Video Lectures

I shall review recent progress in computing D-instanton contribution to string theory amplitudes

Contact topology is the study of certain geometric structures on odd dimensional smooth manifolds. A contact structure is a hyperplane field specified by a one form which satisfies a nondegeneracy condition called maximal non-integrability. The...

Efficient verification of computation is fundamental to computer science and is at the heart of the P vs. NP question. Recently it has had growing practical significance, especially with the increasing popularity of blockchain technologies and cloud...

In this talk, I will describe the construction of contact structures on higher-dimensional spheres with exotic fillability properties. These can then me implemented on more general manifolds via connected sum, yielding a host of exotic higher...

I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-cluster models in the plane with various general boundary conditions.

The results are rigorous for the FK-Ising model...

Filtered Lagrangian Floer homology gives rise to a barcode associated to a pair of Lagrangians.  It is well-known that the lengths of the finite bars and the spectral distance are lower bounds of the Lagrangian Hofer metric. In this talk we are...

Enumerative mirror symmetry is a correspondence between closed Gromov-Witten invariants of a space X, and period integrals of a family Y. One of the predictions of Homological Mirror Symmetry is that the closed Gromov-Witten invariants can be...

Powerful homology invariants of knots in 3-manifolds have emerged from both the gauge-theoretic and the symplectic kinds of Floer theory: on the gauge-theoretic side is the instanton knot homology of Kronheimer-Mrowka, and on the symplectic the...

Solitons are particle-like solutions to dispersive evolution equations whose shapes persist as time evolves. In some situations, these solitons appear due to the balance between nonlinear effects and dispersion, in other situations their existence...

It is an open question as to whether the prime numbers contain the sum A+B of two infinite sets of natural numbers A, B (although results of this type are known assuming the Hardy-Littlewood prime tuples conjecture).  Using the Maynard sieve and the...