Higher structure 2013: operads and deformation theory

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Workshop theme

The notion of an operad was introduced in the late 60's in algebraic topology as a tool to encode higher homotopies. It enjoyed a renaissance in the 90's when M. Kontsevich and others used algebraic operads in deformation theory.

The passage from classical mechanics to quantum mechanics prompted the general mathematical problem of deformation quantization. In Poisson geometry, such a problem was solved by D. Fedosov for symplectic manifolds, by V. Drinfeld for Poisson-Lie groups, and by M. Kontsevich for Poisson manifolds. In 1998, six months after Kontsevich's original proof, D. Tamarkin gave another but purely operadic proof of the deformation quantization of Poisson manifolds, using the formality of the little discs operad, the Deligne conjecture, and the deformation-quantization of Lie bialgebras due to P. Etingof and D. Kazhdan.

The introduction of operadic graph homology in 1991 by M. Kontsevich allowed V. Ginzburg and M. Kapranov, and E. Getzler and J. Jones to develop the Koszul duality theory on the level of algebraic operads. This theory gives a conceptual explanation of the duality between commutative algebras and Lie algebras in Rational Homotopy Theory, developed by D. Quillen and D. Sullivan. It was also shown by M. Kontsevich, E. Getzler, and Y.I. Manin to share nice relationships with moduli spaces of curves, i.e. quantum cohomology and Frobenius manifolds. The operadic calculus play a key role in Quantum Field Theory in mathematical physics since it provides an algebraic way to control higher structures.

The goal of this conference is to cover the most recent and interesting developments of these fields of research.

Timetable

Tuesday 2nd April 2013
09:00 to 09:25	Registration	No Room Required
09:25 to 09:30	Welcome from INI Director, John Toland	No Room Required
09:30 to 10:30	Ulrike Tillmann University of Oxford Homology stability for symmetric diffeomorphisms and their mapping classes	Room 1
10:30 to 11:00	Morning Coffee	No Room Required
11:00 to 12:00	John Francis Northwestern University Factorization homology of topological manifolds	Room 1
12:15 to 13:15	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Alexander Berglund Stockholm University Rational homotopy theory of automorphisms of highly connected manifolds	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Dee Roytenberg Universiteit Utrecht A Dold-Kan-type correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry	Room 1
16:30 to 17:30	Boris Tsygan Northwestern University Operations on Hochschild complexes, revisited	Room 1
17:30 to 19:00	Wine Reception & Poster session	No Room Required

Wednesday 3rd April 2013
09:30 to 10:30	Alberto Cattaneo Universität Zürich Classical and quantum Lagrangian field theories on manifolds with boundaries	Room 1
10:30 to 11:00	Morning Coffee	No Room Required
11:00 to 12:00	Pavol Severa Observatoire Astronomique de l'Universite de Geneve Integration of differential graded manifolds	Room 1
12:15 to 13:15	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Graeme Segal University of Oxford Bott periodicity in Algebra	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Kathryn Hess The Boardman-Vogt tensor product of operadic bimodules	Room 1
16:30 to 17:30	Ieke Moerdijk Radboud Universiteit Nijmegen Two models for infinity-operads	Room 1
19:30 to 22:00	Conference Dinner at Christ's College	No Room Required

Thursday 4th April 2013
09:30 to 10:30	Bertrand Toën Université de Montpellier 2 Symplectic and Poisson structures in the derived setting	Room 1
10:30 to 11:00	Morning Coffee	No Room Required
11:00 to 12:00	Vladimir Dotsenko Trinity College Dublin Givental action is gauge symmetry in a homotopy Lie algebra	Room 1
12:15 to 13:15	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Yuri Ivanovich Manin Max-Planck-Institut für Mathematik, Bonn Computability and Zipf's Law: operadic perspective	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Jon Pridham University of Cambridge Strong homotopy (bi)algebras, homotopy coherent diagrams and derived deformations	Room 1
16:30 to 17:30	Nathalie Wahl Københavns Universitet (University of Copenhagen) Higher string topology	Room 1

Friday 5th April 2013
09:30 to 10:30	Ezra Getzler Northwestern University The nerve of a differential graded algebra	Room 1
10:30 to 11:00	Morning Coffee	No Room Required
11:00 to 12:00	Thomas Willwacher Harvard University Deformations of the En-operad	Room 1
12:15 to 13:15	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Jeffrey Giansiracusa Swansea University Moduli spaces of geometric structures on surfaces and modular operads	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Ralph Cohen Stanford University Gauge theory, loop groups, and string topology	Room 1

Grothendieck-Teichmüller groups, deformation and operads

Higher structure 2013: operads and deformation theory

Speakers

Alexander Berglund Stockholm University
Alberto Cattaneo Universität Zürich
Ralph Cohen Stanford University
Vladimir Dotsenko Trinity College Dublin
John Francis Northwestern University
Ezra Getzler Northwestern University
Jeffrey Giansiracusa Swansea University
Kathryn Hess
Yuri Ivanovich Manin Max-Planck-Institut für Mathematik, Bonn
Ieke Moerdijk Radboud Universiteit Nijmegen
Jon Pridham University of Cambridge
Dee Roytenberg Universiteit Utrecht
Graeme Segal University of Oxford
Pavol Severa Observatoire Astronomique de l'Universite de Geneve
Ulrike Tillmann University of Oxford
Bertrand Toën Université de Montpellier 2
Boris Tsygan Northwestern University
Nathalie Wahl Københavns Universitet (University of Copenhagen)
Thomas Willwacher Harvard University

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Higher structure 2013: operads and deformation theory

Workshop theme

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