Higher Algebraic Structures in Algebra, Topology and Geometry
January 10 - April 29, 2022
There is a long history of finding and using deep algebraic structures in algebraic topology. A very classical example of this is Adams work on understanding the homology of a based loop spaces of simply connected spaces via the co-bar construction. This lead to Eilenberg and Moores work on understanding homology of homotopy pull backs, and is also an important underlying part of Sullivan’s theory of minimal models for finite rational homotopy types.
Another example building on this is that of Koszul duality which relates modules over the dgas defined by the based loop spaces to modules over the cochain dga of the original space, which geometrically are related to fibrations over the space.
However, the structures of a based loop space is just one of many interesting (applicable) examples. Indeed, many questions in algebra, topology and geometry involves additional structure. E.g. smooth structures, algebraic structures, group equivariant structure.
There are several different subfields of algebraic topology which tries to understand such deeper/higher algebraic structures and their applications to geometry. E.g.:
- Algebraic K-theory.
- Operads.
- Equivariant homotopy theory.
- Infinity categories.
The proposed program aims to bring together researchers working in these areas – especially those working in their overlap.
Seminars Scroll to the next upcoming seminar
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Arrow induction and the dependent Yoneda lemma January 11 15:15 - 17:00 -
Smoothing theory deloopings of disk embedding and diffeomorphism spaces January 13 14:15 - 16:00 Smoothing theory deloopings of disk embedding and diffeomorphism spaces
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Postdoc day, Seminar 1: Spectral sequences via décalage January 14 13:30 - 14:00 Postdoc day, Seminar 1: Spectral sequences via décalage
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Postdoc day, Seminar 2: Comparing functor calculi January 14 14:10 - 14:40 Postdoc day, Seminar 2: Comparing functor calculi
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Postdoc day, Seminar 3: Koszul Duality for Categories with a Fixed Object Set January 14 15:10 - 15:40 Postdoc day, Seminar 3: Koszul Duality for Categories with a Fixed Object Set
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Postdoc day, Seminar 4: Local Gorenstein duality in chromatic group cohomology January 14 15:50 - 16:20 Postdoc day, Seminar 4: Local Gorenstein duality in chromatic group cohomology
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A-infinity structures on almost complex manifolds January 18 14:15 - 16:00 A-infinity structures on almost complex manifolds
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Finite type knot invariants and the Goodwillie-Weiss tower January 20 14:15 - 16:00 Finite type knot invariants and the Goodwillie-Weiss tower
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Postdoc day, Seminar 1: Twisted homology operations January 21 13:30 - 14:00 Postdoc day, Seminar 1: Twisted homology operations
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Postdoc day, Seminar 2: Topologically trivial families of smooth h-cobordisms January 21 14:10 - 14:40 Postdoc day, Seminar 2: Topologically trivial families of smooth h-cobordisms
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Postdoc day, Seminar 3: Topology and representation theory of the frame complex of unitary groups January 21 15:10 - 15:40 Postdoc day, Seminar 3: Topology and representation theory of the frame complex of unitary groups
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Postdoc day, Seminar 4: On the high-dimensional rational cohomology of special linear groups January 21 15:50 - 16:20 Postdoc day, Seminar 4: On the high-dimensional rational cohomology of special linear groups
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The Torelli Lie algebra January 25 14:15 - 16:00 The Torelli Lie algebra
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Embedding calculus for surfaces January 27 14:15 - 16:00 Embedding calculus for surfaces
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Combinatorics of multilinear differential operators (…) February 01 14:15 - 16:00 Combinatorics of multilinear differential operators (…)
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Bordism of commuting involutions February 03 14:15 - 16:00 Bordism of commuting involutions
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A spherical HKR theorem February 08 14:15 - 16:00 A spherical HKR theorem
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The Disc-structure space February 10 14:15 - 16:00 The Disc-structure space
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Postdoc day, Seminar 1: Symmetric groups, Hurwitz spaces and moduli spaces of surfaces February 11 13:30 - 14:00 Postdoc day, Seminar 1: Symmetric groups, Hurwitz spaces and moduli spaces of surfaces
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Postdoc day, Seminar 2: G-global algebraic K-theory February 11 14:10 - 14:40 Postdoc day, Seminar 2: G-global algebraic K-theory
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Postdoc day, Seminar 3: Stable operations and topological modular forms February 11 15:10 - 15:40 Postdoc day, Seminar 3: Stable operations and topological modular forms
