Prerak Deep

Welcome to my homepage!

I am Prerak Deep. Currently, I am a course instructor at the Indian Institute of Technology Madras for their BS program. 

Previously, I have worked as a visiting scientist in the Stat-Math Unit, Indian Statistical Institute Kolkata under the mentorship of Professor Mahuya Dutta.  

I successfully defended my PhD thesis in August 2025 and am seeking an Academic/research Position at universities/institutions. My PhD thesis title is Round Surgery Presentations of a Closed Oriented 3-manifold and its Contact Analogue. I worked under the guidance of Dr Dheeraj Kulkarni, Assistant Professor at IISER Bhopal, during my PhD. 

In my PhD, we defined round surgeries on framed links and proved that on the 3-sphere, they are equivalent to Asimov's round surgery. Moreover, we gave round surgery presentations for 3-manifolds in terms of framed links in the 3-sphere and discussed a version of Kirby calculus. Further, we generalised these ideas for the contact 3-manifolds. 

My research interests lie in contact manifolds, surgeries on 3-manifolds, and Kirby calculus. Recently, I have worked on round surgeries on 3-manifolds and their contact analogue, the contact round surgery. We introduced the combinatorial framework in terms of framed links for round surgeries on the 3-sphere. I am also interested in Legendrian virtual knots and Lagrangian surface knots in four-dimensional Euclidean space.