Staff and Research interests
FACULTY AND CENTRE MANAGEMENT
Core faculty:
 Tobias Holck Colding (MIT)
 Søren Galatius
 Niels Martin Møller
 Nathalie Wahl (director of the centre)
 Oscar RandalWilliams (Cambridge)
Centre administration:
Faculty:
 Robert Burklund
 Dustin Clausen
 Jesper Grodal
 Lars Hesselholt
 Joachim Kock (visiting, Universitat Autònoma de Barcelona)
 Jesper Møller
 Ib Madsen (Emeritus)
Faculty research interests
Robert Burklund
I am interested in higher algebra and its applications. Some of my ongoing research programs include: Using surgery theory and Goodwillie calculus to understand moduli spaces of highly connected manifolds. Studying deformations of symmetric monoidal stable categories. Understanding the computational consequences of power operations in chromatic homotopy theory. 

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


Research interests: Differential Geometry, Partial Differential Equations. MIT page 

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

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 

My research belongs to algebraic geometry, category theory, homotopy theory, and combinatorics. Some keywords describing my recent activities are higher categories and operads, polynomial
functors, simplicial groupoids, combinatorial bialgebras, and applications in perturbative renormalisation, free probability, and program semantics. Currently, I am getting into the homotopy theory of finite groups.


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 Ktheory and topological Hochschild homology and their applications. 

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. 

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. 

Oscar RandalWilliams (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, Ktheory, and applications of homotopy theory to geometry. 

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. 

My main research interests may be summarized in the headlines: Algebraic Ktheory and Topological Cyclic Homology; the homological structure of Diffeomorphism Groups; Surgery Theory and its classifying spaces; Rational Homotopy Theory.
UCPH Page Personal Home Page 
ASSOCIATED MEMBERS
POSTDOCS
 Dani Kaufman (2022)
 Ishan Levy (2024)
 Erik Lindell (2024)
 Eric Ling (2022)
 Alexander Mramor (20222025)
 Jan Steinebrunner (2022)
 Adela Zhang (2023)
 Arina Voorhaar (2022)
 Chi Ho Yuen (202324)
 Artemis Aikaterini Vogiatzi
Artemis Aikaterini Vogiatzi Details to follow 

My research concerns abstract homotopy theory, with a particular focus on Goodwillie calculus and its applications. I am also interested in the theory of infinityoperads and higher category theory. 

I am interested in commutative algebra, representation theory, and algebraic topology and their interactions through the shared language of triangulated categories. I’m especially interested in the structure of Hochschild cohomology and how it is used in these areas, such as its interaction with AndréQuillen cohomology and its action on derived categories.
Benjamin's UCPH Page. Benjamin's Personal Webpage


My current research interests lie in stable homotopy theory, representation theory, and semialgebraic geometry. I am studying the interaction of higher semiadditivity with the chromatic filtration and algebraic Ktheory, the theory of Nash stacks and Schwartz functions on them, and relative representation theory of symmetric pairs. 

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. 

I study cluster algebras and their applications to geometry and physics. More Concretely, I am interested in non commutative cluster structures in higher Teichmüller theory, various flavours of generalised cluster structures and their symmetries, Polylogarithm functions and their relations, and connections between cluster algebras and quantum field theories like ChernSimons theory and SYM theory.




Details to follow 

I am interested in algebraic and geometric topology, in particular, topics related to mapping class groups and their cohomology. 

My research interests lie in geometric analysis with applications to spacetime singularities, topology, and low regularity. I'm also interested in the general relativistic hydrogen problem. 

I'm interested in geometric analysis, in particular the mean curvature flow and its singularities. Alexander's UCPH Page 

I'm interested in studying manifolds and their moduli spaces using tools from homotopy theory and higher categories. Concretely, I've studied classifying spaces of bordism categories, topological field theories, and diffeomorphism groups' (stable) homology, particularly in low dimensions. Among the tools I use are infinity(pr)operads, modular infinityoperads and the like. 

I am interested in combinatorial algebraic geometry, that is, the parts of algebraic geometry where geometric phenomena can be reformulated in a purely combinatorial language and the combinatorial methods become essential for further progress. The most wellknown (and yet absolutely amazing) example is the BernsteinKouchnirenko theorem, which describes the number of complex solutions of a polynomial system of equations in terms of the Newton polytopes of the polynomials involved. Within my research, I study resultants and their singularities in the context of Newton polytopes. Arina's UCPH page Arinas's Personal Home Page 

Adela Zhang I am interested in computations in stable homotopy theory, including Koszul duality, power operations, and synthetic homotopy theory. I'm also interested in their applications to manifold topology, in particular generalized configurations spaces. 