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Postdoc day, Seminar 4: Formality and non-zero degree maps February 11 15:50 - 16:20 Postdoc day, Seminar 4: Formality and non-zero degree maps
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Cochain models of operads and topological realizations of the graded Poisson operads February 15 14:15 - 16:00 Cochain models of operads and topological realizations of the graded Poisson operads
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DT invariants of symmetric quivers and the Koszul duality theory February 17 14:15 - 16:00 DT invariants of symmetric quivers and the Koszul duality theory
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Postdoc day, Seminar 1: Adjoining roots to ring spectra and algebraic K-theory February 18 13:30 - 14:00 Postdoc day, Seminar 1: Adjoining roots to ring spectra and algebraic K-theory
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Postdoc day, Seminar 2: An illustration of stratified homotopy theory February 18 14:10 - 14:40 Postdoc day, Seminar 2: An illustration of stratified homotopy theory
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Postdoc day, Seminar 3: Equivariant algebraic K-theory and multiplicative norms February 18 15:10 - 15:40 Postdoc day, Seminar 3: Equivariant algebraic K-theory and multiplicative norms
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Postdoc day, Seminar 4: Galois descent in topological Hochschild homology February 18 15:50 - 16:20 Postdoc day, Seminar 4: Galois descent in topological Hochschild homology
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Some thoughts about monopole h-invariants February 24 14:15 - 16:00 Some thoughts about monopole h-invariants
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Postdoc day, Seminar 1: Characteristic classes of framed fibre bundles February 25 13:30 - 14:00 Postdoc day, Seminar 1: Characteristic classes of framed fibre bundles
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Postdoc day, Seminar 2: Configuration spaces on a wedge of spheres February 25 14:10 - 14:40 Postdoc day, Seminar 2: Configuration spaces on a wedge of spheres
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Postdoc day, Seminar 3: Diagonals of polytopes and higher structures February 25 15:10 - 15:40 Postdoc day, Seminar 3: Diagonals of polytopes and higher structures
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Postdoc day, Seminar 4: Replacing functors by enriched ones February 25 15:50 - 16:20 Postdoc day, Seminar 4: Replacing functors by enriched ones
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Symplectic groups and cobordism categories March 01 14:15 - 16:00 Symplectic groups and cobordism categories
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Hyperelliptic curves, scanning, and moments of quadratic L-functions March 03 14:15 - 16:00 Hyperelliptic curves, scanning, and moments of quadratic L-functions
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An Introduction to Symplectic Geometry for Algebraic Topologists March 04 09:15 - 14:00 An Introduction to Symplectic Geometry for Algebraic Topologists
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Equivariant Hochschild theories from a shadow perspective March 08 14:15 - 16:00 Equivariant Hochschild theories from a shadow perspective
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Configuration space methods applied to automorphism groups of spheres March 10 14:15 - 16:00 Configuration space methods applied to automorphism groups of spheres
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Global localization and equivariant Thom spectra March 15 14:15 - 16:00 Global localization and equivariant Thom spectra
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Franke’s conjecture and derived infinity categories March 17 14:15 - 16:00 Franke’s conjecture and derived infinity categories
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The geometric fixed points of real topological cyclic homology March 22 14:15 - 16:00 The geometric fixed points of real topological cyclic homology
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Lie algebras, Galois theory, and deformations of Calabi-Yau varieties March 24 14:15 - 16:00 Lie algebras, Galois theory, and deformations of Calabi-Yau varieties
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Postdoc day, seminar 1: Equivariant factorization homology March 25 14:15 - 14:45 Postdoc day, seminar 1: Equivariant factorization homology
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Postdoc day, seminar 2: v_1-periodic R-motivic homotopy groups March 25 15:00 - 15:30 Postdoc day, seminar 2: v_1-periodic R-motivic homotopy groups
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Postdoc day, seminar 3: Abelian cycles in the homology of the Torelli group March 25 15:45 - 16:15 Postdoc day, seminar 3: Abelian cycles in the homology of the Torelli group
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Higher Lie theory March 29 14:15 - 16:00 Higher Lie theory
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Stratification for spaces with Noetherian mod p cohomology March 31 14:15 - 16:00 Stratification for spaces with Noetherian mod p cohomology
