Frontiers in Mathematics is an intensive three-day workshop in Mathematics held at Kerala School of Mathematics (KSoM), in association with the National Board for Higher Mathematics (NBHM), for advanced graduate students, research scholars and postdoctoral fellows.

It is a biannual event, held each year around March and October. Each edition is built around a simple idea: devote one full day to one topic. A leading specialist takes you from the foundations all the way to the state of the art, through a series of lectures complemented by tutorial and problem-solving sessions. It is an opportunity for focused, deep learning, and collaboration.

The lectures for this edition are as follows:

• Theory of Fourier Multipliers by Prof. Parasar Mohanty

  Abstract. In this three series lectures we will be discussing the basics of Fourier multipliers on Euclidean Groups.

  Lecture 1: Introduction to Multipliers: In this lecture, we will first briefly recall the basic properties of the Fourier transform on $\mathbb{R}^n, \mathbb{T}^n$ and $\mathbb{Z}^n$. We will then introduce the multiplier spaces $M_q^p$ and characterize the spaces $M_2^2, M_1^1$ and $M_p^1$. One can show that $M_q^p = \{0\}$ if $q < p$. For $p \ge q$, we will see that the elements of $M_q^p$ correspond to convolution operators whose kernels are tempered distributions. Finally we will prove that $M_p^p \subseteq L^\infty(\mathbb{R}^n)$.

  Lecture 2: Transference Principle: In this lecture, we will discuss transference methods and explore the relationship between the multiplier spaces $\text{of }~\mathbb{R}^{n}$, $\mathbb{T}^n$, and $\mathbb{Z}^n$.

  Lecture 3: Ball Multipliers: We will introduce Besicovitch sets and discuss one of Fefferman’s fundamental results on ball multipliers.

• Combinatorial Models in Representation Theory by Prof. K. N. Raghavan

  Abstract to be annouced soon.

• Probability by Prof. Manjunath Krishnapur

  Precise topic to be annouced soon.

We welcome applications from motivated participants across India. Local hospitality will be provided. Limited funding is available to support travel expenses.

Registration form

More details coming soon!