Postdocs and PhD students
Current Postdocs and PhD students  Past Postdocs and PhD students
The current postdocs and PhD students at the Centre for Symmetry and Deformation are here listed with photos and research interests. Click on a name to jump to research interests.
Research interests
Postdocs

Tobias Barthel (PhD, Harvard/Oxford 2014): I am interested in stable homotopy theory and its interactions with representation theory and algebraic geometry. In particular, much of my work is inspired by ideas from chromatic and transchromatic homotopy theory. More recently, I have also been thinking about various forms of (local) duality in algebra and topology.


Daniel Bergh (PhD, Stockholm University): My reserach is in algebraic geometry. More specifically, I am interested in the theory of algebraic stacks, resolution of singularities and motivic invariants. I have also done some work in noncommutative geometry. 

Kaj Börjeson (PhD, Stockholm University 2017): I am interested in topology and algebra, especially topics connected to Koszul duality, rational homotopy theory, Hochschild cohomology, operads and BValgebras. 

Christopher Cave (PhD, Southampton 2015): My research is in coarse geometry which lies in the intersection of topology, geometry and operator algebras. My current interest in studying exact and nonexact groups and their consequences. I also have a lot of interaction with geometric group theory, in particular sequence of expanders graphs and their applications to geometric group theory. 

Dustin Clausen (PhD, MIT 2013): I am interested in connections between homotopy theory and number theory. Currently I'm studying a homotopytheoretic approach to reciprocity laws. This approach is based on the equivalence between the category of finite free Zmodules, which can be thought of as numbertheoretic, and the category of tori, which can be thought of as topological. Combined with the machinery of algebraic Ktheory, this equivalence allows to use topological arguments to obtain numbertheoretic results. 

Simon Gritschacher (PhD, University of Oxford 2016): My research is in algebraic topology and I am specifically interested in generalised cohomology theories, and in spaces of representations and their homotopy theory. 

Márton Hablicsek (PhD, University of WisconsinMadison 2014): My research is in algebraic geometry with focus on Derived Algebraic Geometry and Combinatorial Algebraic Geometry. 

Rune Haugseng (Phd, Massachusetts Institute of Technology 2013): I am interested in algebraic topology and higher category theory, and their connections with other areas such as (derived) geometry and (topological) quantum field theory. 

Markus Hausmann (Phd, University of Bonn, 2016): My research is in algebraic topology, in particular different forms of equivariant homotopy theory. At the moment I am studying global equivariant spectra and try to apply them to problems in equivariant and nonequivariant topology. 

Anssi Lahtinen (PhD, Stanford University, 2010): My research interests lie in algebraic topology and homotopy theory, in particular string topology of classifying spaces and its applications to group homology and cohomology. 

Alexandra Muñoz (PhD, University of New York): My research interests include developing applications of mathematics and physics to better describe cellular function, generalize intracellular chemistry, and remap the cytosolic space. 

David Sprehn (PhD, University of Washington 2015): I work in group cohomology. I am studying the modular cohomology of the general linear groups over finite fields, and of other finite groups of Lie type. More generally, I am interested in group actions and characteristic classes.


Gábor Szabó (PhD, University of Münster 2015): My research focuses on the fine structure of simple C*algebras and the classification of group actions on these objects. I am also interested in the structure of crossed products, in particular regarding the interplay between C*algebras and topological dynamics. 
PhD students

Clemens Borys (advisors: M. Rørdam & M. Musat): My research focuses on the interplay of groups, groupoids and C*algebras. For my Master's thesis I constructed a topological bicategory of C*correspondences, establishing a notion of continuous actions by correspondences, such that these reflect the original notions of continuous fields of C*algebras and C*correspondences by Fell. In a first research project, I will study recent techniques to understand the structure of groupoid C*algebras. 

Kevin Aguyar Brix (advisor: S. Eilers): I am interested in the interrelation between topological dynamical systems and their induced operator algebras.
More precisely, I study to which degree relations such as flow equivalence, orbit equivalence or conjugacy is reflected and remembered in the corresponding C*algebras along with its diagonal.


Benjamin Böhme (advisior: J. Grodal): I am interested in equivariant algebraic topology, especially in the various homotopy theories of Gspaces and Gspectra. Very similar to classical ring theory, idempotents in the Burnside ring A(G) yield splittings of Gspectra. However, not much is known about the "algebraic" properties of these decompositions: In what way do (Einfinity) ring structures of the pieces relate to that of the original spectrum? What information do we obtain when restricting attention to localizations or completions, one prime at a time? The goal of my PhD project is to find answers to some of these questions. 

Zhipeng Duan (advisor: J.M. Møller): My PhD project is concerned about the Ktheory of pposets: More concretely, I will compute the homology groups and Ktheory of the pposets of some specific finite groups G and verify the KnörrRobinson's conjecture in these cases. 

Joshua Hunt (advisor J. Grodal): I will be investigating and calculating Picard groups in algebra and topology. It is expected that this will be done through derived induction theory, relating a Ginvariant object to those obtained by restricting to collections of subgroups. 

Mikala Ørsnes Jansen (advisor: S. Galatius): My research will be in the interplay between homology of groups and the theory of manifolds. Arithmetic groups share many features with diffeomorphism groups of manifolds. One goal will be to better understand the interplay between these two areas. 

Manuel Krannich (advisor: N. Wahl): Currently, my research revolves around homological stability of topological groups. Besides that, I am interested in bordism categories and moduli spaces of manifolds—mainly initiated through my master’s thesis.


Malte Leip (advisors: J. Grodal & L. Hesselholt): My interests lie in homotopy theory, particularly where homotopy theory and algebra meet in the form of higher algebra. My PhD project has a working title of "Topological Hochschild Homology of Log Schemes". 

Espen Auseth Nielsen (advisor: N. Wahl): I am interested in homotopy theory and homotopical algebra. I am studying the Hochschild homology of E_{n}algebras. 

Valerio Proietti (advisor: R. Nest):
In Paris I started working on my Master's thesis on the gap labeling conjecture. This is a problem which originates in solidstate physics and is expressed in the language of noncommutative geometry. The temporary sketch of my PhD thesis is based on the study of Ktheoretic and cohomological invariants for C*algebras arising from dynamical systems associated to actions of finiterank abelian groups. These dynamical systems might emerge from physical contexts, therefore the interplay between modern physics and noncommutative geometry will play a role.


Philipp Lothar Schmitt (advisor: R. Nest): It’s primarily in the field of formal deformation quantization and its links to strict quantization. In my master thesis, I worked on a construction of strict Wick type star products on coadjoint orbits due to Karabegov. I could find a locally convex topology on the sphere with respect to which this star product becomes continuous. 