Tea and coffee will be in the common room on I floor of the Hicks Building. All the talks will be in J11 (the usual seminar room on J floor).
10:30 – 11:00

Tea, Coffee and Biscuits 
11:00 – 12:00 J11 
James Walton (University of Leicester) Topological Invariants of Tiling Spaces Given
some aperiodic tiling (of Euclidean space, say), a fruitful approach to
understanding its properties is to associate to it a moduli space of
"locally isomorphic" tilings, and to then study the topology of this
"tiling space". A common topological invariant to consider in this
context is the Čech cohomology. I will describe how, using a Poincaré
Duality like result, one may describe these groups in a very geometric
way using cellular chains (although noncompactly supported ones) of
the Euclidean space which are "pattern equivariant" (PE) with respect
to the tiling. I will show how, with this perspective, one may give a
simple method to compute these groups for hierarchical tilings. If time
allows, I will also discuss the rotationally invariant PE complexes,
which seem to capture extra information about the rotationally
invariant tilings in the tiling space to the Čech cohomology groups.
These groups can be incorporated into a spectral sequence converging to
the cohomology of the tiling space of rigid motions of a tiling. 
14:00 – 15:00 J11 
Tom Bridgeland (University of Sheffield) Symmetry groups of derived categories of coherent sheavesGiven a smooth projective variety, one can try to compute the group of autoequivalences of its derived category of coherent sheaves. I will give a gentle introduction to what is known about this tricky problem, and try to explain how ideas from mirror symmetry can help in guessing the answer. 
15:00 – 16:00 
Tea, Coffee and Biscuits 
16:00 –17:00 J11  Andy Tonks (London Metropolitan University) Incidence algebras and Möbius inversion for decomposition spaces (joint work with Imma Gálvez, Joachim Kock) The
classical theory of incidence (co)algebras and Möbius inversion for
(locally finite) posets may be generalised in two directions. Firstly
posets may be replaced by categories, as in Leroux's theory, and
secondly the numerical data involved can be seen as arising from the
(homotopy) cardinality of basic combinatorial and algebraic objects, as
suggested by the work of Lawvere and Menni. In this talk we introduce
further generalisations, to what we call decomposition spaces,
fundamental examples of which are provided by weak category objects in
(infinity)groupoids. In particular we obtain the ConnesKreimer Hopf
algebra from a decomposition space of combinatorial forests, and
derived Hall algebras from the Waldhausen Sdot construction of a
stable infinitycategory. 
Everyone who wishes to participate is welcome, particularly postgraduate students. The TTT reimburses travel expenses of participants from the three vertices. The claim forms are available from the main TTT page. NI numbers and details of UK bank accounts are needed.