Mathematisches Institut der Universität Bonn
Endenicher Allee 60
53115 Bonn
Office 4.012 juran(at)math.uni-bonn.de
+49228733641

I am a PostDoc at Markus Hausmann's research group at the University of Bonn.

Before that, I was a PhD student at the Copenhagen Centre for Geometry and Topology, working with Jesper Grodal.

Research Interest: Homotopy theory (equivariant, but recently also motivic), higher category theory. I also like manifolds.

Prepublications

• A genuine equivariant recognition principle for finite groups, preprint, 2025

For G a finite group and V a finite dimensional real G-representation, we prove that an E_V-algebra is equivalent to a V-fold loop space if and only if A^H is group-like for all such that dim V^H ≥ 1.

• On the K-theory of algebraic tori, joint with Bai, Carmeli, Riedel, preprint, 2025, submitted

Given an algebraic torus, by delooping the coweight lattice, one obtains a topological torus with an action of the Galois group. We identify the algebraic K-theory of the algebraic torus with the equivariant Bredon homology of the topological torus with coefficients the K-theory of the base field.

• On orthogonal factorization systems and double categories, preprint, 2025, submitted

We prove that the ∞-category of orthogonal factorization systems embeds fully faithfully into the ∞-category of double ∞-categories. Moreover, we prove an (un)straightening equivalence for double ∞-categories, which restricts to an (un)straightening equivalence for op-Gray fibrations and curved orthofibrations of orthogonal factorization systems.

• Orbifolds, Orbispaces and Global Homotopy Theory, preprint, 2020, to appear in Algebraic & Geometric Topology

My bachelor's thesis

Talks

• July 2024, TU Graz, Topology Seminar, The algebraic K-theory of algebraic tori via equivariant homotopy theory
• August 2024, University Münster, Young Topolgist Meeting, The algebraic K-theory of algebraic tori via equivariant homotopy theory
• September 2024. Utrecht, European Autumn School of Mathematics, The algebraic K-theory of algebraic tori via equivariant homotopy theory
• April 2025, Harvard, Babytop, Equivariant recognition principle
• June 2025, Utrecht University, Topology Seminar, Equivariant recognition principle

Conferences organized

• September 2023, Workshop on Parametrized homotopy theory, Copenhagen
• April 2024, Masterclass on Homotopical methods in manifold theory, Copenhagen
• February 2025, Masterclass on Cobordism categories, Copenhagen

Collaborators

Florian Riedel Qingyuan Bai Shachar Carmeli Natalie Stewart

Other Friends

Shai Keidar Oscar Harr Kristian Toccacelo Fadi Mezher Christian Kremer Marie-Camille Delarue Ruth Wild Azélie Picot Vignesh Subramanian Jordan Levin Dani Kaufman Maxime Ramzi Rin Ray Lea Kornau Ryan Quinn Priya Kaveri Robert Burklund Jan Steinebrunner Adela Zhang Leor Nehauser Rodrigo Fernandes