International Women in Mathematics Day

May 12-13, 2025 | Harish-Chandra Research Institute (HRI)

In 2014, Maryam Mirzakhani (1977-2017) became the first woman to receive the Fields Medal for her work on the geometry and dynamics of Riemann surfaces. The 12th of May, her birthday, was chosen to celebrate Women in Mathematics in her memory.

Speakers

• Dr. Debanjana Mitra (IIT Bombay) on Analysis of PDEs
  
  Title: Ingham inequality and its application to control theory
  Abstract
  Families of non-harmonic exponentials often appear in various fields of mathemat- ics and in particular, control theory. We first review the Ingham inequality, the celebrated generalization of Parseval’s equality, which is one of the key tools to determine some special properties of the exponentials. The Ingham type inequality is extensively used to study the observability and hence the controllability of a linear PDE system, provided the associated linear operator has the spectrum satisfying a suitable gap condition. We shall see this appli- cation to the wave equation and briefly to the one dimensional compressible Navier-Stokes system linearized around a constant steady state.

• Dr. Siddhi Pathak (CMI) on Number Theory
  
  Title: A conjecture of Erdos on the non-vanishing of a certain infinite series
  Abstract
  Let f be a function on the natural numbers, periodic with period N > 1, with f(n) taking values −1 or 1 for 0 < n < N, and f(N) = 0. In the 1950s, Erdos conjectured that for such a function f, the infinite series P n f(n)/n is non-zero, whenever it converges. This is in the same spirit as the non-vanishing of L(1, χ) for non-principal real Dirichlet characters χ, which is an essential step in proving Dirichlet’s theorem on the infinitude of primes in arithmetic progressions. In this talk, we discuss the nuances of Erdos’s conjecture and present a new approach to it, which leads to its resolution in ‘almost all’ cases. More specifically, we describe joint work with Abhishek Bharadwaj and Ram Murty in which we settle Erdos’s conjecture, except for the case when N is a perfect square.

• Prof. Indira Chatterji (University of Côte d'Azur) on Group Theory
  
  Title: Group theory from a geometrical viewpoint
  Abstract
  Groups are algebraic objects that are used across mathematics. If the structure of finite groups is fairly well understood, the world of infinite groups is much wilder. In this talk we will see a few geometric tools to understand several important examples.

• Prof. Malabika Pramanik (University of British Columbia) on Harmonic Analysis
  
  Title: A Journey Through Measure-Universality: Patterns, Size, and the Unexpected
  Abstract
  What does it mean for a pattern to be truly ubiquitous? A subset of the real line is called universal if it appears, in some affine form, inside every set of positive Lebesgue measure. Since the early 20th century, it has been known that all finite sets are universal. Erdős famously conjectured that these are the only ones—a deceptively simple question known as the similarity problem. In this talk, I will explore the ideas behind this question and the rich mathematical world it opens: a landscape where geometry, harmonic analysis, and fractal behavior intertwine. Along the way, I’ll share reflections on the nature of math- ematical discovery how simple questions can lead to deep insights—and what it means to grow with a problem over time.

• Dr. Parangama Sarkar (IIT Palakkad) on Algebra
  
  Title: Multiplicities of weakly graded families of ideals
  Abstract
  In this talk, we will prove the existence of multiplicity for a weakly graded fam- ily of ideals which is bounded below linearly. We will explore Minkowski inequality and Rees’criterion for equality of multiplicities in this setting.

• Dr. Pooja Singla (IIT Kanpur) on Representation Theory
  
  Title: On decomposition of the Gelfand-Graev modules of GLn(R)
  Abstract
  Abstract: Let F be a non-Archimedean local field with the ring of integers O and the residue field k, where k is finite of odd characteristic. While the representation of the finite groups of Lie type GLn(k) and the p-adic groups GLn(F) are well explored, the continuous representations of GLn(O) remain comparatively less understood. It is known that any finite-dimensional continuous representation of GLn(O) arises from representations of GLn(R), where R is a principal ideal local ring of finite length. In this talk, we will examine the challenges involved in constructing irreducible representa- tions of GLn(R), emphasizing the key differences from the GLn(k) case. We will then turn our attention to the decomposition of the Gelfand–Graev (GG) module for GLn(R). While the decomposition of the non-degenerate GG modules is well understood and known to be multiplicity-free, the structure of the degenerate GG modules remains largely unexplored. We will discuss some recent results in this direction. This talk is based on a joint work with Archita Gupta.

Coordinators

• Dr. Amrita Ghosh
• Dr. Mallika Roy