Members and their research interests

The research interests of current and past members of GeoTop Centre are listed below. 

Faculty

Karim Adiprasito

Karim Adiprasito

I am interested in combinatorics, and its connections to algebra and geometry. Broadly speaking, I am interested in encoding smooth and continuous structure in discrete fashion, and then use combinatorial methods to solve them. Currently, I am thinking about the Singer conjecture for aspherical manifolds, and its connections to Hodge Theory of algebraic varieties, and complexity problems for triangulated manifolds.

UCPH page 

Dustin Clausen

Dustin Clausen

So far I have mainly studied algebraic K-theory and its relations to homotopy theory and arithmetic.  More recently I've been studying functional analysis and analytic geometry.

UCPH page

Tobias Holck Colding

Tobias Holck Colding (MIT)

Research interests: Differential Geometry, Partial Differential Equations.

MIT page

Søren Galatius

Søren Galatius

I am interested in aspects of algebraic and geometric topology, algebraic geometry, and number theory.  In particular smooth and topological manifolds, moduli spaces, K-theory, Galois groups and their representations.

UCPH page

Jesper Grodal

Jesper Grodal

My research interests lie in algebraic topology, group theory, and representation theory, and their interactions. This includes group cohomology, equivariant homotopy theory, classifying spaces, group actions via homotopy methods, and the use of homotopy theory to study
algebraic questions, such as local group theory, representations, and Picard groups.


UCPH page           Personal home page

  Lars Hesselholt

Lars Hesselholt

My research interest lies at the intersection of higher algebra and arithmetic geometry. This includes the higher algebra analogues of determinant and trace, namely, algebraic K-theory and topological Hochschild homology and their applications.

UCPH page          Personal home page

Niels Martin Møller

Niels Martin Møller

I am interested in geometric analysis. In particular mean curvature flow, with a focus on singularities and solitons, minimal surfaces, and applications of Riemannian geometry in mathematical physics.

UCPH page          Personal home page

Jesper Møller

Jesper Møller

I am fascinated by the interplay between algebraic topology and finite group theory and combinatorics. More concretely, I study topological and combinatorial properties of subgroups posets or fusion or orbit categories associated to finite groups.

UCPH page           Personal home page

Oscar Randal-Williams

Oscar Randal-Williams (Cambridge): I am interested in Algebraic and Geometric Topology, in particular: moduli spaces, cobordism categories, spaces of manifolds, configuration spaces, mapping class groups, surgery, characteristic classes, K-theory, and applications of homotopy theory to geometry.

University of Cambridge page

Nathalie Wall

Nathalie Wahl

My main research areas are algebraic and geometric topology together with homotopy theory. I am particularly interested in homological stability phenomena, loop spaces, string topology, operads, as well as field theories. 

UCPH page           Personal home page

Ib Madsen

Ib Madsen (Emeritus)

My main research interests may be summarized in the headlines: Algebraic K-theory and Topological Cyclic Homology; the homological structure of Diffeomorphism Groups; Surgery Theory and its classifying spaces; Rational Homotopy Theory.
UCPH Page            Personal Home Page

Postdocs


Picture of Sergei Avvakumov

Sergei Avvakumov

Research interests: geometric topology and applications of topology to problems in geometry, combinatorics, and discrete mathematics.

Picture of Andrea Bianchi

Andrea Bianchi (PhD, University of Bonn)

My research is in algebraic topology, and I am broadly interested in moduli spaces of manifolds and configuration spaces. Currently, I am generalising the notion of Hurwitz spaces, taking coefficients in a quandle, and I am investigating parametrised cobordism categories in low dimension.

UCPH Page

Picture of Arindam Biswas
Arindam Biswas

My research interests include combinatorial group theory, additive number theory, spectral graph theory and expanders, with applications to related aspects of computer science. 

Arindam's UCPH page

Alexander Friedrich

Alexander Friedrich (PhD, University of Potsdam)

My research interests are geometric PDE, variational calculus, and mathematical physics. In particular, I work on translators of the mean curvature flow and generalized Willmore functional which relate to mathematical physics.

