Apurva Nakade

I'm a postdoc at University of Western Ontario, working with Dan Christensen and Chris Kapulkin.

Email (left as an exercise to the reader)
Office Hours all the time
Job Stuff ceeeeEEEEEVVVVVeeeee
Research Statement

Currently, I'm teaching Lean at the USA/Canada Mathcamp.

If you need a recommendation letter from me, please read this very short and useful page first.

Teaching

Too much sanity may be madness
and the maddest of all,
to see life as it is
and not as it should be.

Directed Reading Program

In the past, I've supervised the following reading projects.

  • Jacob Fabe, Fundamental Group from Topology by Munkres (DRP, Fall 2020)
  • Tim Yau, An Introduction to Manifolds by Loring Tu. (DRP, Fall 2019)
  • Ezra Erives, Differential Geometry and Lie Groups for Physicists by Marián Fecko. (Canada/USA Mathcamp, 2019)
  • Hannah Wool, Topology by Munkres. (DRP, Spring 2019)
  • Sydney Timmerman, Differential Geometry and Lie Groups for Physicists by Marián Fecko. (DRP, Fall 2018)
  • Edgar Wang, Algebraic Topology by Hatcher (Ch 1). (Canada/USA Mathcamp, 2018)
  • Alan Yan, Algebraic Topology by Hatcher (Ch 1). (Canada/USA Mathcamp, 2018)
  • Eric Cochran, An Introduction to Manifolds by Loring Tu. (DRP, Spring 2018)
  • Chris Chia, The Knot Book by Adams Collins. (DRP, Fall 2017)

Research

I work in the area of algebraic topology and homotopy theory. I have been working on the following projects to varying degrees of success.

2-groups in Equivariant Elliptic Cohomology

I got serendipitously involved in this project thanks to an MRC Workshop. The goal of this project is to find a 2-categorical interpretation of some of naturally occurring objects (Drinfield double of a group) in mathematical physics and extend them using ideas from Equivariant Elliptic Cohomology.

An application of the h-principle to Manifold Calculus.

This was my PhD thesis, in which I applied homotopy theoretic techniques to study problems for differential geometry. Here is the paper (arXiv version) based on the thesis (Updated on: May 07, 2019). Here are some notes [1], [2] from the talks I gave on this topic.

HoTT and Proof-checking using computers

This is one of the new areas that I am getting involved in thanks to being at UWO. I hope to write more on this soon.

Other projects

  • Spectral lifts of Soergel bimodules, joint with V. Lorman (in preparation)
  • Finding loop space structures in exotic Kac-Moody groups
  • Equivariant Embedding Calculus
  • Protein folding using Markov chains
    During my undergrad, I briefly worked on a project involving some protein folding models using basic linear algebra.
    Information Processing Letters, IPL4801.

Etc.

Fun for me is reading books and writing on my blog about random things. I love to design websites like this one, and my blog's theme using Hugo. I dance whenever and whatever I can. My newest obsession is West Coast Swing. I do yoga at yogashack. I love to travel. I type in dvorak.

In a past life (JHU, Baltimore) I was involved with and highly recommend the following: