Intern Review Anish Kulkarni Stony Brook

Intern Experiences Summer 2018

Simons Center for Geometry and Physics, Stony Brook University

Anish Kulkarni

Process of securing the intern:

I got selected for the S N Bose scholarship. After that, I wrote emails to professors in the US asking for a summer internship opportunity. Logistics: For US visa application: Earlier the better. There's an expedited visa processing option you can use if you are eligible. I used it. Afair, you get one shot at an expedited appointment. Be sure to provide enough proof of eligibility.

What was I working on?

Broad area: Theoretical Physics / Mathematical physics.
Index theory is used to study differential operators on manifolds and topology of those manifolds. In physics, this is useful in anomalies in QFT, topological condensed matter phenomena, etc.

Index theorems relate analytic and topological properties of a manifold. Some of these theorems can be "proved" by considering a supersymmetric quantum mechanical theory on the manifold. My project was to study these proofs and extend them to other index theorems where such a proof is not known. These proofs are useful in physics because they give new methods to compute the index and related quantities.

Theories used:

Essential theories: QFT (path integrals for real and grassmann fields, quantization), GR, some group theory (spinors) and some basic Differential geometry beyond what is typically covered in an undergraduate GR course (I picked up this last topic while doing the project).

Courses that helped me:

Supervised Learning Project (Intro to Quantum Field Theory), General Relativity, Quantum Mechanics 3 (Relativistic).

What did I learn during the internship?

Academic: Learnt how to dig for useful literature. Its worthwhile to know the motivation behind a research problem (big picture). It is very useful to talk to people (post-docs, grad students, professors) outside your project, find out what they're doing, why they're doing it.

Non-academic: Subsistence level cooking.

Places I went to: 

Chicago, New York, Boston.

Contact Details:

anish245@gmail.com