Aberdeen Topology Seminar

The Topology Seminar takes place on Mondays at 16:15 in room 156 in the Fraser Noble Building. The seminar organiser is Richard Hepworth. Information about claiming expenses is here. Older schedules are available here: First half session 2011-12.

2011-12, Second Half Session

• May 7th.
  Ran Levi (Aberdeen)
  Towards classification of unstable Adams operations on p-local compact groups
  Abstract. Homepage.
• April 30th.
  Jarek Kedra (Aberdeen)
  Gromov-Witten invariants of the Kodaira-Thurston manifold
  Abstract. Homepage.
• April 23rd.
  John Greenlees (Sheffield)
  Hasse squares in algebra, geometry and topology
  Abstract. Homepage.
• Extraordinary day and time!
  Tuesday April 17th, 2pm.
  Stephen Theriault (Aberdeen)
  Torsion in gauge groups
  Abstract. Homepage.
• Extraordinary day and time!
  March 20th, 2pm.
  Michael Weiss (Aberdeen)
  Stratified spaces and the Gillet-Grayson model of algebraic K-theory
  Abstract. Homepage.
• Extraordinary day and time!
  March 6th, 2pm.
  David Barnes (Sheffield)
  Orthogonal Calculus and Model Categories
  Abstract. Homepage.
• March 5th.
  Ian Leary (Southampton)
  Platonic polygonal complexes
  Abstract. Homepage.
• February 27th.
  Alex Gonzales (Hebrew University of Jerusalem)
  Extensions of localities: classification and examples
  Abstract.
• February 20th.
  David Quinn (Belfast)
  Finite domination of chain complexes
  Abstract. Homepage.
• February 13th.
  No Seminar
  
• February 6th.
  No Seminar
  
• January 30th.
  Otgonbayar Uuye (Cardiff)
  Restriction maps in \(K\)-theory
  Abstract. Homepage.

Titles and Abstracts

• Ran Levi
  Towards classification of unstable Adams operations on p-local compact groups
  I will discuss recent progress on the classification of unstable Adams operations for p-local compact groups, and its relationship with the concept of connectivity for these objects.
• Jarek Kedra
  Gromov-Witten invariants of the Kodaira-Thurston manifold
  I will present a computation of the Gromov-Witten invariant counting pseudoholomorphic tori in the Kodaira-Thurston manifold. For a fixed symplectic form such an invariant is always trivial. However, if we allow a topologically nontrivial family of symplectic forms then it is nonzero and this will be the case in my talk. This is the first example of a computation for a non-Kahler manifold. It is a joint work with Jonny Evans (ETH).
• John Greenlees
  Hasse squares in algebra, geometry and topology
  The idea is to understand (a) modules over a discrete valuation ring (b) sheaves over an elliptic curve or (c) rational circle-equivariant cohomology theories or (d) other "one dimensional" homotopy categories. This is done by breaking them up into rigid pieces using a Hasse square. [Includes joint work with Ando and Shipley]
• Stephen Theriault
  Torsion in gauge groups
  Let \(M\) be a simply-connected 4-manifold, let \(P\to M\) be a principal \(SU(2)\)-bundle, and let \(G(P)\) be the gauge group of this principal bundle. For \(p\) an odd prime we calculate the mod-\(p\) homology of the classifying space of \(G(P)\) in many cases, including when \(M=S^4\). These calculations are of interest to mathematical physics and Donaldson theory.
• David Barnes
  Orthogonal Calculus and Model Categories
  Orthogonal calculus is a calculus of functors, inspired by Goodwillie calculus. It takes as input a functor from finite dimensional inner product spaces to topological spaces and as output gives a tower of approximations by well-behaved functors. The output captures a lot of important homotopical information and is an important tool for calculations.
  
  In this talk I will report on joint work with Peter Oman in which we use model categories to improve the foundations of orthogonal calculus. This provides a cleaner set of results and makes the role of \(O(n)\)-equivariance clearer. The classification of \(n\)-homogeneous functors in terms of spectra with \(O(n)\)-action can then be phrased as a zig-zag of Quillen equivalences. As an application, we develop a stable variant of orthogonal calculus with topological spaces replaced by orthogonal spectra.
• Ian Leary
  Platonic Polygonal Complexes
  Platonic polygonal complexes are a natural generalization of the 2-skeleta of the regular polyhedra and polytopes and the 2-skeleta of the regular tesselations of Euclidean and hyperbolic spaces. I shall discuss joint work with T. Januszkiewicz, R. Valle and R. Vogeler in which we classify some classes of platonic polygonal complexes. Our most comprehensive results concern the case when the polygons have at least 6 sides (in which case all of the complexes are infinite), but in this talk I will focus on some examples for pentagons, squares and triangles.
• Alex Gonzales
  Extensions of localities: classification and examples
  The language of partial groups and localities was recently introduced by Andy Chermak in his striking proof of existence and uniqueness of centric linking systems associated to saturated fusion systems. We combine his ideas with the theory of group extensions to provide a notion of extension of localities and a classification result which keeps all the flavour of the classical theory. Finally, we show that all the known examples of extensions of centric linking systems are particular cases of this general notion. This is a joint work with Carles Broto.
• David Quinn
  Finite domination of chain complexes
  A topological space \(X\) is finitely dominated if it is a homotopy retract of a finite CW complex. Finite domination can be detected algebraically by considering the homology of the chain complex of its universal covering space with coefficients in a particular pair of rings related to the fundamental group of \(X\).
  
  The chain complex analogue considers when a bounded chain complex \(C\) of finitely generated free \(R[x,1/x]\)-modules is \(R\)-chain equivalent to a bounded chain complex of finitely generated projective \(R\)-modules. This is characterised by the vanishing of the Novikov homology of \(C\), i.e. the homology of \(C\) with coefficients in the Laurent series rings \(R((x))\) and \(R((1/x))\).
  
  In this talk I will discuss joint work with Thomas Huettemann in which we give a generalisation of algebraic finite domination to chain complexes of modules over a Laurent ring in several indeterminates. Similar generalisations exist, however our approach differs using methods of multi-complexes and the language of toric varieties and gives a simpler criterion for finite domination.
• Otgonbayer Uuye
  Restriction maps in \(K\)-theory
  Cyclic groups play a distinguished role in the representation theory of compact Lie groups: any virtual representation which restricts trivially to every finite cyclic subgroup is itself trivial. Jackowski and McClure studied how far this extends to virtual equivariant vector bundles i.e. to equivariant \(K\)-theory. In this talk we explain how to extend their result to finite \(RO(G)\)-gradable modules over \(K\)-theory. The key tool here is an extension of the Atiyah-Segal completion theorem.

Expenses

• Expenses form.
  
• Post your form, together with receipts and/or tickets, to the following address:
• Richard Hepworth
  Institute of Mathematics
  University of Aberdeen
  Aberdeen AB24 3UE
  United Kingdom