Speaker: Arun Maiti
Time and Venue: 9:15-10:15PM, LH-I
Abstract: A Morse function on a Riemannian manifold can be used to study topology of the manifold. In this talk we will see construction of a cellular chain complex known as the Morse complex associated to a Morse function. If time permits we will briefly talk about how geodesics can be studied using Morse theory.
Speaker: Abhash Kumar Jha
Date: 12th February, 2019
Abstract: Modular forms are complex-valued holomorphic function defined on complex upper half plane satisfying certain transformation law with respect to the action of the SL2(Z). A modular form is uniquely determined by its Fourier coefficients. One can associate an L-function to a modular form. In this talk, we shall discuss how special values of certain L-functions appear as a Fourier coefficients of modular forms.
1) Basic familiarity with analysis and linear algebra
Speaker: Rahul Biswas
Date: 5th, February, 2019
Abstract: Finite Element analysis is a numerical method to solve PDEs. FEM turns a PDE into a algebraic system which can be solved to get an approximation to the original solution of the PDE.
This will be a very basic introduction to Finite Element Method. I will discuss some abstract results which can can applied to study the existence and uniqueness of solution of elliptic PDEs. I will also discuss how FEM works with an example ( Poisson equation with zero boundary). If time permits I can also run some MATLAB codes to find discrete solution to the Poisson equation.
1) Basic Functional Analysis
Speaker: Raghavendra Tripathi
Date: 29th January, 2019
Abstract: Determinantal processes were introduced by Macchi in 1957, although the examples of such processes were known before. In this talk, we will define determinantal processes—which are point processes whose correlation functions are given by determinants— and we will prove some nice properties such processes enjoy. In order to motivate the definition we shall also present some examples where such processes naturally arise.
1) Introductory probability theory/measure theory
2) A little bit of Functional Analysis
Speaker: Hassain Maliyekkal
Date: 22nd January, 2019
Time: 9:15pm – 10:15pm
Abstract: In this talk I will discuss about the construction of “p-adic numbers” from rational numbers. Note that “real numbers” are also “constructed” from rational numbers. Also i will discuss the “interesting” differences between real and p-adic numbers.
Speaker: K. Hariram
Date: 20th November, 2018
We will go through a tour of trying to solve for positive integer solutions for the above equation. First we will see how far we can go with elementary methods. Then I will introduce elliptic curves and use them to finally get a solution.
Speaker: Soumitra Ghara
Date: 13th November, 2018
In 1951, von Neumann proved that if T is a contraction on a Hilbert
space, i.e. the operator norm of T is less than or equal to 1, then for any polynomial p,
the operator norm of p(T) is less than or equal to the supremum of |p(z)| over
|z|<1. In this talk, I will start with a proof of this theorem when the Hilbert space
is finite dimensional, and then use a limiting argument to obtain a proof forthe
infinite dimensional case. Then we will see another proof of this theorem using
Sz.-Nazy’s dilation theorem (which will only be stated). If time permits, I will
also discuss some multivariate generalizations of this theorem.
Prerequisites: Linear algebra and elementary functional analysis.