UCPH page

Simon Gritschacher (PhD, University of Oxford): 

My research is in algebraic topology and I am specifically interested in generalised cohomology theories, and in spaces of representations and their homotopy theory.

UCPH page

Ryomei Iwasa

Ryomei Iwasa (PhD, University of Tokyo, 2018):

My research interests are algebraic K-theory, algebraic cycles, motives, Hodge theory and (topological) cyclic homology.

UCPH page

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. 

UCPH page

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.

UCPH page         Personel Homepage

Markus Land

Markus Land (PhD, University of Bonn 2016): 

I work in algebraic topology and homotopy theory, more specifically in algebraic K-theory, L-theory, and relations to high dimensional manifold topology. I am also interested in C*-algebras, topological K-theory and the (stable) classification of 4-manifolds.

UCPH page

Felix Lubbe

Felix Lubbe (PhD, Leibniz University Hannover)

My research focuses on geometric analysis. I am in particular interested in the mean curvature flow in higher codimension, the behavior of graphs in Riemannian and Lorentzian product manifolds under this flow, and applications of the results in homotopy theory and mathematical physics.

UCPH page

Picture of John Ma

John Ma (PhD, University of British Columbia)

My interest lies in geometric analysis. In particular (Lagrangian) mean curvature flow and Ricci flow, with a focus on solitons and ancient solutions. 

UCPH page

Peter Patzt

Peter Patzt (PhD, Die Freie Universität Berlin): My research lies within algebraic topology and is concerned with the cohomology of groups in sequences. Often stability phenomena under the names of homological stability and representation stability occur. I'm particularly interested in the cohomology of arithmetic groups and applications to algebraic K-theory and number theory.


UCPH page            Peter's Personal Homepage

  

Picture fo Patrick Schnider

Patrick Schnider

The main focus of my research lies in discrete and computational geometry, in particular combinatorics of point sets, mass partitions and geometric transversals. I am particularly interested in applications of other areas of mathematics to these type of questions.

Patrick's UCPH page           Patrick's Personal Home Page

Picture of Lukas Woike

Lukas Woike (PhD, University of Hamburg)

My research area lies at the interface of algebraic topology, representation theory and mathematical physics. More specifically, I use higher categories and homotopy theory to construct and investigate topological field theories and modular functors. The results lead to applications to representation categories, in particular non-semisimple ones.

UCPH Page         Personal homepage

Picture of Hailun Zheng
Hailun Zheng (PhD, University of Washington, 2017)

I am interested in combinatorics, with connections to commutative algebra, topology, and convexity. In particular, I study various combinatorial invariants on polytopes and manifolds.


UCPH Page 

PhD students


Alexis Aumonier

Alexis Aumonier (advisor: S. Galatius): 

I am interested in algebraic topology and will try to investigate new aspects of moduli spaces of manifolds from the point of view of homotopy theory.

UCPH page

David Bauer

David Bauer (advisor: N. Wall)

My research interest lies in Algebraic topology, with a particular focus on homological and representation stability of unitary groups and general linear groups.

UCPH page

Calista Kurtz Bernard

Calista Kurtz Bernard (advisor: N. Wall)

My research interests lie mostly in geometric topology and homotopy theory. Currently, my work is on homology operations, but other interests include embedding calculus, cobordism categories, and braid groups.

UCPH page          Personal Homepage

Zhipeng Duan

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.

UCPH page

Picture of Adriano

Adriano Córdova Fedeli

UCPH page

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.

UCPH page

Picture of Ali Muhammad

Ali Muhammad (advisor Niels Martin Møller)

My main research will be within singularity analysis of the mean curvature flow. I am also interested in mathematical problems in General Relativity such as stability.

UCPH page 

Daria Poliakova

Daria Poliakova (advisors: L. Hesselholt & R. Nest)  

My research interests are in algebraic topology and homological algebra. I am interested in questions about homotopy theory of DG-categories (e.g. some homotopy limit computations) and operadic diagonals. I am also interested in Hochschild homology and related theories.

