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branko juran

Department of Mathematical Sciences

Universitetsparken 5, Building 4

2100 Copenhagen Ø

Office 04.4.03, `bj(at)math.ku.dk`

I am a second year PhD Student at the Copenhagen Centre for Geometry and Topology. My supervisor is Jesper Grodal.

*Research Interest:* Stable homotopy theory (equivariant, but recently also motivic), higher category theory

*Projects:* Some of the following projects are in a very early stage. Please get in contact with me if you want to know about details:

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

Algebraic K-theory of algebraic tori (joint with Bai, Carmeli, Riedel): 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.

Geometric fixed points of global spectra (joint with Linskens): We aim to give a description of global spectra in terms of their geometric fixed points, i.e as a partially bilax limit.

#### Prepublications

[1] Orbifolds, Orbispaces and Global Homotopy Theory, preprint, 2020.