The programme is still evolving  offers of talks definitely welcomed!
Monday
Scottish Topology Seminar 
Tuesday  Wednesday  Thursday 
12:15  13:15 Common Room
Lunch 
10.0011.00 room 325
Clark Barwick Modes of equivariance 
10.0011.00 room 325
Clark Barwick Some technical aspects of parametrized higher category theory 
10.0011.00 room 325
Clark Barwick Parametrized higher algebra 
13.1514.15 room 416
Clark Barwick Transfers in equivariant stable homotopy theory 
11.0012.30 Common Room & room 204
Coffee/tea & discussion 
11.0012.30 room 325
Coffee/tea & discussion session 
11.3012.30 room 325
John Berman Burnside categories encoding structure on symmetric monoidal categories 
14:30  15:30 room 416
Andrew Lobb A stable homotopy type for colored Khovanov cohomology 
14.0015.00 room 325  14.0015.00 room 325
Jay Shah Stability and additivity in parametrized higher category theory 
14.30 room 325
Discussion and problem session 
16:00  17:00 room 416
Stefan Schwede Equivariant bordism from the global perspective 
16.0017.00 room 325
Assaf Libman Stable decompositions of classifying spaces (of compact Lie groups and plocal finite groups). 
16.0017.00 room 325
Saul Glasman Calculus and equivariance

This sequence of talks is an exposition of ajoint monograph project with Emanuele Dotto, Saul Glasman, Denis Nardin, and Jay Shah
In this talk, I will explain how to model the seemingly very delicate topological act of stabilization with respect to representation spheres of groups with purely algebraic structures  Mackey functors  and to rewire the whole of equivariant homotopy theory accordingly. This has two benefits: (1) Stripping out these structures permits us to get extremely refined information about – and universal characterizations of – the basic constructions of equivariant stable homotopy theory. (2) At the same time, we are now able to untether equivariant stable homotopy theory from the world of groups; this opens the door to many more interesting structures and many more interactions with other areas.
In this talk, I will dive deeper into the study of the core structures of equivariant homotopy theory. I will introduce orbital ∞categories and the concomitant parametrized ∞category theories. We will look at some universal properties of the parametrized ∞categories of Bspaces and Bspectra for an orbital ∞category B. We will find that there are two interesting sorts of functors between orbital ∞categories – left and right orbital functors. We will describe how these account for the different sorts of "fixed point functors" one encounters. Throughout this talk, I'll weave in as many examples as I can think of.
It's one thing to say how parametrized ∞categories should work, but how do you make everything precise in a way that it can be used? In this talk, I'll introduce the necessary language, I'll explain some of the tricky bits of the theory, and I'll show all of this working on examples. I won't assume any tremendously detailed knowledge of any particular model of ∞categories, however.
In this talk, I'll introduce parametrized ∞operads and parametrized symmetric monoidal ∞categories, and I'll explain how these concepts operate in the examples of primary interest.
Stefan Schwede (Universitaet Bonn)
Equivariant bordism from the global perspective, I & II (pdf file of talk)
Global homotopy theory is, informally speaking, equivariant homotopy theory in which all compact Lie groups acts at once on a space or a spectrum, in a compatible way. In this talk I will advertise a rigorous and reasonably simple formalism to make this precise, using orthogonal specctra. I will then illustrate the formalism by a geometrically motivated example, namely equivariant bordism of smooth manifolds.
Jay Shah (MIT)
Stability and additivity in parametrized higher category theory
There are two equivalent ways to stabilize Gspaces to obtain Gspectra (for G a finite group). On the one hand, one inverts all of the representation spheres; on the other hand, one can form the usual stabilization and then enforce an equivariant additivity condition. We investigate extensions of these procedures to the more general context of cocartesian fibrations over certain base ∞categories.
John Berman (University of Virginia)
Burnside categories encoding structure on symmetric monoidal categories
A number of closely related constructions have at times gone by the name `Burnside category'. We show that these different constructions arise as 2Lawvere theories for various kinds of structured symmetric monoidal categories (cartesian monoidal or additive, for example). More generally, we describe a correspondence between smashing localizations and enriched Burnside categories. A major benefit of this correspondence is that we can directly introduce group actions to some variants of the Burnside category, immediately recovering GuillouMay and Barwick's Gspectra and HillHopkins and Barwick et al.'s Gsymmetric monoidal categories, and obtaining new notions of Gcartesian monoidal and Gadditive categories.
Saul Glasman (Princeton IAS)
Calculus and equivariance
Functors from the category of spectra which are nexcisive in the sense of Goodwillie can be thought of as Mackey functors indexed by the category of finite sets of cardinality at most n and surjections. The proof of this result, which is still a work in progress, contains several interesting ideas, and I'll give a detailed sketch.
Assaf Libman (University of Aberdeen)
Stable decompositions of classifying spaces (of compact Lie groups and plocal finite groups).
[last updated 08/12/2015]