Chennai Mathematical Institute


2.00 pm, Lecture Hall 1
Of Legendrian Knots and First Order Theorem Provers

TVH Prathamesh
Postdoctoral Fellow at Institute of Mathematical Sciences, Chennai.


Legendrian knots are knots in a contact manifold such that the tangent at each point lies in the associated contact hyperplane at the point. First Order Theorem Provers refers to computer softwares that can prove results or produce counter examples of statements expressed in first order logic, with the axioms of the theory as the input.

In this talk, I will discuss a new class of `combinatorial' invariants that we discovered (in a joint work with Dheeraj Kulkarni) of Legendrian knots, that we call Legendrian racks. These invariants can be seen as a modification of the rack invariants of (topological) knots called quandles.

The distinguish feature of these invariants is that through these invariants, one can use first order theorem provers to distinguish Legendrian knots. This talk shall contain a discussion both the mathematical and computational aspects of our work, and the interactions between the two. It will also contain a demonstration of the computational part of the work.

The talks should be accessible to everyone. No prerequisite knowledge of first order logic, knot theory or contact geometry will be assumed.