July 2018
Public Access Category: All |

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Trace formulas for relative Schatten class perturbations

Speaker: Arup Chattopadhyay (IIT Guwahati)

Date-Time: Tuesday, July 10, 2018, 3 PM - 4 PM.

Venue: Ramanujan Hall.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:

Speaker: Dr. Gaddam Sharat, Post-doctoral fellow, TIFR-CAM Bengaluru.

Title of the talk: Numerical Methods for Elliptic Variational Inequalities in Higher Dimensions.

Abstract: In this talk, I will first present a quadratic finite element method for three-dimensional elliptic obstacle problem which is optimally

convergent (with respect to the regularity). I will derive a priori error estimates to show the optimal convergence of the method with respect to the regularity, for this, we have enriched the finite element space with

element-wise bubble functions. Further, a posteriori error estimates are derived to design an adaptive mesh refinement algorithm. The result on a

priori estimate will be illustrated by a numerical experiment. Next, I will discuss two newly proposed discontinuous Galerkin (DG) finite element

methods for the elliptic obstacle problem. Using the localized behaviour of DG methods, I will present a priori and a posteriori error estimates for linear and quadratic DG methods in dimension 2 and 3 without the addition of bubble functions. I will consider two discrete sets, one with integral constraints (motivated as in the previous work) and another with

point constraints at quadrature points. The analysis is carried out in a unified setting which holds for several DG methods with a variable polynomial degree. Later, I will propose a new and simpler residual based a posteriori error estimator for finite element approximation of the elliptic obstacle problem. The results here are two-fold. Firstly, we

address the influence of the inhomogeneous Dirichlet boundary condition in a posteriori error control of the elliptic obstacle problem. Secondly, by

rewriting the obstacle problem in an equivalent form, a simpler a posteriori error bounds which are free from min/max functions will be constructed. To accomplish this, we construct a post-processed solution ˜uh of the discrete solution uh which satisfies the exact boundary conditions although the discrete solution uh may not satisfy. We propose

two post-processing methods and analyse them. We remark that the results known in the literature are either for the homogeneous Dirichlet boundary

condition or that the estimator is only weakly reliable in the case of inhomogeneous Dirichlet boundary condition. Finally, conclusions and possible extensions for the future works will also be discussed.

Venue, Date, and Time:

13th July 2018 (Friday) at 4PM in Ramanujan Hall,

Second floor, Mathematics building.

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Date & Time : Thursday, viz., 19th July 2018 at 4pm

Venue: Ramanujan Hall

Speaker: Dr. Prasant Singh, Technical University of Denmark

The title and abstract are enclosed.

- Time:
- 4:00pm
- Location:
- Room No. 216, Department of Mathematics
- Description:
- Title: Four Flavours of Combinatorics: (Enumerative, Probabilistic,

Extremal, and Geometric)

Speaker: Kunal Dutta (INRIA, France)

Date-Time: Thursday, July 19, 2018, 4 PM.

Venue: 216, Dept. of Mathematics, IITB

Abstract: In this talk we shall see three very different areas of

applications of combinatorics in mathematics and computer science,

illustrating four different flavours of combinatorial reasoning.

First, we shall look at Haussler's Packing Lemma from Computational

Geometry and Machine Learning, for set systems of bounded VC

dimension. We shall go through its generalization to the Shallow

Packing Lemma for systems of shallow cell complexity, and see how it

can be used to prove the existence of small representations of set

systems, such as epsilon nets, M-nets, etc. Joint works with Arijit

Ghosh (IMSc, Chennai), Nabil Mustafa (ESIEE Paris), Bruno Jartoux (ESIEE

Paris) and Esther Ezra (Georgia Inst. Tech., Atlanta).

Next, we consider lower bounds on the maximum size of an independent

set, as well as the number of independent sets, in k-uniform

hypergraphs, together with an extension to the maximum size of a

subgraph of bounded degeneracy in a hypergraph. Joint works with C. R.

Subramanian (IMSc, Chennai), Dhruv Mubayi (UIC, Chicago) and Jeff

Cooper (UIC, Chicago) and Arijit Ghosh.