PHD STUDENTS
 Dagur Tomas Asgeirsson (2021
 Qingyuan Bai (20222025)
 Jonathan Clivio (20232026)
 Pierre Elis (2021)
 Oscar Bendix Harr (20222025)
 Branko Juran (20222025)
 Priya Kaveri (20232026)
 Marius Kjærsgaard (20222026)
 Fadi Mezher (20222025)
 Azélie Picot (20232026)
 Isaac Moselle (20232027)
 Maxime Ramzi (20212024)
 Florian Riedel (20232026)
 Robert Szafarczyk (20232027)
 Philippe Valentin Vollmuth (20232027)
 Harish Upadhyaya (20232026)
Dagur Tomas Asgeirsson (advisor: D. Clausen) My research concerns aspects of condensed mathematics. It was my background in algebraic geometry that sparked my interest in the subject, but I am currently studying modern homotopy theory and learning the language of ∞categories, which are crucial to understanding and answering more advanced questions in the field Dagur's UCPH Page Personal website 

I'm interested in the idea of sheaf theory in a broad sense, which means I like to think about gluing structures from local pieces. This also leads to general interests in geometry, topology and (higher) category theory. I used to be very curious about homological mirror symmetry and maths inspired by physics. (I still am!). 

Jonathan Clivio (advisor: N. Wahl)
I am interested in algebraic topology. My main interest lies in graph complexes and how they can be used to relate questions from string topology and algebra.
UCPH Page 

Pierre Elis (advisor: N. Wahl) I am interested in homotopy theory and in the geometry of manifolds. In particular, my PhD should focus on homotopy theoretic techniques to capture geometric information such as invariants of manifolds, homotopy types of bordism categories or/and moduli spaces of manifolds. Currently, I am studying string topology questions. 

I am interested broadly in algebraic topology, and specifically in homological stability and equivariant homotopy theory. 

Branko Juran I am interested in equivariant stable homotopy theory and its relation to manifold theory and representation theory. See Branko's UCPH Page See Branko's Homepage


I am interested in various topics in algebraic geometry and their connections to homotopy theory.'


I am interested in the topology of manifolds with an emphasis on 4manifolds, their (stable) classifications, and their (stable) automorphism groups. My initial approach to these subjects went via surgery theory, particularly Kreck's modified surgery theory. Currently, I am studying homotopy theoretic approaches such as bordism categories and moduli spaces. 

Priya Kaveri (advisor: Niels Martin Møller) My broad areas of interest are Analysis and Geometry. Currently, I am interested in the study of classical minimal surfaces in symmetric spaces of nonpositive curvature. I am also interested in the Spectral theory of Hyperbolic Surfaces. UCPH Page Personal Homepage 

I'm interested in homotopy theory and higher algebra, as well as representation theory. I am currently studying the connections between homotopy theory and the modular representations of finite groups.


Azélie Pico 

Maxime Ramzi (advisors: J. Grodal and M. Land ) I'm interested in categorical and higher algebra, and equivariant versions thereof; especially as they relate to representation theory  whether it's classical representation theory, or in more derived contexts. In particular, I study invariants such as Ktheory and topological Hochschild homology and I try to see what information I can extract from them about representation theory." UCPH Page Personal homepage 

Florian Riedel (advisors R. Burklund and J. Grodal) My main interests are in stable homotopy theory and higher algebra. I am learning chromatic homotopy theory and spectral algebraic geometry and want to investigate how the theory of power operations gives rise to different variants of the category of spaces. In general, I am interested in anything with ‘derived’ in it. Florian's UCPH page. Florian's personal homepage 

I am interested in higher algebra and its relations to algebraic topology and geometry. Right now I am learning chromatic homotopy theory and algebraic Ktheory. I think chromatic homotopy theory is essential to really understand the inner workings of higher algebra, whereas Ktheory is a great place to apply higher algebraic machinery as it connects to several other branches of mathematics in an important way. 

My main interest lies in the interaction between stable homotopy theory, higher algebra and algebraic geometry. Currently, I am trying to get a better grasp of spectral algebraic geometry over nonconnective rings. 

Harish Upadhyaya (advisor: Niels Martin Møller) I am primarily interested in Geometric Analysis. More specifically, I'm interested in minimal surfaces and flows such as the Mean Curvature Flow, and the Ricci flow. I'm also interested in PDE and variational aspects of other geometric problems. 

