Nima Rasekh's Academic Home Page

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(deutsche Version)

I am currently a postdoctoral researcher at the Max Planck Institute for Mathematics in Bonn. I am also on the academic job market, seeking tenure track positions.
For more information about me check out:

I am a homotopy theorist, meaning I like to understand how two things are equal. Homotopical thinking has already found many applications throughout mathematics, such as algebra, geometry and mathematical physics, and I am always excited about finding new applications and connections. If you want get a better sense of homotopical thinking you can check out this excellent article by Emily Riehl discussing the rise of higher category theory or this other general science article about the nature of equalities.

In my passion to make homotopical thinking more accessible to a wider range of mathematicians and computer scientists I am also pursuing formalization of mathematics and particularly homotopical structures. You can find my work on my Github page.

I have also taught a course focused on homotopy theory and higher category theory that I would like to expand upon in the future. In the meantime you can find the lecture notes for my course.

Before coming to Bonn I spent three years as a collaborateur scientifique (postdoctoral researcher) at the École Polytechnique Fédérale de Lausanne working in the research group of Kathryn Hess. I was a PhD student at the University of Illinois at Urbana-Champaign, where I worked with my advisor Charles Rezk.

Email: rasekh [at]
Office: B25
Address:Vivatsgasse 7, 53111 Bonn

Current Projects

Here is a summary of some of my ongoing research projects and formalizations that I am pursuing:

  1. Limits in (∞,n)-Categories (joint with Lyne Moser and Martina Rovelli) Paper 1 - Paper 2 - Talk Slides - Talk Recording (by Lyne Moser):
    Developing a theory of limits for weak models of (∞,n)-Categories using double categorical methods and cones, generalizing both recent two categorical developments, as well as (∞,1)-categorical notions of limits. As part of the work we have already completed two papers establishing the necessary (∞,n)-categorical background: A homotopy coherent nerve for (∞,n)-categories and An (∞,n)-categorical straightening-unstraightening construction.
  2. Geometric Structures on Condensed Anima (joint with Qi Zhu) Talk Notes:
    Establishing relevant topos theoretic properties of condensed anima, which play an important role in the context of condensed mathematics established by Clausen and Scholze.
  3. Formalizing Double Categories in Coq Unimath (joint with Benedikt Ahrens, Paige North and Niels van der Weide) Talk Slides 1 - Talk Slides 2 - Talk Notes:
    Formalizing double categories in Coq UniMath with the goal of establishing appropriate univalence principles. A first notion of univalent double category with future prospects can be found in our first paper Univalent Double Categories.
  4. Formalizing ∞-Categories in Rzk:
    Contributing to the formalization of ∞-categories via the proof assistant Rzk first started by Nikolai Kudasov, Emily Riehl and Jonathan Weinberger building on a type theoretic work of Riehl & Shulman and Buchholtz & Weinberger.
  5. ∞-Categories in Non-standard Mathematics Talk Notes 1 - Talk Notes 2 - Talk Recording:
    Studying properties of ∞-categories internal to ∞-topoi with non-standard internal logic, which generalizes results by Martini & Wolf and builds on my work on filter quotient ∞-topoi.

Publications & Preprints & Notes

A chronological list of my papers can be found on my ArXiv page or my Google Scholar page. Thematically, my work breaks down into three broad themes:

Formalization of Homotopy Theory:

Limits in (∞,n)-Categories:

Homotopy Coherent Hochschild Homology:

Other Work: