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Timetable (HHHW02)

Equivariant and motivic homotopy theory

Monday 13th August 2018 to Friday 17th August 2018

Monday 13th August 2018
09:00 to 09:50 Registration
09:50 to 10:00 Welcome from David Abrahams (INI Director)
10:00 to 11:00 Daniel Dugger (University of Oregon)
Surfaces with involutions
I will talk about the classification of surfaces with involution, together with remarks on the RO(Z/2)-graded Bredon cohomology of these objects.
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Jeremiah Heller (University of Illinois)
tba
INI 1
12:30 to 13:30 Lunch at Churchill College
13:30 to 14:30 Free Time
14:30 to 15:30 Agnes Beaudry (University of Colorado)
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INI 1
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Clark Barwick (University of Edinburgh)
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INI 1
17:00 to 18:00 Welcome Wine Reception at INI
Tuesday 14th August 2018
09:00 to 10:00 Marc Levine (Universität Duisburg-Essen)
tba
INI 1
10:00 to 11:00 Poster Session in Discussion Room
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Magdalena Kedziorek (EPFL - Ecole Polytechnique Fédérale de Lausanne)
tba
INI 1
12:30 to 13:30 Lunch at Churchill College
13:30 to 14:30 Free Time
14:30 to 15:30 Marc Hoyois (Massachusetts Institute of Technology)
Motivic infinite loop spaces and Hilbert schemes
Co-authors: Elden Elmanto (Northwestern University), Adeel A. Khan (Universität Regensburg), Vladimir Sosnilo (St. Petersburg State University), Maria Yakerson (Universität Duisburg-Essen)

We prove a recognition principle for motivic infinite loop spaces over a perfect field of characteristic not 2. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. Our main result is that grouplike framed motivic spaces are equivalent to the full subcategory of motivic spectra generated under colimits by suspension spectra. As a consequence, we deduce some representability results for suspension spectra of smooth varieties and various motivic Thom spectra in terms of Hilbert schemes of points in affine spaces.
Related Links
INI 1
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Teena Gerhardt (Michigan State University)
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INI 1
Wednesday 15th August 2018
09:00 to 10:00 Douglas Ravenel (University of Rochester)
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INI 1
10:00 to 11:00 Oliver Roendigs (Universität Osnabrück); (Universitetet i Oslo)
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INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Vesna Stojanoska (University of Illinois at Urbana-Champaign)
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INI 1
12:30 to 13:30 Lunch at Churchill College
13:30 to 17:00 Free Afternoon INI 1
19:30 to 22:00 Formal Dinner at Gonville & Caius College
Thursday 16th August 2018
09:00 to 10:00 Mark Behrens (University of Chicago)
tba
INI 1
10:00 to 11:00 Tom Bachmann (Universität Duisburg-Essen)
Motivic normed spectra and Tambara functors
Motivic normed spectra are a motivic analogue of the G-commutative ring spectra from genuine equivariant stable homotopy theory. The category of G-commutative ring spectra such that the underlying genuine equivariant spectrum is concentrated in degree zero (i.e. is a Mackey functor) is in fact equivalent to the category of G-Tambara functors. I will explain an analogous motivic result: the category of normed motivic spectra (over a field), such that the underlying motivic spectrum is an effective homotopy module, is equivalent to a category of homotopy invariant presheaves with generalized transfers and étale norms.
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Anna Marie Bohmann (Vanderbilt University)
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INI 1
12:30 to 13:30 Lunch at Churchill College
13:30 to 14:30 Free Time
14:30 to 15:30 Mona Merling (Johns Hopkins University)
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INI 1
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 Fabien Morel (Ludwig-Maximilians-Universität München)
Etale and motivic variations on Smith's theory on action of cyclic groups
In this talk, after recalling some facts on Smith's theory in classical topology, I will present some analogues in algebraic geometry using \'etale cohomology first, and I will also give analogues in \A^1-homotopy theory and motives of Smith's theory concerning the multiplicative group \G_m, which behaves like a  "cyclic of order 2".
INI 1
Friday 17th August 2018
09:00 to 10:00 Aravind Asok (University of Southern California)
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INI 1
10:00 to 11:00 Carolyn Yarnall (University of Kentucky)
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INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Kirsten Wickelgren (Georgia Institute of Technology)
Some results in A1-enumerative geometry
We will discuss several applications of A1-homotopy theory to enumerative geometry. This talk includes joint work with Jesse Kass and Padmavathi Srinivasan.




INI 1
12:30 to 13:30 Lunch at Churchill College
13:30 to 14:30 Free Time
14:30 to 15:30 Thomas Nikolaus (Universität Münster)
Cyclotomic spectra and Cartier modules
We start by reviewing the notion of cyclotomic spectra and basic examples such as THH. Then we introduce the classical algebraic notion of an (integral, p-typical) Cartier module and its higher generalization to spectra (topological Cartier modules). We present examples such as Witt vectors and K-theory of endomorphisms. The main result, which is joint work with Ben Antieau, is that there is a close connection between the two notions.
INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons