My current research focuses on the burgeoning field of synthetic homotopy theory. I am interested in exploring the application of methods from synthetic homotopy theory in simplicial, cubical, equivariant homotopy theory, and K-theory.

I am also working on formalization of Reedy categories in Lean proof assistant.


PhD Thesis

Published in University of Birmingham (UK), 2019

Under supervision of Steve Vickers

First Year Progress Report

Published in School of Computer Science, University of Birmingham, 2015

A general report of the first year including background studies submitted to my thesis committee

Talks And Presentations

Toposes In Como

June 29, 2018

Conference talk, Toposes in Como, Chiostro di Sant’Abbondio, Università degli Studi dell’Insubria, Como, Italy

Fibrations Of Toposes

September 16, 2017

Conference talk, PSSL 101, School of Mathematics, University of Leeds, Leeds, UK

Topology Seminar at Johns Hopkins (2021-2022)

With Maru Sarazola and Tim Campion we are organizing Topology Seminar at Johns Hopkins If you are interested in giving a talk, either in person at Hopkins or via Zoom, please drop a line.

Reading Group on Arithmetic Universes (2018-2019)

With Alexander Oldenziel, Joost van Dijk and a few others we have an informal weekly reading sessions on Arithmetic Universes and Goedel's incompleteness theorem in Utrecht and Amsterdam.

CARGO (2016-2019)

I am one of the organizers of category theory reading group (CARGO). The meetings takes place at the school of computer science on a weekly basis. The participants are mostly PhD students and research fellows in theoretical computer science.

Read more about it here .

  • From 2015-2017, CARGO meetings used to takes place at the school of computer science on every Tuesday at 2:00 p.m. in room 245. For the academic year of 2017-2018 we have our meetings on Thursdays at 11:00 a.m. in the same room.
  • Here is the archive of talks: CARGO archive. Feel free to subscribe to our mailing list. Let me also mention the archive of our Theory Seminars talks on Fridays. I have given four talks in theory seminars and numerous talks in CARGO. Sometimes I find enough time and I write the notes of the talks which can be found in below.
  • Here is a list of topics considered to be discussed in Autumn 2017 in Category Reading Group seminars as well as informal archive for suggested topics since Summer 2015: Potential topics and Informal archive.

Expository Papers And Notes

Writing notes helps me to grasp a mathematical concept or construction and they become less elusive in my mind. Here are the notes from some of my talks for which I had time to type them up. Any reports of mistakes and errors from the reader are always welcome.

A topos without points


An example of a topos (from logic) that does not have any points.

A learning wishlist


A list of tricks/theorems/constructions/concepts/theories I wished to know but never had time/opportunity to learn them!

Principal Bundles

Incomplete as they stand (April, 2018)

A review of theory of principal bundles and higher principal bundles

Principal Bundles

Incomplete as they stand (April, 2018)

A review of theory of principal bundles and higher principal bundles

Three Sites Of Relative Schemes

Incomplete as they stand (April, 2018)

Warning: in construction! We introduce three Grothendieck topologies on the category of based schemes; the Zariski, the étale and the fpqc topology

Academic Records

Here is my Curriculum Vitae