Algebra & topology

The Algebra & Topology research program explores the areas of:

  • Algebraic geometry (moduli spaces, motives, arithmetic aspects especially involving Witt vectors, classical invariant theory, Gromov-Witten invariants)
  • Representation theory (geometric representation theory, categorification, tensor categories)
  • Algebraic topology
  • K-theory
  • Analytic number theory
  • Operator algebras
  • Low-dimensional and symplectic topology
  • Homological algebra (derived and triangulated categories, Grothendieck duality)

The Algebra & Topology group holds a regular seminar on Tuesdays at 4pm, in G35, the seminar room in the John Dedman building. We typically take the speaker out to lunch or dinner on the day of the seminar; students in particular are welcome to join us. (There is also a Google calendar which often contains information about the seminar series further into the future than the MSI calendar)

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Project Supervisors
Algebraic topology
Arithmetic algebraic geometry
Arithmetic and Geometry over Finite Fields
Combinatorial and Geometric Group Theory
Complex cobordism & stable homotopy
Computability in Algebra and Geometry
Crystallographic groups
Dirac operators and application
Enriched monoidal categories
Fermat's last theorem
Galois theory in topology
Geometry of Gauge fields
Group Actions and Invariants
Homological Algebra and Algebraic Geometry
Interactive and automated theorem proving
Kervaire invariant one problem
Mathematical Aspects of Conformal Field Theory
Model Categories
Model categories in algebraic topology
Morse theory in dimensions three and four
Number theory & algebraic geometry
Readings in Commutative Algebra and Algebraic Geometry
Reflection groups, cacti and crystals
Representation theory and combinatorics of symmetric groups
Riemann zeta function & the distribution of primes
Spectral Sequences in Algebraic Topology
Statistical shape analysis using algebraic topology
Surface mapping class groups
Topics in contact geometry
Topics in low-dimensional topology
Topics in representation theory
Topology of Singularities