Prerak Deep
Prime Minister's Research Fellow
About Me
Welcome to my homepage!
I am a fifth year Ph.D. student at Indian Institute of Science Education and Research Bhopal. I am a recipient of the Prime Minister Research Fellowship. I am working in the field of Geometry and Topology under the supervision of Dr Dheeraj Kulkarni.
Currently, I am working in contact topology, on a problem that involves Kirby's theorem.
I had organised the Geometry and Topology Seminar Series (GaTs) and Graduate Student Seminars at IISER Bhopal.
Annual Progress (May 22-April 23)
This year, we have explored the possibility of the first Kirby move. We observed three necessary conditions to define the contact analogue of the first Kirby move. Later, we found there are diagrams in the literature satisfying those conditions.
I have read the research articles about the Contact k-surgery and Handle moves on a given contact surgery diagram. To understand these research articles, I have gone through some referred research articles, which includes 1. On the classification of tight contact structure on S^1 \times D^2, Lens spaces, and T^2 \times [0,1] by Ko Honda; 2. Contact surgery and symplectic handlebodies by Weinstein; 3. Surgery diagrams for contact 3-manifolds by F. Ding, H. Geiges, A. Stipsicz; 4. Knots and contact geometry I : Torus knots and the figure eight knot by J. Etnyre and K. Honda; and 5. Legendrian and transversal knots by J. Etnyre. Moreover, I also covered my background in Convex surface theory, Lutz twists, and Bypasses.
Advisor Information
Dr Dheeraj Kulkarni is my research advisor. He is an assistant professor at the Department of Mathematics, Indian Institute of Science Education and Research Bhopal. Broadly, his interest lies in Geometry and Topology. In particular, he is interested in Contact and Symplectic Topology.
Contact details:
Email: dheeraj@iiserb.ac.in
Telephone: +91 755 269 1277
Group Homepage: https://sites.google.com/a/iiserb.ac.in/homepage-dheeraj-kulkarni/
My Contact Details:
Email: prerakd@iiserb.ac.in
Office Address:
#106, AB 1A (Gravity), IISER Bhopal, Bypass Road, Village Bhauri, Bhopal- 462066, Madhya Pradesh, India.
Telephone: +91 755 269 1274