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Postdoc day, seminar 1: A general descent principle for compact support extensions April 01 14:15 - 14:45 Postdoc day, seminar 1: A general descent principle for compact support extensions
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Postdoc day, seminar 2: The integration of curved absolute homotopy Lie algebras April 01 15:00 - 15:30 Postdoc day, seminar 2: The integration of curved absolute homotopy Lie algebras
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Postdoc day, seminar 3: The stable cohomology of self-equivalences of connected sums of products of spheres April 01 15:45 - 16:15 Postdoc day, seminar 3: The stable cohomology of self-equivalences of connected sums of products of spheres
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Twisted generating functions and the nearby Lagrangian conjecture (I) April 05 13:30 - 14:30 Twisted generating functions and the nearby Lagrangian conjecture (I)
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Twisted generating functions and the nearby Lagrangian conjecture (II) April 05 15:00 - 16:00 Twisted generating functions and the nearby Lagrangian conjecture (II)
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Complex cobordism, Hamiltonian loops and global Kuranishi charts April 07 15:15 - 16:15 Complex cobordism, Hamiltonian loops and global Kuranishi charts
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Algebraic K-theory of elliptic cohomology April 12 14:15 - 16:00 Algebraic K-theory of elliptic cohomology
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A Seiberg-Witten Floer stable homotopy type April 13 14:15 - 16:00 A Seiberg-Witten Floer stable homotopy type
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A new proof of best slope stability for the mapping class group of surfaces April 14 14:15 - 16:00 A new proof of best slope stability for the mapping class group of surfaces
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THH, shadows, and bicategorical traces April 19 14:15 - 16:00 THH, shadows, and bicategorical traces
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Braided Hopf algebras, operads, and partitions April 21 14:15 - 16:00 Braided Hopf algebras, operads, and partitions
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From elliptic genera to equivariant topological modular forms April 26 14:15 - 16:00 From elliptic genera to equivariant topological modular forms
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Koszul self-duality of E_n operads in spectra April 28 14:15 - 16:00 Koszul self-duality of E_n operads in spectra
Recordings
Participants
| Name | University | Country | Arrival and Departure |
|---|---|---|---|
| Mohammed Abouzaid | University: Columbia University | Country: United States | Arrival and Departure: Apr 4 - Apr 10 |
| Daniel Alvarez-Gavela | University: Massachusetts Institute of Technology | Country: United States | Arrival and Departure: Apr 3 - April 9 |
| Gregory Arone | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - April 29 |
| Alexis Aumonier | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Jan 10, Apr 11 - Feb 6, Apr 29 |
| Russell Avdek | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Tobias Barthel | University: Max Planck Institute for Mathematics | Country: Germany | Arrival and Departure: Apr 4 - Apr 13 |
| Tilman Bauer | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: |
| Özgur Bayindir | University: City, University of London | Country: United Kingdom | Arrival and Departure: Jan 27 - Mar 27 |
| Eva Belmont | University: University of California San Diego | Country: United States | Arrival and Departure: Mar 16 - Mar 26 |
| Alexander Berglund | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Andrea Bianchi | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Jan 30 - Feb 19 |
| Thomas Blom | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 13 - Apr 29 |
| Dorin Boger (Online) | University: | Country: | Arrival and Departure: |
| Lukas Brantner | University: University of Oxford / Université Paris-Saclay (Orsay) | Country: United Kingdom / France | Arrival and Departure: Mar 17, Apr 17 - Mar 30, Apr 28 |
| Urtzi Buijs | University: University of Malaga | Country: Spain | Arrival and Departure: Apr 23 - Apr 29 |
| Natalia Castellana | University: Universitat Autònoma de Barcelona | Country: Spain | Arrival and Departure: Mar 21 - Apr 8 |
| Wojtek Chacholski | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Sylvain Courte | University: Université Grenoble Alpes | Country: France | Arrival and Departure: Apr 3 - Apr 9 |
| Come Dattin | University: Utrecht University | Country: Sweden | Arrival and Departure: |
| Jack Morgan Davies | University: Utrecht University | Country: The Netherlands | Arrival and Departure: Feb 6 - Mar 20 |
| Georgios Dimitroglou Rizell | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Emanuele Dotto | University: University of Warwick | Country: United Kingdom | Arrival and Departure: Mar 20 - Apr 2 |
| Sylvain Douteau | University: Stockholm University | Country: Sweden | Arrival and Departure: Feb 7 - Apr 29 |
| Coline Emprin | University: Ecole Normale Supérieure de Paris | Country: France | Arrival and Departure: Mar 23 - Apr 4 |
