Autumn 2023

Talk-7 (04/10/2023)

Title: The history of matrix positive semidefiniteness preservers.

Speaker: Shivangi Yadav

Abstract:- What functions preserve positive semidefiniteness when applied entrywise to positive semidefinite matrices? This question has a long history beginning with Schur, Schoenberg, and Rudin, and has also recently received renewed attention due to its several applications in statistics. However, effective characterizations of entrywise functions preserving positivity in a fixed dimension remain open to date. In this talk, I will give a historical account and state-of-the-art of this problem.

Talk-6 (27/09/2023)

Title: An overview of inverse boundary value problems  

Speaker: Anamika Purohit 

Abstract:- In this talk, we will discuss the inverse boundary value problems that determine the internal coefficients of the differential equation from measurements made at the region's boundary and its applications. We will further introduce the Calde{\'r}on Problem (also called the inverse conductivity problem) and discuss some main tools for proving the uniqueness of the inverse boundary value problems.

Talk-5 (20/09/2023)

Title: Radon transform in CT scans. 

Speaker: Chandni Thakkar

Abstract:-  In this talk, we plan to discuss some problems arising in the field of integral geometry having applications in various imaging techniques. We will discuss in detail about the Radon transform and its importance in the technique of CT scans. If time permits, we will discuss some other important integral transforms. 

Talk-4 (13/09/2023)

Title: Counting Ideals in Numerical Semigroups

Speaker: Parth Chavan 

Abstract:- If $S$ is a numerical semigroup, let $m(S,k)$ denote the number of ideals of $S$ with codimension $k$ and let $n(S,k)$ denote the number of ideals of $S$ with conductor $k$. We compute the generating function of the sequence $m(S,k)$ for all numerical semigroups of embedding dimension $2$ and for $S = \langle 3,n+2,2n+1\rangle$. We also prove that the sequence $n(S,k)$ becomes stationary after a certain term and compute these stationary terms for numerical semigroups of the form $\langle n,n+1 \rangle$.

Talk-3 (23/08/2023)

Title: Extreme values of the zeta function

Speaker: Shashank Chorge 

Abstract:- We compute extreme values of the Riemann zeta function at the critical points of the zeta function in the critical strip. i.e. the points where $\zeta^{\prime}(s)=0$ and $\Re s<1$. We show that the values taken by the zeta function at these points are very similar to the extreme values taken without any restrictions. We will show the geometric significance of such points. We also compute extreme values of Dirichlet $L$ - functions at the critical points of the zeta function to the right of $\Re s=1$. It shows the statistical independence of $L$-functions and zeta function in a certain way as these values are very similar to the values taken by $L$-functions without any restriction.

Talk-2 (16/08/2023)

Title: Fundamental Solution to the Laplace Operator   

Speaker: Poonam Rani

Abstract:- The concept of weak solution is an important aspect of the theory of partial differential equations; in this regard, we will study the basics of Distributions and convolution of functions and generalize it to convolution of distributions. Using these concepts, we will construct a fundamental solution to the Laplace operator.

Talk-1 (10/08/2023)

Title: A brief overview of C*- algebra 

Speaker: Akshay Bhuva

Abstract:-  C*-algebra: Some facts from Banach algebra, definition and example of C*-algebra, classification of commutative unital C*-algebra (If time permits brief overview for non-commutative case).