The HD formula implies several fundamental

theorems about complete ideals proved by Zariski, Lipman, Rees and Huneke-Sally. We

shall prove these in a series of talks.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Dr. Kunal Dutta will give a Skype talk on 8th October at 2.30 pm in

Ramanujan hall. He is a faculty candidate.

A file with the title and abstract of his talk is attached

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr. Amit Kumar

Department of Mathematics

IIT Madras

Date and Time: Tuesday, 09/10/2018, 4:00 pm -- 5:00 pm

Venue: Ramanujan Hall

Title: Approximations related to (k_1,k_2)-runs

Abstract: See Attachment.

- Time:
- 5:00pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Aneek Maiti.

Date and Time: Tuesday, 09/10/2018, 5-6pm

Venue: Ramanujan Hall.

Title: Free resolution of a finitely generated graded module and Hilbert function.

Abstract: Let M be a finitely generated graded module over a polynomial ring of a field. Then we can define a function corresponding to that module which is called "Hilbert Function". Now in my lecture I will tell you how to compute that function for such a module, with examples of course. I will also introduce "Betti numbers" and will show how these things are connected to each other.

- Time:
- 11:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Dr Vaibhav,

Date and Time: Wed 12 Oct from 11:30 am-12:30pm.

Venue: Ramanujan Hall, talk via Skype.

Title and Abstract: TBA.

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Alexander Volfovsky

Department of Statistical Sciences

Duke University

Date and Time: Thursday, 11/10/2018, 3:00 pm -- 4:00 pm

Venue: Ramanujan Hall

Title: Design of experiments for networks with interference

Abstract: Randomized experiments have long been considered to be a gold standard for causal inference. The classical analysis of randomized experiments was developed under simplifying assumptions such as homogeneous treatment effects and no treatment interference leading to theoretical guarantees about the estimators of causal effects. In modern settings where experiments are commonly run on online networks (such as Facebook) or when studying naturally networked phenomena (such as vaccine efficacy) standard randomization schemes do not exhibit the same theoretical properties. To address these issues we develop a randomization scheme that is able to take into account violations of the no interference and no homophily assumptions. Under this scheme, we demonstrate the existence of unbiased estimators with bounded variance. We also provide a simplified and much more computationally tractable randomized design which leads to asymptotically consistent estimators of direct treatment effects under both dense and sparse network regimes.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Title: Bloch Wave Homogenization of Almost Periodic Operators

Speaker: Vivek Tewary, PhD student, Department of Mathematics, IIT Bombay,

Time: 4 p.m.- 5p.m., 11-10-18, Thursday.

Venue: Room 215, Department of Mathematics

Abstract: Bloch wave homogenization is a spectral method for obtaining

effective coefficients for periodically heterogeneous media. This method

hinges on the direct integral decomposition of periodic operators, which

is not available in a suitable form for almost periodic operators. In

particular, the notion of Bloch eigenvalues and eigenvectors does not

exist for almost periodic operators. However, we are able to recover the

homogenization result in this case, by employing a sequence of periodic

approximations to the almost periodic operator.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- PDE & Numerical Analysis Seminar

Date and Time: 12th October 2018, at 4PM

Venue: Ramanujan Hall, Mathematics Department.

Speaker: Samala Rathan, VNIT, Nagpur.

Title: "High-resolution shock capturing high-order WENO schemes for hyperbolic conservation laws"

Abstract of the seminar:

"In this talk, we present a class of new higher order WENO spatial approximation

schemes to solve the hyperbolic conservation laws along with the use of total

variation diminishing (TVD)/strong stability preserving Runge-Kutta (SSPRK)

temporial derivative approximation techniques. The objective of these developments

aim for the improvements, in obtaining higher resolution and efficiency of the

solution which retains the desired order of accuracy in smooth regions and in the

presence of critical points. These improvements have been achieved by mainly

focusing on the construction of new smoothness indicators which plays a key role in

the spatial derivative approximation of flux function via the nonlinear weights in WENO

algorithm. With these new measurements, higher-order WENO schemes viz fifth and

seventh-order WENO schemes have been constructed and subsequently imposed a

sufficient condition on the parameters in the weight functions which recovers the

optimal order for smooth regions of solution that includes the critical points.

Numerical results show that these new schemes achieve optimal-order of accuracy.

These schemes also show the advantage of resolving the sharper results for shock

waves, contact discontinuities and the regions that contain high-frequency waves."

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Jerome Droniou

Affiliation: Monash University, Melbourne

Time: Monday (15-10-18), 2.30 PM-3.30 PM.

Venue: Ramanujan Hall.

Tiitle: What the second Strang lemma and the Aubin-Nitsche trick should be

Abstract: The second Strang lemma gives an error estimate for linear

problems written in variational formulation, such as elliptic equations.

It covers both conforming and non-conforming methods, it is widely spread

in the finite element community, and usually considered as the starting

point of any convergence analysis.

