I am a graduate student in Mathematics at Jesus College, Oxford, and a member of the Topology research group. I am interested in Algebraic and Geometric Topology, in particular: mapping class groups, moduli spaces, cobordism categories, spaces of manifolds, configuration spaces, characteristic classes, K-theory and applications of homotopy theory to geometry. My supervisor is Ulrike Tillmann. My CV is here.

E-mail:

Publications

The homology of the stable non-orientable mapping class group ( PDF). Algebraic & Geometric Topology 8 (2008) 1811–1832.
Inspired by Galatius' calculation of the homology of the stable oriented mapping class group, with finite field coefficients, we do the same for the non-orientable mapping class group. We determine the mod 2 homology as a Hopf algebra, and note that at odd primes the homology has a simpler description. This enables us to compute the integral homology up to degree 6.

On the divisibility of characteristic classes of non-orientable surface bundles ( PDF), with Johannes Ebert. Topology and its Applications 156 (2008) 246-250.
Following the work of Galatius, Madsen and Tillmann on the divisibility of the Miller-Morita-Mumford classes in the integral cohomology of the stable mapping class group of oriented surfaces, we study the divisibility of the zeta classes introduced by Wahl in the integral cohomology of the stable non-orientable mapping class group. We find them to be indivisible.

Preprints

Monoids of moduli spaces of manifolds ( PDF), with Søren Galatius.

Resolutions of moduli spaces and homological stability ( PDF).

Some exotic mapping class groups and moduli spaces. In preparation.

Embedded Cobordism Categories and Spaces of Manifolds ( PDF).

Other documents

Monoids of moduli spaces of manifolds, for the "Manifold Perspectives" Oberwolfach report. Full volume here.

Adams E₂ pages of Madsen-Tillmann spectra

Spectrum	E2 page	Module definition
MTO1	Here	Here
MTO2	Here	Here
MTSO2	Here	Here

I have computed the (mod 2) Adams E₂ terms for the stable homotopy groups of some Madsen-Tillmann spectra. Recall that MTO₂ / MTSO₂ are respectively the homotopy-types of the non-orientable / oriented stable mapping class groups, after plus-construction. This uses Robert Bruner's program for calculating Ext groups over the Steenrod algebra. I wrote a MAGMA program to give the description in terms of generators (up to a given degree) of these modules over the Steenrod alegebra, in a format admissible for the program mentioned above. There is also a chart for the beginning of MTSO(2) with some differentials filled in here, which are those which can be deduced from John Rognes' "Two-primary algebraic K-theory of pointed spaces", Topology 41 ( PDF).

Teaching

Lie Groups, Michaelmas 2009. Thursdays at 17:00, weeks 2 to 8.

Algebraic Topology, Hilary 2009. Wednesdays at 11:00, weeks 2 to 8.

C3.1a Topology and Groups, Michaelmas 2008. Tuesdays at 10:00 and Wednesdays at 17:00, weeks 2, 3, 5, 6, 7, 8 and week 1 of Hilary term.
Note: the 5th week class on Wednesday has been moved to 10:00, to allow for the Graduate studies open day.

C3.1a Revision consultations for Lie Groups, Trinity 2008, SR1 Tuesdays 09:00, weeks 1 to 5.
Note: the first week class has been moved to Friday of second week, at 09:00 in the Higman room.

C3.1a Lie Groups, Michaelmas 2007.

B14 Revision consultations for Algebraic Topology, Trinity 2007.

B14 Algebraic Topology, Hilary 2007.

B12 Topology and Groups, Michaelmas 2006.

Travel

21^st-25^th April 2008 - Westfälischen Wilhelms-Universität Münster, visiting Ulrike Tillmann, and talking about "Geometric delooping of cobordism categories" (abstract).

26^th-31^st May 2008 - "Topology in the Swiss Alps" Young Topologists' Meeting in Le Châtelard, Switzerland.

16^th-20^th June 2008 - "Homotopical Group Theory and Topological Algebraic Geometry Workshop" at the University of Copenhagen.

23^rd-27^th June 2008 - "Homotopical Group Theory and Topological Algebraic Geometry Conference" at the Max Planck Institute, Bonn.

18^th-24^th August 2008 - Third Arolla Conference on Algebraic Topology in Arolla, Switzerland.

8^th-9^th December 2008 - Sheffield University, Sheffield, talking about "Homology of the stable non-orientable mapping class group".

6^th-20^th January 2009 - Stanford University, Palo Alto, visiting Soren Galatius and talking about "Homology of the stable non-orientable mapping class group".

11^th-15^th May 2009 - University of Bonn, visiting Johannes Ebert, and talking about "Monoids of moduli spaces of manifolds".

24^th-30^th May 2009 - Manifold Perspectives, Mathematisches Forschungsinstitut Oberwolfach.

8^th-11^th June 2009 - 25^th Nordic and 1^st British-Nordic Congress of Mathematicians, in Oslo, Norway. Speaking in the Algebraic Topology special session.

14^th-15^th September 2009 - 24^th British Topology Meeting, in Leicester.

1^st-5^th February 2010 - Visiting the Copenhagen Topology department.

11^th-24^th April 2010 - Stanford University, Palo Alto, visiting Soren Galatius.

Last updated 14^th January 2010