Transpennine Topology Triangle

11:00 -11:30 Foyer in front of Engineering Lecture Theatre 1 (ENG LT1)

Tea, Coffee and Biscuits

11:30-12:30 Engineering Lecture Theatre 1 (ENG LT1)

Imma Gálvez Carrillo (UPC Barcelona): Incidence algebras with Möbius inversion from decomposition spaces.

12:30-14:00 Lunch Break

14:00-15:00 Engineering Lecture Theatre 1 (ENG LT1)

Mariam Pirashvili (University of Leicester): Second cohomotopy and nonabelian cohomology.

15:00-16:00 Engineering Lecture Theatre 1 (ENG LT1)

Joe Palacios Baldeon (University of Liverpool): Symmetric powers of motivic spaces.

16:00-16:30 Foyer in front of Engineering Lecture Theatre 1 (ENG LT1)

Tea, Coffee and Biscuits

16:30-17:30 Engineering Lecture Theatre 1 (ENG LT1)

Behrang Noohi (Queen Mary University of London): Singular chains on topological stacks.

from 17:30 Department of Mathematics, College House

Wine reception as part of the 150th Anniversary of the London Mathematical Society (LMS).

This event will be in conjunction with the LMS sponsored workshop on 'Cluster Algebras and Finite Dimensional Algebras'

Campus Map: http://www2.le.ac.uk/maps/campus-map

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Titles and Abstracts

Speaker: Imma Gálvez Carrillo (UPC Barcelona)

Title: Incidence algebras with Möbius inversion from decomposition spaces.

Abstract: Decomposition
spaces are simplicial (infinity-)groupoids that satisfy a certain
exactness condition (encoding decomposition), strictly weaker than the
usual Segal condition (encoding composition). A decomposition
space comes with an associated incidence coalgebra, whose dual gives
rise to an incidence algebra, with Möbius inversion. The coefficients
involved in this `algebra' are infinity-groupoids, but under suitable
finiteness conditions homotopy cardinality can be taken and we are back
in the realm of classical incidence algebras. One important example of
a decomposition space is the Waldhausen S-construction of an abelian
(or stable infinity-) category, whose incidence algebra is a
derived Hall algebra, and many other convolution algebras that arise
classically as ad hoc quotients of incidence algebras of posets can be
obtained more canonically from decomposition spaces.

[Joint
work with J Kock (Universitat Autňnoma de Barcelona) and A
Tonks (University of Leicester). Reference: arXiv:1404.3202.]Speaker: Mariam Pirashvili (University of Leicester)

Title: Second cohomotopy and nonabelian cohomology.

Abstract: The
main difficulty in the theory of non-abelian cohomology is that for
cosimplicial groups only zero-th and first dimensional cohomotopy are
known. In this talk we introduce a new class of cosimplicial groups,
called centralised cosimplicial groups, for which we are able to define
a second cohomotopy, with all expected properties. The main examples of
such cosimplicial groups come from 2-categories.

Speaker: Joe Palacios Baldeon (University of Liverpool)

Title: Symmetric powers of motivic spaces.

Abstract: Motivic
spaces depend of two coordinates, simplicial and geometric, where the
geometric coordinate means, namely, the category of quasi-projective
schemes over a field. Geometric symmetric powers of motivic spaces are
left Kan extensions of the abstract, or categoric, symmetric powers
defined on the geometric coordinate. In my talk, I will explain how
they provide a Lambda structure on the unstable motivic homotopy
category. I will also sketch a comparison of four kinds of symmetric
powers in the stable motivic homotopy category.

Speaker: Behrang Noohi (Queen Mary University of London)

Title: Singular chains on topological stacks.

Abstract: I will discuss
ongoing work (with Thomas Coyne) on the construction of singular chains
on topological stacks and explain how it fits with the existing
approaches to defining homotopy types of topological stacks.

[Reference: arXiv:1502.04995.]

Everyone who wishes to participate is welcome, particularly postgraduate students. Those from the TTT nodes can claim travel expenses, by completing the standard forms, which are available at the TTT Homepage.