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

  • Arrow induction and the dependent Yoneda lemma January 11 15:15 - 17:00

    Arrow induction and the dependent Yoneda lemma

  • Smoothing theory deloopings of disk embedding and diffeomorphism spaces January 13 14:15 - 16:00

    Smoothing theory deloopings of disk embedding and diffeomorphism spaces

  • Postdoc day, Seminar 1: Spectral sequences via décalage January 14 13:30 - 14:00

    Postdoc day, Seminar 1: Spectral sequences via décalage

  • Postdoc day, Seminar 2: Comparing functor calculi January 14 14:10 - 14:40

    Postdoc day, Seminar 2: Comparing functor calculi

  • 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

  • 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

  • A-infinity structures on almost complex manifolds January 18 14:15 - 16:00

    A-infinity structures on almost complex manifolds

  • Finite type knot invariants and the Goodwillie-Weiss tower January 20 14:15 - 16:00

    Finite type knot invariants and the Goodwillie-Weiss tower

  • Postdoc day, Seminar 1: Twisted homology operations January 21 13:30 - 14:00

    Postdoc day, Seminar 1: Twisted homology operations

  • 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

  • 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

  • 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

  • The Torelli Lie algebra January 25 14:15 - 16:00

    The Torelli Lie algebra

  • Embedding calculus for surfaces January 27 14:15 - 16:00

    Embedding calculus for surfaces

  • Combinatorics of multilinear differential operators (…) February 01 14:15 - 16:00

    Combinatorics of multilinear differential operators (…)

  • Bordism of commuting involutions February 03 14:15 - 16:00

    Bordism of commuting involutions

  • A spherical HKR theorem February 08 14:15 - 16:00

    A spherical HKR theorem

  • The Disc-structure space February 10 14:15 - 16:00

    The Disc-structure space

  • 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

  • Postdoc day, Seminar 2: G-global algebraic K-theory February 11 14:10 - 14:40

    Postdoc day, Seminar 2: G-global algebraic K-theory

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Some thoughts about monopole h-invariants February 24 14:15 - 16:00

    Some thoughts about monopole h-invariants

  • 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

  • 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

  • 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

  • Postdoc day, Seminar 4: Replacing functors by enriched ones February 25 15:50 - 16:20

    Postdoc day, Seminar 4: Replacing functors by enriched ones

  • Symplectic groups and cobordism categories March 01 14:15 - 16:00

    Symplectic groups and cobordism categories

  • Hyperelliptic curves, scanning, and moments of quadratic L-functions March 03 14:15 - 16:00

    Hyperelliptic curves, scanning, and moments of quadratic L-functions

  • An Introduction to Symplectic Geometry for Algebraic Topologists March 04 09:15 - 14:00

    An Introduction to Symplectic Geometry for Algebraic Topologists

  • Equivariant Hochschild theories from a shadow perspective March 08 14:15 - 16:00

    Equivariant Hochschild theories from a shadow perspective

  • Configuration space methods applied to automorphism groups of spheres March 10 14:15 - 16:00

    Configuration space methods applied to automorphism groups of spheres

  • Global localization and equivariant Thom spectra March 15 14:15 - 16:00

    Global localization and equivariant Thom spectra

  • Franke’s conjecture and derived infinity categories March 17 14:15 - 16:00

    Franke’s conjecture and derived infinity categories

  • The geometric fixed points of real topological cyclic homology March 22 14:15 - 16:00

    The geometric fixed points of real topological cyclic homology

  • 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

  • Postdoc day, seminar 1: Equivariant factorization homology March 25 14:15 - 14:45

    Postdoc day, seminar 1: Equivariant factorization homology

  • 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

  • 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

  • Higher Lie theory March 29 14:15 - 16:00

    Higher Lie theory

  • Stratification for spaces with Noetherian mod p cohomology March 31 14:15 - 16:00

    Stratification for spaces with Noetherian mod p cohomology

  • 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

  • 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

  • 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

  • Twisted generating functions and the nearby Lagrangian conjecture (I) April 05 13:30 - 14:30

    Twisted generating functions and the nearby Lagrangian conjecture (I)

  • Twisted generating functions and the nearby Lagrangian conjecture (II) April 05 15:00 - 16:00

    Twisted generating functions and the nearby Lagrangian conjecture (II)

  • Complex cobordism, Hamiltonian loops and global Kuranishi charts April 07 15:15 - 16:15

