Equivariant and motivic homotopy theory

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Workshop theme

Equivariant and motivic homotopy are two of the most active areas in algebraic topology, bringing together researchers in topology, algebra, representation theory, and algebraic geometry. Equivariant homotopy theory has been a fundamental component of algebraic topology since its inception. The Sullivan and Segal conjectures explored how to understand homotopy fixed points unstably and stably, and trace methods in algebraic K-theory are one of the most successful approaches to computing algebraic K-groups. More recently, equivariant homotopy has experienced an exciting renaissance featuring applications to geometry. These include the solution by Hill-Hopkins-Ravenel of the Kervaire invariant one problem and Manolescu's solution of the triangulation conjecture. Though a newer area, motivic homotopy is a hugely active research field, bringing together ideas in algebraic topology and algebraic geometry. From Voevodsky's proof of the Milnor conjecture to the Rost-Voevodsky proof of Block-Kato, motivic homotopy theory has significantly impacted algebraic geometry.

This workshop will bring together researchers interested in these exciting areas, exploring new mathematics and discussing deep foundational work. Additionally, there are significant and subtle interactions between equivariant and motivic homotopy, with each providing intuition and strategies of proof for the other. We hope to further develop and build upon these connection.

Timetable

Monday 13th August 2018
09:00 to 09:50	Registration	No Room Required
09:50 to 10:00	Welcome from David Abrahams (INI Director)	No Room Required
10:00 to 11:00	Daniel Dugger University of Oregon Surfaces with involutions	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Jeremiah Heller University of Illinois A motivic Segal conjecture	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Free Time	No Room Required
14:30 to 15:30	Agnes Beaudry University of Colorado Pic(E-Z/4) and Tools to Compute It	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Clark Barwick University of Edinburgh Exodromy and endodromy	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 14th August 2018
09:00 to 10:00	Marc Levine Universität Duisburg-Essen Quadratic Welschinger invariants	Room 1
10:00 to 11:00	Poster Session in Discussion Room	Discussion Room
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Magdalena Kedziorek Universiteit Utrecht Algebraic models for rational equivariant commutative ring spectra	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Free Time	No Room Required
14:30 to 15:30	Marc Hoyois Massachusetts Institute of Technology Motivic infinite loop spaces and Hilbert schemes	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Vesna Stojanoska University of Illinois at Urbana-Champaign Galois extensions in motivic homotopy theory	Room 1

Wednesday 15th August 2018
09:00 to 10:00	Doug Ravenel University of Rochester Model category structures for equivariant spectra	Room 1
10:00 to 11:00	Oliver Roendigs Universität Osnabrück On very effective hermitian K-theory	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Teena Gerhardt Michigan State University Hochschild homology for Green functors	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 17:00	Free Afternoon	Room 1
19:30 to 22:00	Formal Dinner at Gonville & Caius College	No Room Required

Thursday 16th August 2018
09:00 to 10:00	Mark Behrens University of Chicago C_2 equivariant homotopy groups from real motivic homotopy groups	Room 1
10:00 to 11:00	Tom Bachmann Universität Duisburg-Essen Motivic normed spectra and Tambara functors	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Anna Marie Bohmann Vanderbilt University Graded Tambara functors	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Free Time	No Room Required
14:30 to 15:30	Mona Merling Johns Hopkins University Toward the equivariant stable parametrized h-cobordism theorem	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Fabien Morel Ludwig-Maximilians-Universität München Etale and motivic variations on Smith's theory on action of cyclic groups	Room 1

Friday 17th August 2018
09:00 to 10:00	Aravind Asok University of Southern California On Suslin's Hurewicz homomorphism	Room 1
10:00 to 11:00	Carolyn Yarnall University of Kentucky Klein four-slices of HF_2	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Kirsten Wickelgren Georgia Institute of Technology Some results in A1-enumerative geometry	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Free Time	No Room Required
14:30 to 15:30	Thomas Nikolaus Universität Münster Cyclotomic spectra and Cartier modules	Room 1

Organisers

John Greenlees University of Sheffield
Daniel Isaksen Wayne State University
Kyle Ormsby Reed College
Charles Rezk University of Illinois

