branko juran
Department of Mathematical Sciences
Universitetsparken 5, Building 4
2100 Copenhagen Ø
Office 04.4.03, bj(at)math.ku.dk
+453532984
I am a third year PhD Student at the Copenhagen Centre for Geometry and Topology. My supervisor is Jesper Grodal. In September 2025, I will join Markus Hausmann's research group at the University of Bonn.
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 Kaufmann Maxime Ramzi Rin Ray Lea Kornau Ryan Quinn Priya Kaveri Robert Burklund Jan Steinebrunner Adela Zhang