Staff and Research interests

 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.  

Robert's UCPH Page    Robert's homepage

Dustin Clausen (Institut des Hautes Études Scientifiques,Université Paris-Saclay, Paris)

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.

Dustin's homepage

Tobias Holck Colding (MIT)

Research interests: Differential Geometry, Partial Differential Equations.

Tobias' homepage

Søren Galatius (Columbia University, New York)

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.

Søren's homepage

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

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

Incoming new member

Henrik's UCPH profile Henrik's UCPH Homepage

 Ryomei Iwasa

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

UCPH page

Joachim Kock (Universitat Autònoma de Barcelona)

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.

UCPH page           Personal home page

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 (Emeritus)

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 (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 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 (Emeritus)

Brian D. Harvie

Incoming new member

Brian's UCPH page    Brian's Personal Home Page

Chris Hone

Incoming new member

Chris' UCPH Page     Chris' Personal Home Page

 Erik Lindell

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

Eric's UCPH page.     Eric's Personal Home Page

Eric Ling

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.

Eric's UCPH Page    Eric's Personal Home Page

Deven Manam

Incoming new member

Thomas Jan Mikhail

My research interests centre on type-theoretic foundations of higher category theory, and decomposition spaces as well as negative sets.

Thomas' UCPH page

Artemis Aikaterini Vogiatzi

My research interests lie in geometric analysis, particularly geometric flows, such as (high codimension) mean curvature flow, and differential geometry. She studies the evolution under the mean curvature flow of smooth, n-dimensional, compact submanifolds that satisfy specific curvature conditions immersed in a Riemannian manifold of dimension n+m, where the main focus is on the case of high codimension, m≥2. I am also interested in the mean curvature flow of codimension one submanifolds.

Artemis' UCPH page.   Artemis' Personal Homepage

Sebastian Wolf

Incoming new member

Arina Voorhaar

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 well-known (and yet absolutely amazing) example is the Bernstein-Kouchnirenko 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.

Arina's UCPH page           Adela's Personal Home Page

Omer Bojan 

Incoming New Member

Jonathan Clivio (advisor: Nathalie 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.

Jonathan's UCPH Page.    Jonathan's Personal Home Page

Oscar Bendix Harr (advisors: Jesper Grodal and Nathalie Wahl)

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

Oscar's UCPH Profile     Oscar's Personal Homepage

Jan Ole Hesse 

(advisor: Ryomei Iwasa)

Incoming New Member

Branko Juran (advosor: Jesper Grodal)

I am interested in equivariant stable homotopy theory and its relation to manifold theory and representation theory.

Branko's UCPH Page    Branko's Homepage

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 non-positive curvature. I am also interested in the Spectral theory of Hyperbolic Surfaces.

Priyas' UCPH Page Priyas' Personal Homepage

Lucas Phillip Noer Larsen (advisor: Ryomei Iwasa)

I am interested in motivic homotopy theory and plan to study motivic filtration(s) of motivic spectra associated to localising invariants

Lucas' UCPH profile

Chenglong Ma (advisors: Lars Hesselholt and Emanuel Reinecke]

I plan to explore the interface between homotopy theory and arithmetic geometry. I intend to follow Devalapurkar’s spectral version of the geometric Langlands program as an initial guide for my studies under the supervision of Professors 

Changlong's UCPH profile

Fadi Mezher (advisors: Nathalie Wahl and Professor Søren Galatius)

I am interested in the topology of manifolds with an emphasis on 4-manifolds, 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.

Fadi's UCPH page

Isaac Moselle (advisor: Jesper Grodal)

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.

UCPH Page.   

Anna Mustata

Incoming Member

Florian Riedel (advisors Robert Burklund and Jesper 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

Robert Szafarczyk (advisor: Robert Burklund)

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

See Robert's UCPH page

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. 

UCPH Page

Philippe Valentin Vollmuth (Advisors: Robert Burklund and Jesper Grodal)

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 non-connective rings.

see Phillippe's UCPH page

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.

Dagur Tomas Asgeirsson

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

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.

Personal homepage

 Sergei Avvakumov (Former postdoc)

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

Qingyuan Bai (former PhD student, advisors: Dustin Clausen and Lars Hesselholt)

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!).

Qingyuan's UCPH Page 

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.

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.

Andrea Bianchi

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

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. 

Thomas Blom

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

Personal Homepage

Benjamin Peter Briggs

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, (right-angled) Artin groups and Coxeter groups as well as various spaces associated to these.

Personal homepage

Shachar Carmeli

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

Shachar's Homepage

Imma Gálvez Carrillo (former visiting faculty)

Imma Gálvez Carrillo

Visiting Faculty

Ronno Das

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 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.

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.

Pierre's Personal Homepage

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.

Simon's personal homepage

Oscar Bendix Harr

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

See Oscar's Personal Homepage

Joshua Hunt 

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.

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

Branko Juran (advosor: Jesper Grodal)

I am interested in equivariant stable homotopy theory and its relation to manifold theory and representation theory.

Branko's Homepage

Dani Kaufman

 Dani's UCPH page.    Dani's homepage

Marius Kjærsgaard

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

Marius' UCPH Page

 Anssi Lahtinen  

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.

Personel Homepage

 Markus Land (former postdoc): 

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.

Ishan Levy

Details to follow

See Ishan's homepage

John Ma (former postdoc)

John's Personal Homepage

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.

 Felix Lubbe (former postdoc): 

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.

Jeroen van der Meer (former Phd student, 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!

Alexander Mramor

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

 Alexander's UCPH Page

 Florian Naef (former postdoc)

Homepage at Trinity College Dublin

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 three-manifolds.

Peter Patzt (former postdoc):

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.

Peter's Personal Homepage

Azélie Pico

I am interested in moduli spaces of manifolds and their interactions with homotopy theory. I am particularly interested in cobordism categories, whose homotopy type is strongly related to the study of manifold bundles and their characteristic classes.

 UCPH Page             Personal homepage 

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 DG-categories (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 K-theory 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.

Patrick's Personal Home Page

 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.

Jan Steinebrunner 

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 infinity-operads and the like.

Jan's Personal Home Page

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 G-equivariant categories using methods from homotopy theory.

Kaif Hilman Bin Muhammad Borhan Tan (former PhD student, 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

Bernardo Villarreal (former postdoc)
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.

Guchuan Li (former postdoc)
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.

Thomas Wasserman (former postdoc)
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.

Lukas Woike (former postdoc)

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.

Personal homepage

Chi Ho Yuen

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.

personal homepage

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 Ginzburg-Landau theory of superconductivity, both at equilibrium and under various dynamics.

Personal Homepage

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

Hailun's Personal Homepage