# About me

My name is Guillaume Brunerie and I’m a researcher in mathematics and computer science working mainly in *homotopy type theory*, a field combining mathematics (in particular homotopy theory, category theory, and constructive mathematics) and theoretical computer science (in particular type theory, logic, and proof assistants).

I am currently a postdoctoral researcher in the Logic Group of Stockholm University since September 2018.

Previously, I was a postdoctoral member of the School of Mathematics of the Institute for Advanced Study in Princeton, New Jersey.

(last updated in June 2019)# Curriculum Vitae, papers and talks

## CV

You can find my full CV here.

## PhD thesis

From September 2013 to August 2016, I was a PhD student at the Laboratoire J.A. Dieudonné under the supervision of Carlos Simpson. I successfully defended my thesis on June 15th 2016.

*On the homotopy groups of spheres in homotopy type theory*(187 pages, in English, with a 20-page summary in French at the end). You can also download the slides of the oral presentation.

## Publications

*The James construction and*. Guillaume Brunerie. Journal of Automated Reasoning, Special Issue on Homotopy Type Theory and Univalent Foundations, Springer. doi:10.1007/s10817-018-9468-2.*π*_{4}(𝕊^{3}) in homotopy type theory*A Cubical Approach to Synthetic Homotopy Theory*. Dan Licata and Guillaume Brunerie. 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2015), pages 92–103, IEEE. doi:10.1109/LICS.2015.19.. Dan Licata and Guillaume Brunerie. Certified Programs and Proofs (CPP 2013), volume 8307 of Lecture Notes in Computer Science (LNCS), pages 1–16. Springer. doi:10.1007/978-3-319-03545-1.*π*_{n}(*S*^{n}) in Homotopy Type Theory

## Preprints and other writings of interest

*Cartesian Cubical Type Theory*. Carlo Angiuli, Guillaume Brunerie, Thierry Coquand, Kuen-Bang Hou (Favonia), Robert Harper, Daniel R. Licata. Preprint.*The Steenrod squares in homotopy type theory (extended abstract)*. Guillaume Brunerie. TYPES 2017*Homotopy Type Theory: Univalent Foundations of Mathematics*. The Univalent Foundations Program (collective book), Institute for Advanced Study, 2013

## Slides of talks

*Computer-generated proofs for the monoidal structure of the smash product*, HoTTEST Seminar, November 2018*Experiments in cubical type theory*, Joint Mathematics Meetings, AMS Special Session on Homotopy Type Theory (a Mathematics Research Communities Session), San Diego, California, January 2018*Homotopy type theory: working invariantly in homotopy theory*, Short talks by postdoctoral members, School of Mathematics, IAS, Princeton, New Jersey, September 2017*Invariant homotopy theory in the univalent foundations*, Short talks by postdoctoral members, School of Mathematics, IAS, Princeton, New Jersey, September 2016*Custom definitional equalities in Agda*, in the “Univalent Foundations and Proof Assistants” session of the International Congress on Mathematical Software (ICMS 2016), Berlin, Germany, July 2016*A Cubical Approach to Synthetic Homotopy Theory*, at LICS 2015, Kyoto, Japan, July 2015*Homotopy Type Theory*, at the conference “Journées francophones des languages applicatifs”, Fréjus, France, January 2014*An elementary definition of weak ∞-groupoids*, in the session “Progress in Higher Categories” of the CMS Summer Meeting, Halifax, Nova-Scotia, Canada, June 2013*Le théorème de complétude de Gödel*(in French), in the “Séminaire de mathématiques des élèves du lycée Louis le Grand”, Paris, France, February 2009

## Videos of talks

*Computer-generated proofs for the monoidal structure of the smash product*, for the electronic seminar HoTTEST*Homotopy type theory: working invariantly in homotopy theory*, Short talks by postdoctoral members, School of Mathematics, IAS, Princeton, New Jersey, September 2017*Invariant homotopy theory in the univalent foundations*, Short talks by postdoctoral members, School of Mathematics, IAS, Princeton, New Jersey, September 2016*The fourth homotopy group of the three-dimensional sphere*), at the “Workshop on Homotopy Type Theory and Univalent Foundations of Mathematics, Fields Institute, Toronto, Ontario, Canada, May 2016*Homotopy Theory in Type Theory*, with Dan Licata and Peter Lumsdaine, at the seminar of the Institute for Advanced Study, Princeton, New Jersey, April 2013*The James construction and*, at the seminar of the special year of the IAS, Princeton, New Jersey, March 2013*π*_{4}(*S*^{3}), at the seminar of the special year of the IAS, Princeton, New Jersey, February 2013*π*_{2}(*S*^{2}) in HoTT*Weak infinity-groupoids, part I*(no video for part II), at the seminar of the special year of the IAS, Princeton, New Jersey, January 2013

## Others writings

- A poster on homotopy type theory (in French, 2015).
- A Python script generating Agda code for semi-simplicial types, truncated at any given level (script, result for
*n*= 10) *Structure topologique de l’espace des réseaux unitaires*, initiation to research on the proof that the space of unitary lattices of ℝ^{2}is homemorphic to the complement of the trefoil knot in*S*^{3}(in French, 2009).*Densdisigeblaj spacoj*, a proof of a theorem in point-set topology: every metric space without isolated points can be partitioned in two dense subspaces (in Esperanto, 2008).

# Other interests

I’m also interested in programming and free software, and I have some experience with various programming languages like Javascript, Python, Lua, OCaml, C, shell scripting, Haskell. Some of my projects are available on my GitHub page.