    Complex cobordism, Hamiltonian loops and global Kuranishi charts

  • Algebraic K-theory of elliptic cohomology April 12 14:15 - 16:00

    Algebraic K-theory of elliptic cohomology

  • A Seiberg-Witten Floer stable homotopy type April 13 14:15 - 16:00

    A Seiberg-Witten Floer stable homotopy type

  • 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

  • THH, shadows, and bicategorical traces April 19 14:15 - 16:00

    THH, shadows, and bicategorical traces

  • Braided Hopf algebras, operads, and partitions April 21 14:15 - 16:00

    Braided Hopf algebras, operads, and partitions

  • From elliptic genera to equivariant topological modular forms April 26 14:15 - 16:00

    From elliptic genera to equivariant topological modular forms

  • Koszul self-duality of E_n operads in spectra April 28 14:15 - 16:00

    Koszul self-duality of E_n operads in spectra

Participants

Name University Country Arrival and Departure
Mohammed
Abouzaid
University: Columbia University City: United States Arrival and Departure: Apr 4 - Apr 10, 2022
Daniel
Alvarez-Gavela
University: Massachusetts Institute of Technology City: United States Arrival and Departure: Apr 3 - April 9, 2022
Gregory
Arone
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - April 29, 2022
Alexis
Aumonier
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 10, Apr 11 - Feb 6, Apr 29, 2022
Russell
Avdek
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Tobias
Barthel
University: Max Planck Institute for Mathematics City: Germany Arrival and Departure: Apr 4 - Apr 13, 2022
Tilman
Bauer
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: -
Özgur
Bayindir
University: City, University of London City: United Kingdom Arrival and Departure: Jan 27 - Mar 27, 2022
Eva
Belmont
University: University of California San Diego City: United States Arrival and Departure: Mar 16 - Mar 26, 2022
Alexander
Berglund
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Andrea
Bianchi
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 30 - Feb 19, 2022
Thomas
Blom
University: Stockholm University City: Sweden Arrival and Departure: Jan 13 - Apr 29, 2022
Dorin
Boger (Online)
University: City: Arrival and Departure: -
Lukas
Brantner
University: University of Oxford / Université Paris-Saclay (Orsay) City: United Kingdom / France Arrival and Departure: Mar 17, Apr 17 - Mar 30, Apr 28, 2022
Urtzi
Buijs
University: University of Malaga City: Spain Arrival and Departure: Apr 23 - Apr 29, 2022
Natalia
Castellana
University: Universitat Autònoma de Barcelona City: Spain Arrival and Departure: Mar 21 - Apr 8, 2022
Wojtek
Chacholski
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Sylvain
Courte
University: Université Grenoble Alpes City: France Arrival and Departure: Apr 3 - Apr 9, 2022
Come
Dattin
University: Utrecht University City: Sweden Arrival and Departure: -
Jack Morgan
Davies
University: Utrecht University City: The Netherlands Arrival and Departure: Feb 6 - Mar 20, 2022
Georgios
Dimitroglou Rizell
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Emanuele
Dotto
University: University of Warwick City: United Kingdom Arrival and Departure: Mar 20 - Apr 2, 2022
Sylvain
Douteau
University: Stockholm University City: Sweden Arrival and Departure: Feb 7 - Apr 29, 2022
Coline
Emprin
University: Ecole Normale Supérieure de Paris City: France Arrival and Departure: Mar 23 - Apr 4, 2022
Hadrien
Espic
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Søren
Galatius
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 19 - Feb 4, 2022
Jesper
Grodal
University: University of Copenhagen City: Denmark Arrival and Departure: Feb 16, Mar 14, Apr 9 - Feb 25, Mar 25, Apr 24, 2022
Louis
Hainaut
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Markus
Hausmann
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Alice
Hedenlund
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Kathryn
Hess
University: École Polytechnique Fédérale de Lausanne City: Switzerland Arrival and Departure: Apr 10 - Apr 24, 2022
Mike
Hill
University: University of California, Los Angeles City: United States Arrival and Departure: Mar 13 - Apr 11, 2022
Kaif
Hilman
University: University of Copenhagen City: Denmark Arrival and Departure: Feb 14 - Apr 29, 2022
Geoffroy
Horel
University: Université Paris Nord City: France Arrival and Departure: Jan 10 - Jan 30, 2022
Asaf
Horev
University: City: Arrival and Departure: Jan 10 - Apr 29, 2022
Axel
Husin
University: City: Arrival and Departure: Jan 22 - Apr 29, 2022
Alvin
Jin
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Jan 17 - Apr 29, 2022
Magdalena
Kedziorek