For all its potency, it has a number of limitations which prevents its

direct application to other popular methods, such as dG methods, Virtual

Element Methods, Hybrid High Order schemes, Mimetic Methods, etc. Ad-hoc

adaptations can be found for some of these methods, but no general `second

Strang lemma' has been developed so far in a framework that covers all

these schemes, and others, at once.

In this talk, I will present a `third Strang lemma' that is applicable to

any discretisation of linear variational problems. The main idea to

develop a framework that goes beyond FEM and covers schemes written in a

fully discrete form is to estimate, in a discrete energy norm, the

difference between the solution to the scheme and some interpolant of the

continuous solution. I will show that this third Strang lemma is much

simpler to prove, and use, than the second Strang lemma. It also enables

us to define a clear notion of consistency, including for schemes for

which such a notion was not clearly defined so far, and for which the Lax

principle `stability + consistency implies convergences' holds.

I will also extend the analysis to the Aubin-Nitsche trick, presenting a

generalisation of this trick that covers fully discrete schemes and

provides improved error estimates in a weaker norm than the discrete

energy norm. We will see that the terms to estimate when applying this

Aubin-Nitsche trick are extremely similar to those appearing when applying

the third Strang lemma; work done in the latter case can therefore be

re-invested when looking for improved estimates in a weaker norm.

I will conclude by briefly presenting applications of the third Strang

lemma and the abstract Aubin-Nitsche trick to discontinuous Galerkin and

Finite Volume methods.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Statistics Seminar.

Speaker: Prof. Palash Ghosh

Centre for Quantitative Medicine

DUKE-NUS Medical School

National University of Singapore

Date: Monday, 15/10/18.

Time: 4:00--5:00 pm.

Venue: Ramanujan Hall

Title: Dynamic Generalized Odds-Ratio (dGOR): A novel approach to assess

Dynamic Treatment Regimes (DTR) with An Ordinal Outcome.

Abstract: See Attachment.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- PDE & Numerical Analysis Seminar

Date and Time: 16th October 2018, at 4PM

Venue: Ramanujan Hall, Mathematics Department.

Speaker: Prof. Ravi Prakash, University of Concepcion, Chile.

Title: "Homogenization: Oscillating Boundary Domains"

Abstract of the seminar:

Homogenization is a branch of science where we try to understand microscopic structures via a macroscopic medium. Hence, it has applications in various branches of science and engineering. This study is basically developed from material science in the creation of composite materials though the contemporary applications are much far and wide. It is a process of understanding the microscopic behavior of an in-homogeneous medium via a homogenized medium. Mathematically, it is a kind of asymptotic

analysis. We are interested in the asymptotic behavior of elliptic boundary value problems posed in domains with highly oscillating boundary. In fact, we will consider different types of unfolding operators to study many types of oscillating boundary domains with various model problems posed in them. We will also see some interesting optimal boundary control problem posed in such domains. In total, the presentation will start from the asymptotic behavior of Laplacian in a simple rectangular oscillating boundary domains to the future possibilities of the shapes of oscillations in the boundary keeping in mind the mathematical issues arise in topology optimization.

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG Seminar

Speaker: Neeraj Kumar.

Time: 5pm, Tuesday, 16 October 2018.

Venue: Ramanujan Hall.

Title: Wilf's conjecture on numerical semigroups

Abstract: The aim of the talk is to give a brief survey on the Wilf's

conjecture, and to present a commutative algebra formulation of it. We

will verify Wilf's conjecture in some cases.

A numerical semigroup $S$ is a subset of the nonnegative integers $N$ that

is closed under addition, contains 0, and has finite complement in $N$.

The Frobenius number $F$ of numerical semigroup $S$ is the largest integer

not in $S$. Let $d$ be the minimal number of generators of $S$ and $n$ be

the number of representable integers in the interval $[0, F]$. Wilf's

conjecture states that $F +1 \leq n d$.

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Somnath Jha

Title: A duality for Selmer groups

Time: 14:30 - 15:30, Wednesday, October 17, 2018.

Venue: Ramanujan Hall, Department of Mathematics

Abstract: Selmer group is an important object of study in number theory.

We will discuss a twisting result in the setting of so called

"non-commutative" Iwasawa theory. We will further use this to deduce a

duality result for certain Selmer groups. (This talk is based on joint

works with T. Ochiai, G. Zabradi and S. Shekhar.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Department Colloquium.

Speaker: Harsha Hutridurga.

Time: 4pm, Wednesday, October 17, 2018.

Venue: Ramanujan Hall.

Title: An overview of the theory of Hypocoercivity.

Abstract: In this talk, we attempt to give a brief introduction to the

theory of Hypocoercivity which has become an indispensable tool in the

study of relaxation to equilibrium states for mathematical models arising

in statistical physics. The essential ideas behind this theory will be

motivated via simple examples. The role of certain functional inequalities

while deriving explicit rates of convergence will be made precise during

this talk. This talk concludes by addressing a certain degenerate kinetic

Fokker-Planck equation. Incidentally, the study of the trend to

equilibrium for this degenerate model finds link to the acclaimed

Geometric Condition from the theory of control for wave propagation.

