Algebraic Topology

Algebraic Topology is rich and diverse area of mathematics that develops and applies a variety of algebraic, categoric and combinatorial techniques to solve problems in many areas of maths.

It was originally born in the 1920's and 30's to study various topological and geometric issues, but since then has had spectacular effect in areas such as number theory, mathematical physics, algebraic geometry, dynamics, logic, algebra, computer science and even social theory, and it continues to provide foundational insight into core areas of geometry and topology.

In Leicester we have a very active research group that covers both fundamental work within algebraic topology and homological algebra as well as some of its important applications to other parts of mathematics. Current research of members of the group includes both stable and unstable homotopy theory and their relation to algebraic geometry, category theory, dynamical systems, mathematical physics, structured spectra, homological algebra, aperiodic tilings and moduli spaces and stacks of various kinds.

Leicester is home to the London Maths Society funded "Transpennine Topology Triangle", a joint topology seminar run with the Universities of Manchester and Sheffield at which staff and students meet about 6 times a year for talks, collaboration and generally keeping in touch with the topological community in England. Leicester has also regularly hosted the British Topology Meeting as well as workshops on the interfaces with other areas of mathematics such as "Algebraic methods in geometry and physics" in 2008 and "Aperiodic Order" in 2009.

Current members

Some recent publications

• M Barge, B Diamond, J Hunton & L Sadun, "Cohomology of Substitution TilingSpaces," Ergodic Theory and Dynamical Systems 30 (2010), 1607-1627.
  
• A. Lazarev, A.A. Voronov, Graph homology: Koszul and Verdier duality, Advances in Mathematics, Volume 218, Issue 6,  2008, 1878-1894.
  
• P. Frediani, F. Neumann, Etale homotopy types of moduli stacks of algebraic curves with symmetries. K-Theory 30 (2003), 315-340.
  
• S.Paoli, Weakly globular cat^n-groups and Tamsamani's model, Advances in Mathematics, 222 (2009) 621-727.
  
• Baues, Hans-Joachim; Jibladze, Mamuka; Pirashvili, Teimuraz, Third Mac Lane cohomology. Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 2, 337–367.

Current PhD students

Chris Braun, Willian Obeng-Denteh, Issac Owusu-Mensah (Willian and Issac are Frank's students under the MARM project, physically working in Africa), Khadijah Sharaf, Jamie Walton, Mirza Zeki

Recent PhDs:

• "Cohomology of Lambda Rings" by Michael Robinson (2010)
  
• "Euler characteristics and cohomology for quasiperiodic projection tilings" by Claire Irving (2006)
• Past members and postdocs: James Cranch, Marcello Felisatti, Le Minh Ha, Thomas Huettemann

Grants

The Algebraic Topology group has received funding from:

• The Engineering and Physical Sciences Research Council (EPSRC)
• The Leverhulme trust
• The European Union
  
• The British Council
• The London Maths Society (LMS)
  
• The Royal Society
• Nuffield Foundation
• The Spanish and Catalan Research Council
  
• Italian Research Council INDAM