Prahladh Harsha
Tata Institute of Fundamental Research, Mumbai
Prahladh Harsha is Professor at Tata Institute of Fundamental Research, Mumbai. He obtained his PhD under the supervision of Professor Madhu Sudan from Massachusetts Institute of Technology (MIT), and he completed his postdoctoral work at Microsoft Research-Silicon Valley, and was a research assistant professor at the Toyota Technological Institute at Chicago. He was elected Fellow of the Indian Academy of Sciences in 2024.
Session 1C: Inaugural Lectures by Fellows/Associates
Swagata Dasgupta
Solving linear high-order differential equations in nearly linear time
Standard divide-and-conquer methods are used to obtain nearly linear time algorithms for computing modular inverses of polynomials. How these methods can be extended to obtain similar nearly linear time algorithms for solving high-order differential equations will be explained. More precisely, given a $(m+2)$-variate polynomial $Q(x,y_0,\dots,y_m) = A(x) + \sum_{i = 0}^m B_i(x) * y_i$, How to obtain all low-degree polynomials $f(x)$ that satisfy the following differential equation will be shown: $Q\left(x, f(x), \frac{df}{dx}, \dots,\frac{d^m f}{dx^m}\right) \equiv 0$. Such differential equations arise naturally in several settings. How they help to obtain nearly linear time list-decoding algorithms for univariate multiplicity codes will be illustrated.