- Two Problems of Number Theory, LSR, Delhi, 2009.
- The Isomorphism Conjecture, Talk at CiE, Heidelberg, 2009.
- The P <> NP Problem, CNR Rao Lecture, IIT Kanpur, 2008.
- Rings and Integer Lattics in Computer Science, A series of lectures at Annual Workshop in Computational Complexity, Barbados.
- Numbers of Strange Kind and Their Applications, Talk at Bio-Informatics Institute (Singapore) & Indo-US FoS, (Irvine), 2007.
- Primality Tests Based on Fermat's Little Theorem, Talk at ICDCN, Guwahati, 2006.
- Determinant versus Permanent, Talk at ICM, Madrid, 2006. A slightly different version is here.
- A Short History of "PRIMES is in P", Talk at ICALP, Venice, 2006.
- Is n a Prime Number?, Beeger lecture, Delft, 2006.
- Proving Lower Bounds via Pseudo-random Generators, Talk at FSTTCS, Hyderabad, 2005.
- Fermat's Last Theorem: From Integers to Elliptic Curves, Talk to members of Indian olympiad teams, Mumbai, 2005.
- A Survey of Techniques Used in Algebraic and Number Theoretic Algorithms, Tutorial conducted at Kunming, China, 2005.
- Automorphisms of Finite Rings and Applications to Complexity of Problems, Survey talk at Institute of Science, Beijing, China, 2005.