Algebra & Geometry
The Algebra & Geometry section's research includes Algebraic and Arithmetic Geometry, Combinatorics, Geometric Group Theory, Geometry & Geometric Analysis, Number Theory, Representation Theory, and Topology, and has permanent faculty K. Adiprasito, D. Clausen, S. Eilers, E. Feliu, S. Galatius, J. Grodal, L. Hesselholt, H.Holm, I. Kiming, J. Matz, J. M. Møller, N. M. Møller, R. Nest, D. Osajda, F. Pazuki, M. Risager, H. Schlichtkrull, and N. Wahl, along with around 20 postdocs and 20 PhD students. Our section proudly hosts the Copenhagen Center for Geometry and Topology (GeoTop). Several section members are also part of the Analysis & Quantum section, which together with AG represent pure mathematics at UCPH.
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AG Section News
Our research covers a large range of algebraic geometry, spanning from derived algebraic geometry and K-theory, over arithmetic geometry, to combinatorial algebraic geometry, as well as applied algebraic geometry.
Permanent faculty with interests within this research area include:
- Karim Adiprasito (combinatorial aspects of algebraic geometry, combinatorial Hodge theory)
- Dustin Clausen (arithmetic geometry, algebraic K-theory)
- Elisenda Feliu (applied algebraic geometry, applications to mathematical biology)
- Lars Hesselholt (arithmetic geometry, algebraic K-theory)
- Søren Galatius (moduli spaces)
- Ian Kiming (algebraic number theory, arithmetic geometry, Galois representations, automorphic forms)
- Fabien Pazuki (abelian varieties, rational points, heights, arithmetic dynamics, Drinfeld modules)
The two research seminars most relevant to this area are the Number Theory seminar and the Algebra/Topology seminar. See also the group on Mathematical Biology, for applications of algebraic geometry.
For questions about this area (MSC 13-14), contact Lars Hesselholt, or any of the other researchers listed above.
Our research covers diverse aspects of combinatorics, with a list of keywords given after the faculty below.
Permanent faculty with interests within this area include:
- Karim Adiprasito (combinatorics, discrete geometry, subspace arrangements, combinatorial Hodge theory, moduli spaces of combinatorial objects, polytopes).
- Søren Eilers (operator algebraic methods in combinatorics, counting problems)
- Jesper Grodal (combinatorial topology, subgroup complexes and poset geometry)
- Jesper M. Møller (topological methods in combinatorics, Euler characteristics, lattices)
- Damian Osajda (combinatorial methods in group theory)
Visitors within this area usually speak in Algebra/Topology seminar.
For questions about this area (MCS 5-8), contact Karim Adiprasito, or any of the other researchers above.
Our research covers a range of topics within geometry and geometric analysis, with keywords indicated after the researchers listed below.
Permanent faculty with research interests within this area include:
- Ryszard Nest (non-commutative geometry, index theorems)
- Niels M.Møller (Riemannian geometry, PDEs, mean curvature flow, minimal surfaces)
- Jasmin Matz (symmetric spaces, interaction with analytic number theory)
- Henrik Schlichtkrull (representations of real reductive Lie groups)
And also:
- Tobias Colding (MIT, Copenhagen Center for Geometry & Topology visiting professor
See also under TOPOLOGY and COMBINATORICS for the more algebraic and combinatorial aspects of geometry.
Visitors within this area usually speak in the Geometry seminar. See also the Copenhagen Center for Geometry & Topology.
For questions about this area (MSC 51-53,58), contact Niels Martin Møller, or any of the other researchers above.
We cover a wide range of topics within algebraic and analytic number theory, with key words listed under the faculty members below.
Permanent faculty with interests within this research area include:
- Dustin Clausen (reciprocity laws, algebraic K-theory, number theory via higher algebra)
- Lars Hesselholt (algebraic K-theory, higher algebra)
- Ian Kiming (algebraic number theory, arithmetic geometry, Galois representations, automorphic forms)
- Jasmin Matz (analytic number theory, arithmetic groups, trace formula)
- Fabien Pazuki (abelian varieties, rational points, heights, arithmetic dynamics, Drinfeld modules)
- Morten Risager (analytic number theory, automorphic forms, L-functions)
Faculty, postdocs and PhD students meet at the regular Number Theory seminar .
For questions about this area (MSC 11-12), contact Fabien Pazuki, or any of the other researchers above.
We cover a diverse set of topics within representation theory and non-commutative algebra, with a sample list of topics given under the faculty members below.
Permanent faculty with interests within this research area include:
- Jesper Grodal (homotopical methods in Lie theory and representation theory of finite groups)
- Henrik Holm (homological algebra and its applications to category and representation theory)
- Ryszard Nest (non-commutative geometry, quantum groups)
- Jasmin Matz (automorphic representations, symmetric spaces)
- Henrik Schlichtkrull (representations of real reductive Lie groups, symmetric spaces)
Visitors in this area usually speak in either the Algebra/Topology seminar or the Number Theory seminar.
For questions about this area (MSC 15-22), contact Jasmin Matz, or any of the other researcher above.
We cover a wide range of topics in algebraic, geometric, and combinatorial topology, with a sample of topics listed under the faculty members below.
Permanent faculty with interests within this research area include:
- Karim Adiprasito (combinatorial methods in topology, Hodge theory, moduli spaces of combinatorial objects, metric geometry)
- Dustin Clausen (higher algebra, algebraic K-theory, interactions with number theory)
- Søren Galatius (algebraic and geometric topology, moduli spaces of manifolds)
- Jesper Grodal (homotopy theory, equivariant topology, classifying spaces, interaction with representation theory)
- Lars Hesselholt (algebraic K-theory, higher algebra)
- Jesper M. Møller (unstable homotopy theory)
- Damian Osajda (geometric group theory)
- Nathalie Wahl (geometric topology, homotopy theory, homological stability, string topology, operads, field theories)
Faculty, postdocs and PhD students meet at Algebra/Topology seminar. See also the Copenhagen Center for Geometry & Topology.
For questions about this area (MSC 54-57), contact Nathalie Wahl, or any of the other researchers above.
- The Algebra/Topology seminar usually meets Mondays at 15:15, preceded by cookies from around 14:45. It covers a wide range of topics within the general label of algebra and topology. Talks are usually blackboard talks and last 60 minutes. See the calendar for a list of upcoming (and past) events.
- The Number Theory seminar usually meets Fridays 14:15-15:15. The current organizers are Fabien Pazuki and Jasmin Matz.
- The Geometry Seminar.
For a searchable list of current courses see here.
For questions about the BS program, you can contact our head of bachelor studies Fabien Pazuki.
For questions about the MS program, you can contact our head of master's studies Magdalena Musat.
For questions about the PhD program, you can contact our head of PhD studies Morten Risager.