FORMER MEMBERS OF GEOTOP
 Karim Adiprasito (20202024)
 Alexis Aumonier (20192023)
 Sergei Avvakumov (20202022)
 Thomas Blom (20232024)
 David Bauer (20202021)
 Calista Kurtz Bernard (202021)
 Arindam Biswas (20212022)
 Andrea Bianchi (20202023)
 Benjamin Briggs (20222024)
 Shachar Carmeli (20212024)
 Imma Gálvez Carrillo (visiting, Universitat Politècnica de Catalunya )
 Ronno Das (202122)
 Benjamin Brück (2020)
 Zhipeng Duan (20172020)
 Pierre Elis (20212024)
 Adriano Córdova Fedeli (20202023)
 Simon Gritschacher (201721)
 Bernardo Herrera (20192020)
 Mikala Jansen (20202024)
 Marius Kjærsgaard (20222024)
 Josh Hunt (20162020)
 Ryomei Iwasa (201822)
 Mikala Jansen (20202024)
 Marius Kjærsgaard (20222024)
 Malte Leip (2017)
 Guchuan Li (20192020)
 Felix Lubbe (20192021)
 John Ma (20202023)
 Jeroen van der Meer (20192022)
 Ali Muhammad (20202023)
 Sam Nariman (20192020)
 Florian Naef (20212022)
 Peter Patzt (20202021)
 Daria Poliakova (2018)
 Piotr Pstragowski (20192020)
 Nasrin Altafi Razlighi (2021)
 Patrick Schnider (20202022)
 Jan Steinebrunner (20222024)
 Vignesh Subramanian (20202023)
 Kaif Muhammad Borhan Tan (201822)
 Thomas Wasserman (20182020)
 Maxime Ramzi (20212024)
 Robin Sroka (20182021)
 Johanna Steinmeyer (20182023)
 Lukas Woike (20202022)
 Chi Ho Yuen (20232024)
 Jingxuan Zhang (20202023)
 Hailun Zheng (20202022)
 Nanna Aamand (20192023)
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.


Alexis Aumonier (Former PhD student, 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. 


Sergei Avvakumov (Former postdoc) Research interests: geometric topology and applications of topology to problems in geometry, combinatorics, and discrete mathematics. 

David Bauer (Former PhD student,advisor: N. Wahl) My research interest lies in Algebraic topology, with a particular focus on homological and representation stability of unitary groups and general linear groups. 

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.


Calista Kurtz Bernard (Former PhD student, 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. 

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

My research concerns abstract homotopy theory, with a particular focus on Goodwillie calculus and its applications. I am also interested in the theory of infinityoperads and higher category theory.


I am interested in commutative algebra, representation theory, and algebraic topology and their interactions through the shared language of triangulated categories. I’m especially interested in the structure of Hochschild cohomology and how it is used in these areas, such as its interaction with AndréQuillen cohomology and its action on derived categories.


Benjamin Brück (Former postdoc, 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, (rightangled) Artin groups and Coxeter groups as well as various spaces associated to these. 

My current research interests lie in stable homotopy theory, representation theory, and semialgebraic geometry. I am studying the interaction of higher semiadditivity with the chromatic filtration and algebraic Ktheory, the theory of Nash stacks and Schwartz functions on them, and relative representation theory of symmetric pairs.


Imma Gálvez Carrillo (former visiting faculty) Visiting Faculty 

My research is in algebraic topology, often using the connections between topology and arithmetic. I am particularly interested in the topology of moduli spaces and results involving stability. 

Zhipeng Duan (former PhD student, 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.


Pierre Elis (advisor: N. Wahl) I am interested in homotopy theory and in the geometry of manifolds. In particular, my PhD should focus on homotopy theoretic techniques to capture geometric information such as invariants of manifolds, homotopy types of bordism categories or/and moduli spaces of manifolds. Currently, I am studying string topology questions.


Adriano Córdova Fedeli (former PhD student) I am interested in algebraic geometry, and recently I have been learning about algebraic K theory, chromatic homotopy theory and on how they relate. 

Alexander Friedrich (former postdoc) 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. 

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

Joshua Hunt (former PhD student, 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.


Ryomei Iwasa (former postdoc, 2018): My research interests are algebraic Ktheory, algebraic cycles, motives, Hodge theory and (topological) cyclic homology. 

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.


I am interested in various topics in algebraic geometry and their connections to homotopy theory.'


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. 

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

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


Ali Muhammad (former PhD student, 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. 

Malte Leip (former PhD student, 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. 

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. 

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!


Sam Nariman (former postdoc): 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 threemanifolds.


