Room 326

Of Legendrian Knots and First Order Theorem Provers

T V H Prathamesh

IMSc

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 statetements 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.