- Time:
- 3:30pm - 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Parvez Sarwar

Title: Algebraic K-theory and homology stability

Time: 15:30 - 16:30, Thursday, October 18

Venue: Ramanujan Hall

Abstract: We shall begin with the homotopy invariance property of

K-theory. After reviewing monoids and monoid algebras, we present some

results which are monoid version of the homotopy invariance property in

K-theory. This answers a question of Gubeladze. Next, we will discuss the

monoid version of Weibel's vanishing conjecture and some results in this

direction. Finally, we will talk about the homology stability for groups.

Here we present a result which improves homology stability for symplectic

groups. If the time permits, some application of the homology stability

will be given to the hermitian K-theory.

- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- PDE seminar on Control and homogenization:

Title: Control of wave equation.

Speaker: Debanjana Mitra,

Time: Thursday, 18-10-18, 4p.m.-5p.m.

Venue: Room 215, Department of Mathematics, IIT Bombay.

Abstract: In this talk, we will mainly discuss on the control of wave

equation. At the first part of the talk, we will give an overview of the

control of wave equation and mention some important results in this

direction. Then in the second part, the control of wave equation using

Hilbert uniqueness method will be discussed.

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar

Time & Date: 5pm, 23rd October

Venue: Ramanujan Hall

Speaker: Kriti Goel

Title: An introduction to Local Cohomology

Abstract: In this talk, we will look at three different ways to calculate

the local cohomology modules and some of the properties of these modules.

No pre-requisites are required for the talk, so all are welcome!

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium

Time & Date: 4pm, 24th October

Venue: Ramanujan Hall

Speaker: Trygve Johnsen

Title: An introduction to codes and matroids

Abstract: In this talk we will tell what the purpose of an error-correcting code is, and we will in particular study linear codes. We will relate some of the most important properties of such codes with those of another class of mathematical objects, namely matroids. These are objects that arise in a natural way, either from undirected (multi)graphs, or, as the name indicates, from matrices. Furthermore, if time permits, we will sketch briefly how algebraic geometry over finite fields enter the picture when defining and producing codes with good properties.

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Talk over Skype

25th October

Dr. Omprokash Das

2:30-3:30pm

Venue: Ramanujan Hall

Title of the Talk: The Minimal Model Program (MMP) and its Applications.

Abstract: The Minimal Model Program (MMP) or the Mori Program is one of the fundamental tools of birational classifications and the construction of Moduli Spaces of higher dimensional varieties. In this talk I will explain the main ideas of MMP and its various applications. Finally I will talk about the recent progress of MMP in positive characteristic.

- Time:
- 4:00pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- PDE seminar on Control and homogenization:

Title: Control of wave equation.

Speaker: Debanjana Mitra,

Time: Thursday, 25-10-18, 4p.m.-5p.m.

Venue: Room 215, Department of Mathematics, IIT Bombay.

Abstract: In this talk, we will continue the discussion on the control of

wave equation from where we stopped at the previous lecture. The control

of wave equation using Hilbert uniqueness method will be discussed.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Dr. Samya Ray from IIT Kanpur

25 Oct at 4:00 pm.

Venue: Ramanujan Hall

Please find attached the title/abstract of the talk.

- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Speaker: Soumyadip Thandar

Time and Venue: 4pm, room 215

Title: General position theorem

Abstract: Let X be a smooth projective variety contained in CP^n. We say X is nondegenerate if it is not contained in any proper hyperplane. Given a variety of dimension m in CP^n, we intersect it with m many hyperplanes and get bunch of points. This number is independent of the choice of the hyperplanes and is defined to be the degree of the variety. A set of k points in CP^n is said to be in general position, if every subset of n+1 points spans all of CP^n. We will prove the general position theorem which states that given an irreducible nondegenerate curve C in CP^n ( where n is \geq 3) of degree d, a general hyperplane meets C in d points which are in general position. Using this we will show any nondegenerate variety X in CP^n , degree \geq 1+codim(X).

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Time: Monday, 29th Oct, 3:30 - 5:00 p.m.

Venue: Room 215, Maths Building.

Title. Complete modules and base conditions of linear system - I

Speaker. R.V.Gurjar

Abstract. We will discuss Zariski's theory of complete modules and their

relation to base points of linear systems.

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Time & Date: 5pm, 30th October

Venue: Ramanujan Hall

Speaker: Kriti Goel

Title: Grothendieck-Serre formula

Abstract: The Grothendieck-Serre formula was proved by J.P.Serre in 1955.

The formula expresses the difference of the Hilbert function and Hilbert

polynomial of a finite graded module over a standard graded Noetherian

ring, in terms of length of certain local cohomology modules.

In this talk, we will look at the proof of the formula.