Postdoc and PhD research interests – University of Copenhagen

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Symmetry and Deformation > About the centre > Postdoc/PhD research

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.

Postdocs PhD students


Research interests

Postdocs


Sara E. Arklint (PhD, Copenhagen 2012): My research is concerned with classification of nonsimple (purely infinite) C*-algebras. So far I've been focusing on the classification functor filtered K-theory, and on the classification of Cuntz-Krieger algebras and graph algebras.

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. 

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 non-exact 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 homotopy-theoretic approach to reciprocity laws. This approach is based on the equivalence between the category of finite free Z-modules, which can be thought of as number-theoretic, and the category of tori, which can be thought of as topological. Combined with the machinery of algebraic K-theory, this equivalence allows to use topological arguments to obtain number-theoretic results.

Márton Hablicsek (PhD, University of Wisconsin-Madison 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 non-equivariant topology.

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 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.

Rasmus Sylvester Bryder (advisors: M. Musat and M. Rørdam): My research interests lie in the field of operator algebra. At the moment I'm looking into the relationship between groups and their reduced group C*-algebras, with an overall goal being to determine how different group C*-algebras can be from other classes of C*-algebras.

Benjamin Böhme (advisior: J. Grodal): I am interested in equivariant algebraic topology, especially in the various homotopy theories of G-spaces and G-spectra. Very similar to classical ring theory, idempotents in the Burnside ring A(G) yield splittings of G-spectra. However, not much is known about the "algebraic" properties of these decompositions: In what way do (E-infinity) 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.

Martin Søndergaard Christensen (advisor: M. Rørdam): I am primarily interested in the theory of operator algebra, in particular the classification of C*-algebras. Currently I am studying certain divisibilty and comparibility properties of C*-algebras A, usually expressed in terms of the Cuntz semigroup Cu(A), in an effort to understand the relationship between these properties and structural properties of the associated central sequence algebra.

Zhipeng Duan (advisor: J.M. Møller): My PhD project is concerned about the K-theory of p-posets: More concretely, I will compute the homology groups and K-theory of the p-posets of some specific finite groups G and verify the Knörr-Robinson'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 G-invariant 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. 

Isabelle Laude (advisor J. Grodal): My primary interest is the connections between group theory and homotopy theory, particularly in the case of p-local finite groups and localities. I study mapping spaces with target the classifying space for a p-local finite group to understand the homotopical analogs of group theoretical concepts such as elements of p-power order and centralizers for the classifying space of a p-local finite group.

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.

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

 

Philipp Schmitt 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.