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 Ktheory and number theory. 

Piotr Pstragowski (former postdoc): 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.


Daria Poliakova (former PhD student, advisors: L. Hesselholt & R. Nest) My research interests are in algebraic topology and homological algebra. I am interested in questions about homotopy theory of DGcategories (e.g. some homotopy limit computations) and operadic diagonals. I am also interested in Hochschild homology and related theories. 

Maxime Ramzi (advisors: J. Grodal and M. Land ) I'm interested in categorical and higher algebra, and equivariant versions thereof; especially as they relate to representation theory  whether it's classical representation theory, or in more derived contexts. In particular, I study invariants such as Ktheory and topological Hochschild homology and I try to see what information I can extract from them about representation theory."


Nasrin Altafi Razlighi (former postdoc):
My research interests lie in commutative algebra, algebraic geometry, computational algebra, and combinatorics. I am currently working on the Hilbert functions of Gorenstein algebras. 

Patrick Schnider (former postdoc): 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.


Robin Sroka (former PhD student, 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. 



I'm interested in studying manifolds and their moduli spaces using tools from homotopy theory and higher categories. Concretely, I've studied classifying spaces of bordism categories, topological field theories, and diffeomorphism groups' (stable) homology, particularly in low dimensions. Among the tools I use are infinity(pr)operads, modular infinityoperads and the like.


Johanna Steinmeyer (Former PhD student, 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.


Vignesh Subramanian (former PhD student, advisor: J. Grodal) I am interested in topology and representation theory. The research for his PhD will concern computing Picard groups of suitable Gequivariant categories using methods from homotopy theory. 



Kaif Hilman Bin Muhammad Borhan Tan (former PhD student, advisor J. Grodal)


Bernardo Villarreal (former postdoc) My work is in the homotopy theory of spaces of representations and classifying spaces. Bernardo has moved on to Ciudad Universitaria, Mexico City. 

Guchuan Li (former postdoc) I am interested in algebraic topology, with a particular emphasis on chromatic homotopy theory and its interaction with equivariant homotopy theory. 

Thomas Wasserman (former postdoc) 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. 

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 nonsemisimple ones.


I am interested in the interaction between (oriented) matroids, tropical geometry and (real) algebraic geometry; he also studies other geometric aspects of oriented matroids and their applications in combinatorics.


Jingxuan Zhang (former PhD student, advisor: Niels Martin Møller) I am interest in nonlinear PDE arising from statistical physics. In particular, I study the geometric features in the GinzburgLandau theory of superconductivity, both at equilibrium and under various dynamics.



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


 Karim Adiprasito (20202024)
 Alexis Aumonier (20192023)
 Sergei Avvakumov (20202022)
 David Bauer (20202021)
 Calista Kurtz Bernard (202021)
 Andrea Bianchi (20202023)
 Arindam Biswas (2021)
 Thomas Blom (20232024)
 Benjamin Briggs (20222025)
 Benjamin Brück (2020)
 Shachar Carmeli (20212024)
 Imma Gálvez Carrillo (visiting)
 Ronno Das (20212022)
 Zhipeng Duan (20172020)
 Pierre Elis (20212024)
 Adriano Córdova Fedeli (20202023)
 Alexander Friedrich (20202021)
 Simon Gritschacher (202021)
 Bernardo Herrera (20202020)
 Josh Hunt (2020)
 Ryomei Iwasa (20202022)
 Mikala Jansen (20202024)
 Marius Kjærsgaard (20222024)
 Anssi Lahtinen (20202021)
 Markus Land (20202022)
 Guchuan Li (20202020)
 Malte Leip (20202021)
 Felix Lubbe (20202021)
 John Ma (20202023)
 Jeroen van der Meer (20192022)
 Ali Muhammad (20202023)
 Florian Naef (20212022)
 Sam Nariman (20192020)
 Peter Patzt (2020)
 Daria Poliakova (20202021)
 Piotr Pstragowski (20192020)
 Maxime Ramzi (20212024)
 Nasrin Altafi Razlighi (2021)
 Patrick Schnider (20202022)
 Robin Sroka (20202021)
 Jan Steinebrunner (20222024)
 Johanna Steinmeyer (20182023)
 Vignesh Subramanian (20202023)
 Kaif Muhammad Borhan Tan (20182022)
 Thomas Wasserman (20182020)
 Lukas Woike (20202022)
 Chi Ho Yuen (20232024)
 Jingxuan Zhang (20202023)
 Hailun Zheng (20202027)
 Nanna Aamand (20192023)