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