Home /  [HYBRID WORKSHOP] Introductory Workshop: Floer Homotopy Theory

Workshop

[HYBRID WORKSHOP] Introductory Workshop: Floer Homotopy Theory September 12, 2022 - September 16, 2022
Registration Deadline: September 17, 2022 almost 2 years ago
To apply for Funding you must register by: June 06, 2022 about 2 years ago
Parent Program:
Location: SLMath: Eisenbud Auditorium, Atrium
Organizers Sheel Ganatra (University of Southern California), Tyler Lawson (University of Minnesota Twin Cities), LEAD Robert Lipshitz (University of Oregon), Nathalie Wahl (University of Copenhagen)
Speaker(s)

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Description
Image
A Fleur Homotopy.
This will be a hybrid workshop with in-person participation by members of the semester-long program and speakers. Online participation will be open to all who register.  Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications. The workshop will feature: - A Homotopy Theory lecture series by Anna Marie Bohmann and Alexander Kupers, aimed at symplectic geometers - A Floer Theory lecture series by Dusa McDuff and Chris Wendl, aimed at algebraic topologists - Paired hour talks on several subjects, connecting classical ideas to recent results:  (a) String topology by Oancea and Hingston (b) Infinity structures and operads by Bottman and Wilkins (c) Atiyah-Bott-Shapiro orientations and the Cohen-Jones-Segal construction by Klang and Kragh (d) Monopole Floer theory and homotopy theory by Lin, Shi, and Xu. - Moderated question-and-answer sessions about Floer theory and homotopy theory.  
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Floer homology

  • stable homotopy theory

  • gauge theory

  • string topology

  • pseudoholomorphic curves

  • Khovanov homology

  • categorification

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Sep 12, 2022
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Floer Homology Foundations Pt 1
Dusa McDuff (Barnard College)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Stable homotopy foundations: The Pontryagin-Thom construction
Alexander Kupers (University of Toronto)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Infinity Structures and Operads Pt 1
Nicholas Wilkins (Massachusetts Institute of Technology)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Infinity Structures and Operads Pt 2
Nathaniel Bottman (Max-Planck-Institut für Mathematik)
04:30 PM - 06:20 PM
  Reception
Sep 13, 2022
Tuesday
09:30 AM - 10:30 AM
  Floer Homology Foundations Pt 2
Chris Wendl (Humboldt-Universität)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Stable Homotopy Foundations: Generalized Cohomology Theories
Anna Marie Bohmann (Vanderbilt University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Loop Spaces and Poincaré Duality Part 1: Topological Aspects
Nancy Hingston (College of New Jersey)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Loop Spaces and Poincaré Duality Part 2: Symplectic Aspects
Alexandru Oancea (Institut de Mathématiques de Jussieu)
04:45 PM - 06:00 PM
  Floer Homology Q&A 1
Sep 14, 2022
Wednesday
09:00 AM - 10:00 AM
  Floer Homology Foundations Pt 3
Chris Wendl (Humboldt-Universität)
10:00 AM - 10:20 AM
  Break
10:20 AM - 11:20 AM
  Stable homotopy foundations: Introduction to spectra
Anna Marie Bohmann (Vanderbilt University)
11:20 AM - 11:35 AM
  Break
11:35 AM - 12:35 PM
  Floer Homology Foundations Pt 4
Dusa McDuff (Barnard College)
Sep 15, 2022
Thursday
09:30 AM - 10:30 AM
  Floer Homology Foundations Pt 5
Chris Wendl (Humboldt-Universität)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Stable homotopy foundations: Atiyah duality and Poincaré duality
Alexander Kupers (University of Toronto)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Thom Spectra and Orientations
Inbar Klang (Columbia University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Spectral Orientations in Floer Theory
Thomas Kragh (Uppsala University)
04:45 PM - 06:00 PM
  Floer Homotopy Q&A 2
Sep 16, 2022
Friday
09:00 AM - 10:00 AM
  Stable homotopy foundations: Duality in Morava K-theory
Anna Marie Bohmann (Vanderbilt University)
10:00 AM - 10:15 AM
  Break
10:15 AM - 11:15 AM
  Monopole Floer Theory and Homotopy Theory, Pt 1
Jianfeng Lin (Tsinghua University), XiaoLin Danny Shi (University of Washington), Zhouli Xu (University of California, San Diego)
11:15 AM - 11:30 AM
  Break
11:30 AM - 12:30 PM
  Monopole Floer Theory and Homotopy Theory, Pt 2
Jianfeng Lin (Tsinghua University), XiaoLin Danny Shi (University of Washington), Zhouli Xu (University of California, San Diego)