Speakers

Aravind Asok University of Southern California
Tom Bachmann Universität Duisburg-Essen
Clark Barwick University of Edinburgh
Agnes Beaudry University of Colorado
Mark Behrens University of Chicago
Anna Marie Bohmann Vanderbilt University
Daniel Dugger University of Oregon
Teena Gerhardt Michigan State University
Jeremiah Heller University of Illinois
Marc Hoyois Massachusetts Institute of Technology
Magdalena Kedziorek EPFL - Ecole Polytechnique Fédérale de Lausanne
Marc Levine Universität Duisburg-Essen
Mona Merling Johns Hopkins University
Fabien Morel Ludwig-Maximilians-Universität München
Thomas Nikolaus Universität Münster
Doug Ravenel University of Rochester
Oliver Roendigs Universität Osnabrück
Vesna Stojanoska University of Illinois at Urbana-Champaign
Kirsten Wickelgren Georgia Institute of Technology
Carolyn Yarnall University of Kentucky

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Participants

Gregory Arone Stockholm University
Aravind Asok University of Southern California
Ran Azouri Universität Duisburg-Essen
Tom Bachmann Universität Duisburg-Essen
Scott Balchin University of Warwick
David Barnes Queen's University Belfast
Tobias Barthel Københavns Universitet (University of Copenhagen)
Maria Basterra University of New Hampshire
Agnes Beaudry University of Colorado
Mark Behrens University of Chicago
Julie Bergner University of Virginia
Irina Bobkova University of Rochester
Anna Marie Bohmann Vanderbilt University
Benjamin Böhme University of Copenhagen
Natalia Castellana Universitat Autònoma de Barcelona
Daniel Dugger University of Oregon
Giorgio Flora Università degli Studi di Pavia
Martin Gallauer University of California, Los Angeles
Teena Gerhardt Michigan State University
Paul Goerss Northwestern University
John Greenlees University of Sheffield
Rok Gregoric University of Texas at Austin
Jesper Grodal Københavns Universitet (University of Copenhagen)
Bert Guillou University of Kentucky
Araminta Gwynne Massachusetts Institute of Technology
Markus Hausmann Københavns Universitet (University of Copenhagen)
Fabian Hebestreit University of Bonn
Jeremiah Heller University of Illinois
Hans-Werner Henn
Gijs Heuts University of Copenhagen
Eric Hogle University of Oregon
Asaf Horev Hebrew University of Jerusalem
Marc Hoyois Massachusetts Institute of Technology
Joshua Hunt University of Copenhagen
Daniel Isaksen Wayne State University
Magdalena Kedziorek Universiteit Utrecht
Inbar Klang Stanford University
Dimitar Kodjabachev University of Sheffield
Nick Kuhn University of Virginia
Jonas Irgens Kylling Matematisk Institutt, Oslo
Tyler Lawson University of Minnesota
Tobias Lenz Rheinische Friedrich-Wilhelms-Universität Bonn; Max-Planck-Institut für Mathematik, Bonn
Kathryn Lesh Union College
Marc Levine Universität Duisburg-Essen
Lennart Meier Rheinische Friedrich-Wilhelms-Universität Bonn
Mona Merling Johns Hopkins University
Ieke Moerdijk Universiteit Utrecht
Fabien Morel Ludwig-Maximilians-Universität München
Thomas Nikolaus Universität Münster
Kyle Ormsby Reed College
Viktoriya Ozornova University of Bonn
Irakli Patchkoria University of Bonn
Luca Pol University of Sheffield
Kate Ponto University of Kentucky
J.D. Quigley University of Notre Dame
Oscar Randal-Williams University of Cambridge
Doug Ravenel University of Rochester
Nicolas Ricka Wayne State University
Oliver Roendigs Universität Osnabrück
Steffen Sagave Radboud Universiteit Nijmegen
Tomer Schlank Hebrew University of Jerusalem
Stefan Schwede Rheinische Friedrich-Wilhelms-Universität Bonn
XiaoLin Danny Shi Harvard University
Igor Sikora University of Sheffield
Wolfgang Steimle Universität Augsburg
Vesna Stojanoska University of Illinois at Urbana-Champaign
Danny Sugrue Queen's University Belfast
Markus Szymik Universität Bielefeld
Ulrike Tillmann University of Oxford
Nathalie Wahl Københavns Universitet (University of Copenhagen)
Kirsten Wickelgren Georgia Institute of Technology
Jordan Williamson University of Sheffield
Dylan Wilson University of Chicago
Maria Yakerson Universität Duisburg-Essen
Carolyn Yarnall University of Kentucky
Mingcong Zeng University of Rochester