The last problem is on the decomposition, into irreducible

representations, of the Weil representation of the full symplectic

group associated to a finite module of odd order over a Dedekind

domain. We shall discuss how a poset structure defined on the orbits

of finite abelian p-groups under automorphisms can be used to show the

decomposition of the Weil representation is multiplicity-free, as well

as parametrize the irreducible subrepresentations, compute their

dimensions in terms of p, etc. Joint works with Amritanshu Prasad

(IMSc, Chennai).

- Time:
- 4:00pm - 6:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Speaker: Ronnie Sebastian.

Title: Weil conjectures - Rationality and Functional Equation

Abstract: In this talk we will assume that certain cohomology theories

exist, and demonstrate how to prove rationality and functional equation of

the zeta function. A large part of the talk will be using tools from

linear

algebra and algebraic topology. We will mostly be following the nice set of

notes available here: http://www.math.lsa.umich.edu/~mmustata/lecture5.pdf

Time: 4-6 PM.

Venue: Room 215

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

Date and Time: 24th July at 2:30 pm.

Venue: Ramanujan Hall, Department of Mathematics

Speaker: Dr. Naveen Narisetty, Department of Statistics, University of Illinois at Urbana

Champaign

Title: Variable Selection Techniques for Analyzing High Dimensional Data sets

Abstract: In the modern big data era, data sets with a large number of features is a common phenomenon. In this talk, I will present an overview of high dimensional variable selection methods along with some recent advances both from the frequentist and Bayesian viewpoints. Both computational and theoretical challenges and ways to address them will be discussed.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Dr. P. V. Sukhatme Memorial Lecture

Date and Time: 24th July at 3:30 pm.

Venue: Ramanujan Hall, Department of Mathematics

Speaker: Prof. Vijay Nair, Emeritus Professor, Department of Statistics, University of Michigan, Ann Arbor, USA.

Title of the talk: Big Data, Machine Learning, and Data Science

Abstract: In this presentation, I will provide some personal perspectives on the so-called Big Data movement, its impact, potential benefits and challenges. As part of this, I will discuss developments in, and applications of, machine learning with a focus on supervised learning. I will also spend a few minutes on the new field of Data Science. This will be a non-technical talk.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Speaker : Dr. Vivek Mukundan

Title : Implicitization problem and the defining ideal of the Rees algebra.

When : Thursday 26 July, 2.00-3.30 pm

2 Aug 2.00-3.30 pm

Venue: Room 215

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

Abstract: Consider a rational map from P^{n-1}—>P^n parametrized by homogeneous polynomials f_0,\dots,f_n of degree d. We study the equations defining the graph of the map whose coordinate ring is the Rees algebra of the ideal generated by f_0, .., f_n. We provide new methods to construct these equations using work of Buchsbaum and Eisenbud. Furthermore, for certain classes of ideals, we show that our construction is general. These classes of examples are interesting, in that, there are no known methods to compute the defining ideal of the Rees

algebra of such ideals. These new methods also give rise to effective criteria to check that φ is birational onto its image.

- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Title: Weil conjectures - Rationality and Functional Equation

Abstract: In this talk we will assume that certain cohomology theories exist, and demonstrate how to prove rationality and functional equation of the zeta function. A large part of the talk will be using tools from linear algebra and algebraic topology. We will mostly be following the nice set of notes available here: http://www.math.lsa.umich.edu/~mmustata/lecture5.pdf

- Time:
- 5:00pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Seminar: CACAAG.

Time: 5-6:30 pm, Tuesday, July 31.

2018.

Venue: TBA.

Speaker: Dr. Samir Shukla.

Title: An introduction to some graph coloring complexes

Abstract: Graph complexes are simplicial complexes arising from graphs. In

this talk we mainly focus on two types of complexes: Neighborhood

complexes and Hom complexes. The topology of these complexes are closely

related to the chromatic number of the underlying graphs. We give a brief

survey of the research have been done with respect to them in recent

years. We also discuss some open problems related to them.