Gallery - Lodha Mathematical Sciences Institute (LMSI)

The Vision Behind the Lodha Mathematical Sciences Institute (LMSI)

LMSI seeks to build upon India’s rich tradition of mathematical excellence and aims to serve as a beacon of innovation and rigour, attracting the best minds from around the world and fostering a culture of intellectual curiosity and discovery. Hear from some of our founding leaders, Abhishek Lodha, Ashish Kumar Singh and Dr. V Kumar Murty, expressing their optimis

Good Locally Testable Codes | Prof. Alex Lubotzky

This lecture explores locally testable error-correcting codes that achieve constant rate and distance, constructed using Ramanujan Left/Right Cayley square complexes. These codes extend expander codes into higher dimensions and connect to deep ideas from group theory and topology. The talk also introduces the broader landscape of expander graphs and High Dimensional Expanders (HDX), highlighting their growing importance in mathematics and computer science, along with emerging applications and research directions.

A Triple Convolution Sum of the Divisor Function | Prof Ram Murty

We consider triple convolutions of the shifted divisor function and explore a conjecture of Browning through the lens of the theory of arithmetical functions of several variables. We obtain unconditionally upper and lower bounds of the right order of magnitude that supports this conjecture. This is joint work with Biswajyoti Saha and Bikram Misra.

Distribution of Mordell-Weil Ranks, Discriminants and Special Primes | Prof Dinesh Thakur

We describe some results, guesses and heuristics, and discuss some arithmetic statistics questions in both the number field and function field contexts. In more details, we discuss heuristics and evidence on average ranks of various families of elliptic curves over number fields. Then we discuss statistical distribution of primes of rational function field according to their (refined) discriminants, and characterization and statistics of analogs of Wilson and Wieferich primes for function fields.

6 - Torsion in class groups of Quadratic Fields | Prof Frank Thorne

In this lecture, Prof. Frank Thorne examines the distribution and behavior of 6-torsion elements in the class groups of quadratic fields. The discussion focuses on recent quantitative results and the broader implications for conjectures in arithmetic statistics and algebraic number theory.

Arithmetic purity of Strong Approximation and the Geometric Sieve | Prof Zhizhong Huang

(Based on joint work with Y. Cao (Jinan) and R. Zhang (Chongqing).Given a nice variety over a number field that satisfies strong approximation (i.e. rational points are dense in the adelic space), a question first proposed by O. Wittenberg asks whether this property holds true when one removes any Zariski closed subset of codimension at least two. We shall present several qualitative and quantitative positive answers to Wittenberg’s question. Our method combines effective counting results from homogeneous dynamics and various sieve methods, e.g. the affine linear sieve (developed by P. Sarnak et al.) and the geometric sieve (first discovered by T. Ekedahl).