| Hadrien Espic | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Søren Galatius | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Jan 19 - Feb 4 |
| Jesper Grodal | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Feb 16, Mar 14, Apr 9 - Feb 25, Mar 25, Apr 24 |
| Louis Hainaut | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Markus Hausmann | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Alice Hedenlund | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Kathryn Hess | University: École Polytechnique Fédérale de Lausanne | Country: Switzerland | Arrival and Departure: Apr 10 - Apr 24 |
| Mike Hill | University: University of California, Los Angeles | Country: United States | Arrival and Departure: Mar 13 - Apr 11 |
| Kaif Hilman | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Feb 14 - Apr 29 |
| Geoffroy Horel | University: Université Paris Nord | Country: France | Arrival and Departure: Jan 10 - Jan 30 |
| Asaf Horev | University: | Country: | Arrival and Departure: Jan 10 - Apr 29 |
| Axel Husin | University: | Country: | Arrival and Departure: Jan 22 - Apr 29 |
| Alvin Jin | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 17 - Apr 29 |
| Magdalena Kedziorek | University: Radboud University | Country: The Netherlands | Arrival and Departure: Feb 6 - Apr 16 |
| Thomas Kragh | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Achim Krause | University: Muenster University | Country: Germany | Arrival and Departure: Feb 7 - Mar 27 |
| Josefien Kuijper | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Julian Külshammer | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Alexander Kupers | University: University of Toronto | Country: Canada | Arrival and Departure: Jan 17 - Feb 17 |
| Guillaume Laplante-Anfossi | University: Université Sorbonne Paris Nord | Country: France | Arrival and Departure: Feb 13, Apr 14 - Mar 5, Apr 29 |
| Kathryn Lesh | University: Union College | Country: United States | Arrival and Departure: Mar 13 - Apr 30 |
| Matthew Magill | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Martin Markl | University: The Czech Academy of Sciences | Country: Czech Republic | Arrival and Departure: Jan 27 - Mar 2 |
| Lennart Meier | University: Utrecht University | Country: The Netherlands | Arrival and Departure: Apr 19 - Apr 29 |
| Ieke Moerdijk (Online) | University: Utrecht University | Country: The Netherlands | Arrival and Departure: |
| Marco Nervo | University: Utrecht University | Country: The Netherlands | Arrival and Departure: Apr 1 - Apr 29 |
| Bob Oliver (Online) | University: Université Paris 13 | Country: France | Arrival and Departure: |
| Irakli Patchkoria (Online) | University: University of Aberdeen | Country: United Kingdom | Arrival and Departure: |
| Dan Petersen | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Kevin Piterman | University: University of Buenos Aires | Country: Argentina | Arrival and Departure: Jan 14 - Apr 30 |
| Luca Pol | University: University of Regensburg | Country: Germany | Arrival and Departure: Jan 10, Feb 13 - Jan 29, Apr 7 |
| Sanaz Pooya | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Nils Prigge | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Maxime Ramzi | University: | Country: | Arrival and Departure: |
| Oscar Randal-Williams | University: University of Cambridge | Country: United Kingdom | Arrival and Departure: Jan 10 - Feb 12 |
| Sven Raum | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Birgit Richter (Online) | University: Fachbereich Mathematik, Universität Hamburg | Country: Germany | Arrival and Departure: |
| Victor Roca Lucio | University: Université Paris 13 | Country: France | Arrival and Departure: Mar 24 - Apr 8 |
| John Rognes | University: University of Oslo | Country: Norway | Arrival and Departure: Apr 7 - Apr 14 |
| David Rydh | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Feb 17 - Apr 29 |
| Bashar Saleh (Online) | University: Universitat de Barcelona | Country: Spain | Arrival and Departure: |
| Paolo Salvatore | University: Università di Roma Tor Vergata | Country: Italy | Arrival and Departure: Apr 25 - Apr 30 |
| Robin Sroka | University: McMaster University | Country: Canada | Arrival and Departure: Jan 9 - Apr 22 |
| Matthew Stoffregen | University: Michigan State University | Country: United States | Arrival and Departure: Apr 3 - Apr 16 |
| Robin Stoll | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |
| Vignesh Subramanian | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Jan 20 - Apr 29 |
| Victor Turchin | University: Kansas State University | Country: United States | Arrival and Departure: Jan 23 - Feb 9 |
| Bruno Vallette | University: Université Sorbonne Paris Nord | Country: France | Arrival and Departure: Mar 27 - Apr 7 |
| Nathalie Wahl | University: University of Copenhagen | Country: Denmark | Arrival and Departure: Apr 9 - Apr 30 |
| Michael Weiss | University: University of Muenster | Country: Germany | Arrival and Departure: Mar 2 - Mar 20 |
| Craig Westerland | University: University of Minnesota, Twin Cities | Country: United States | Arrival and Departure: Mar 28 - Apr 22 |
| Thomas Willwacher (Online) | University: ETH Zurich | Country: Switzerland | Arrival and Departure: |
| Tomas Zeman | University: Stockholm University | Country: Sweden | Arrival and Departure: Jan 10 - Apr 29 |