An Introduction to Distribution Theory and Applications

Course: An Introduction to Distribution Theory and Applications [May 28 - June 1, 2025]

Abstract: Real-world phenomena often involve shocks and discontinuities, but classical calculus demands smooth solutions, creating a dilemma! Take Burger’s equation: even smooth initial data can evolve into shocking jumps. To resolve this, mathematicians invented distributions, generalized functions where derivatives work "weakly." This sparked a revolution, with entropy, viscosity, and other weak solutions enriching PDE theory. While full rigor needs functional analysis, we’ll explore this powerful framework, extending calculus and Fourier transforms beyond classical limits. In this course, we mainly restrict ourselves to the new calculus of distributions and its properties, including Fourier transform of functions that cannot be defined classically. 

Instructor: Nandakumaran A.K, IISc Bengaluru

Background required: Those with a good background in Distribution Theory and its Applications (M.Sc. first year level) will be able to follow these lectures. We will give an overview of the theory that is accessible to a wide audience. PhD Scholars and young faculty members are also eligible to apply. 

Deadline for application: May 22, 2025.  

The list of selected candidates will be available on the website by 24th May 2025.