University: Radboud University City: The Netherlands Arrival and Departure: Feb 6 - Apr 16, 2022
Thomas
Kragh
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Achim
Krause
University: Muenster University City: Germany Arrival and Departure: Feb 7 - Mar 27, 2022
Josefien
Kuijper
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Julian
Külshammer
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Alexander
Kupers
University: University of Toronto City: Canada Arrival and Departure: Jan 17 - Feb 17, 2022
Guillaume
Laplante-Anfossi
University: Université Sorbonne Paris Nord City: France Arrival and Departure: Feb 13, Apr 14 - Mar 5, Apr 29, 2022
Kathryn
Lesh
University: Union College City: United States Arrival and Departure: Mar 13 - Apr 30, 2022
Matthew
Magill
University: Uppsala University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Martin
Markl
University: The Czech Academy of Sciences City: Czech Republic Arrival and Departure: Jan 27 - Mar 2, 2022
Lennart
Meier
University: Utrecht University City: The Netherlands Arrival and Departure: Apr 19 - Apr 29, 2022
Ieke
Moerdijk (Online)
University: Utrecht University City: The Netherlands Arrival and Departure: -
Marco
Nervo
University: Utrecht University City: The Netherlands Arrival and Departure: Apr 1 - Apr 29, 2022
Bob
Oliver (Online)
University: Université Paris 13 City: France Arrival and Departure: -
Irakli
Patchkoria (Online)
University: University of Aberdeen City: United Kingdom Arrival and Departure: -
Dan
Petersen
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Kevin
Piterman
University: University of Buenos Aires City: Argentina Arrival and Departure: Jan 14 - Apr 30, 2022
Luca
Pol
University: University of Regensburg City: Germany Arrival and Departure: Jan 10, Feb 13 - Jan 29, Apr 7, 2022
Sanaz
Pooya
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Nils
Prigge
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Maxime
Ramzi
University: City: Arrival and Departure: -
Oscar
Randal-Williams
University: University of Cambridge City: United Kingdom Arrival and Departure: Jan 10 - Feb 12, 2022
Sven
Raum
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Birgit
Richter (Online)
University: Fachbereich Mathematik, Universität Hamburg City: Germany Arrival and Departure: -
Victor
Roca Lucio
University: Université Paris 13 City: France Arrival and Departure: Mar 24 - Apr 8, 2022
John
Rognes
University: University of Oslo City: Norway Arrival and Departure: Apr 7 - Apr 14, 2022
David
Rydh
University: KTH Royal Institute of Technology City: Sweden Arrival and Departure: Feb 17 - Apr 29, 2022
Bashar
Saleh (Online)
University: Universitat de Barcelona City: Spain Arrival and Departure: -
Paolo
Salvatore
University: Università di Roma Tor Vergata City: Italy Arrival and Departure: Apr 25 - Apr 30, 2022
Robin
Sroka
University: McMaster University City: Canada Arrival and Departure: Jan 9 - Apr 22, 2022
Matthew
Stoffregen
University: Michigan State University City: United States Arrival and Departure: Apr 3 - Apr 16, 2022
Robin
Stoll
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022
Vignesh
Subramanian
University: University of Copenhagen City: Denmark Arrival and Departure: Jan 20 - Apr 29, 2022
Victor
Turchin
University: Kansas State University City: United States Arrival and Departure: Jan 23 - Feb 9, 2022
Bruno
Vallette
University: Université Sorbonne Paris Nord City: France Arrival and Departure: Mar 27 - Apr 7, 2022
Nathalie
Wahl
University: University of Copenhagen City: Denmark Arrival and Departure: Apr 9 - Apr 30, 2022
Michael
Weiss
University: University of Muenster City: Germany Arrival and Departure: Mar 2 - Mar 20, 2022
Craig
Westerland
University: University of Minnesota, Twin Cities City: United States Arrival and Departure: Mar 28 - Apr 22, 2022
Thomas
Willwacher (Online)
University: ETH Zurich City: Switzerland Arrival and Departure: -
Tomas
Zeman
University: Stockholm University City: Sweden Arrival and Departure: Jan 10 - Apr 29, 2022

Preprints

  1. The Disc-structure space - Manuel Krannich Alexander Kupers
  2. Two-variable fibrations, factorisation systems and ∞-categories of spans - Rune Haugseng Fabian Hebestreit Sil Linskens Joost Nuiten
  3. The localisation theorem for the K-theory of stable ∞-categories - Fabian Hebestreit Andrea Lachmann Wolfgang Steimle
  4. Stability of concordance embeddings - Thomas Goodwillie Manuel Krannich Alexander Kupers
  5. Two remarks on spaces of maps between operads of little cubes - Geoffroy Horel Manuel Krannich Alexander Kupers
  6. Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions - Jonas Bergström Adrian Diaconu Dan Petersen Craig Westerland