Lonely Runner Conjecture, proposed by Jörg M. Wills and so nomenclatured by Luis Goddyn, has been an object of interest since it was first conceived in 1967: Given positive integers k and n1,n2,...,nk there exists a positive real number t such that the distance of t·nj to the nearest integer is at least 1\(k+1), ∀ 1 ≤ j ≤ k. The problem that originated in Diophantine approximation almost 6 decades ago, is still widely open. Through this talk I will attempt to share some interesting insights that have flown through academic circles over the long steady life of the problem, along with some new key results.

Short Bio:
Avinash Bhardwaj is presently a faculty member in the Department of Industrial Engineering and Operations Research at IIT Bombay. His research interests broadly span mathematical optimization with particular interests in discrete and combinatorial optimization.