UCPH Page

Johanna Steinmeyer

Johanna Steinmeyer (Advisor K. Adiprasito)

I am interested in combinatorics, especially whenever it hints at an underlying structure coming from another area of mathematics. This often manifests as problems stated in terms of simplicial complexes or lattice polytopes, and techniques adapted from algebraic geometry and algebraic topology.

UCPH page

Robin Sroka (advisor: N. Wahl): 

My research interests lie at the intersection of algebraic topology and geometric group theory. The preliminary goal of my PhD project is to investigate the relation between homological stability phenomena and properties of certain (semi-)simplicial sets.

UCPH page

Kaif Muhammad Borhan Tan

Kaif Hilman Bin Muhammad Borhan Tan (advisor J. Grodal)

My research interest is in algebraic topology in general. At the moment, I am mostly interested in exploring equivariant stable homotopy theory, in particular localisations and completions in inductive techniques as well as some possible consequences of the classical completion theorems.

UCPH page

Jeroen van der Meer


Jeroen van der Meer (advisor: J. Grodal)

My research area will lie in the application of homotopy theory to the study of algebraic groups and their representations. But ask me again in a few months, and I'll give you a more precise answer as to what I am to do!

UCPH page

Picture of Vignesh Subramanian

Vignesh Subramanian (advisor: J. Grodal)

I am interested in topology and representation theory. The research for his PhD will concern computing Picard groups of suitable G-equivariant categories using methods from homotopy theory.

UCPH page

 

Jingxuan Zhang

Jingxuan Zhang (advisor: Niels Martin Møller

I am interest in nonlinear PDE arising from statistical physics. In particular, I study the geometric features in the Ginzburg-Landau theory of superconductivity, both at equilibrium and under various dynamics.


UCPH Page   Personal Homepage

Nanna Havn Aamand

Nanna Aamand (advisor: N. Wahl): I am interested in the intersection between algebraic topology and mathematical physics, more precisely in the study of topological quantum field theories.

UCPH page

 

Former members of GeoTop

Benjamin Brück

Benjamin Brück (PhD, University of Bielefeld,2020)
GeoTop, 2020-2020

My main research interest lies in geometric group theory, with a focus on topological methods. In the past years, I have in particular studied free groups and their automorphisms, (right-angled) Artin groups and Coxeter groups as well as various spaces associated to these.

Personal homepage

Zhipeng Duan

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 am interested in using algebraic topology to understand modular representation theory; so far this has focused on studying the stable module category of a finite group.

 

Sam Nariman

Sam Nariman (PhD, Stanford University): My research interests, in general, include applications of homotopy theory in studying moduli space of geometric structures and in particular foliated manifold bundles, stable homology of moduli spaces, automorphism groups of manifolds, in particular three-manifolds.

 

Piotr Pstrągowski

Piotr Pstragowski (PhD, Northwestern University): 

I study interactions between homotopy theory and algebraic geometry in various forms, such as chromatic and motivic homotopy theory, as well as derived algebraic geometry.

 

Picture of Bernardo Villarreal Herrera

Bernardo Villarreal (PhD, University of British Columbia Vancouver, 2017)
GeoTop, 2019-2020

My work is in the homotopy theory of spaces of representations and classifying spaces.

Bernardo has moved on to Ciudad Universitaria, Mexico City.

Personal homepage

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Guchuan Li (PhD, Northwestern University, 2019)
SYM/GeoTop, 2019-20

 I am interested in algebraic topology, with a particular emphasis on chromatic homotopy theory and its interaction with equivariant homotopy theory.

Picture of Thomas Wasserman

Thomas Wasserman (PhD, Oxford 2018)
GeoTop, 2018-20

My research focuses on Topological Quantum Field Theories in low dimensions and connects with Conformal Field Theory, Fusion Categories and Higher Categories, as well as some Physics.