Du 24 au 28 février 2020
IRMA
Organizer : Christine Vespa (IRMA Strasbourg) Invited Speakers :
- Aurélien Djament (CNRS - Université de Lille)
- Nariya Kawazumi (The University of Tokyo)
- Yusuke Kuno (Tsuda University - Tokyo)
- Pedro Tamaroff (Trinity College - Dublin)
Venue : Salle de conférences, IRMA building, University of Strasbourg.
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Lundi 24 février 2020
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10:00
Yusuke Kuno, Tsuda University - Tokyo
Formality of the Goldman-Turaev Lie bialgebra and its applications (1)
The space spanned by free homotopy classes of loops in an oriented surface has the structure of a Lie bialgebra, called the Goldman-Turaev Lie bialgebra. It is defined in terms of intersections and self-intersections of loops. In this series of lectures, we explain that this Lie bialgebra is formal in the sense that it is isomorphic (non-canonically) to its associated graded. We also discuss applications of our method to the study of the mapping class group of the surface. Roughly, the first two lectures will focus on the Lie bracket (Goldman bracket), and the last two lectures on the Lie cobracket (Turaev cobracket). This is based on a joint work with Anton Alekseev and Florian Neaf. -
Mardi 25 février 2020
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10:00
Yusuke Kuno, Tsuda University - Tokyo
Formality of the Goldman-Turaev Lie bialgebra and its applications (2)
The space spanned by free homotopy classes of loops in an oriented surface has the structure of a Lie bialgebra, called the Goldman-Turaev Lie bialgebra. It is defined in terms of intersections and self-intersections of loops. In this series of lectures, we explain that this Lie bialgebra is formal in the sense that it is isomorphic (non-canonically) to its associated graded. We also discuss applications of our method to the study of the mapping class group of the surface. Roughly, the first two lectures will focus on the Lie bracket (Goldman bracket), and the last two lectures on the Lie cobracket (Turaev cobracket). This is based on a joint work with Anton Alekseev and Florian Neaf. -
11:15
Igor Burban, (Paderborn University)
Non-commutative nodal curves and mirror symmetry for compact surfaces with boundary (Séminaire Analyse)
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14:00
Christine Vespa, Université de Strasbourg
On the PROP of the stable cohomology of the groups Aut(F_n) with bivariant coefficients
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Mercredi 26 février 2020
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10:00
Nariya Kawazumi, The University of Tokyo
Formality of the Goldman-Turaev Lie bialgebra and its applications (3)
The space spanned by free homotopy classes of loops in an oriented surface has the structure of a Lie bialgebra, called the Goldman-Turaev Lie bialgebra. It is defined in terms of intersections and self-intersections of loops. In this series of lectures, we explain that this Lie bialgebra is formal in the sense that it is isomorphic (non-canonically) to its associated graded. We also discuss applications of our method to the study of the mapping class group of the surface. Roughly, the first two lectures will focus on the Lie bracket (Goldman bracket), and the last two lectures on the Lie cobracket (Turaev cobracket). This is based on a joint work with Anton Alekseev and Florian Neaf. -
11:15
Aurélien Djament, CNRS-Université de Lille
Homological comparison of several categories of free groups, and applications
After some reminders on the use of functor homology to approach stable homology of sequences of groups with twisted coefficients, and how it works for linear groups (after Scorichenko), I will explain what happens for automorphism groups of free groups. It needs to introduce several categories of free groups (with different kinds of morphisms) and more intermediate steps. I will especially give the idea of the proof of a cancellation result for reduced covariant polynomial coefficients (on the ordinary category of free groups), obtained with Vespa (Commentarii 2015) and of some step of the proof of the result obtained for contravariant polynomial coefficients (Compositio 2019), and also give a conjecture for bivariant polyomial coefficients. -
Jeudi 27 février 2020
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10:00
Nariya Kawazumi, The University of Tokyo
Formality of the Goldman-Turaev Lie bialgebra and its applications (4)
The space spanned by free homotopy classes of loops in an oriented surface has the structure of a Lie bialgebra, called the Goldman-Turaev Lie bialgebra. It is defined in terms of intersections and self-intersections of loops. In this series of lectures, we explain that this Lie bialgebra is formal in the sense that it is isomorphic (non-canonically) to its associated graded. We also discuss applications of our method to the study of the mapping class group of the surface. Roughly, the first two lectures will focus on the Lie bracket (Goldman bracket), and the last two lectures on the Lie cobracket (Turaev cobracket). This is based on a joint work with Anton Alekseev and Florian Neaf. -
11:15
Pedro Tamaroff, Trinity College Dublin
(Derived) PBW theorems for algebras over operads
We provide an abstract monadic framework for Poincaré-Birkhoff-Witt type theorems about universal enveloping algebras of various algebraic structures, with special interest in operads and their algebras. Our main result establishes that the universal envelope functor associated to a map of monads enjoys a Poincaré-Birkhoff-Witt property if and only if this map makes its codomain a free right module over its domain. As an application, we give a new proof of the classical Poincaré-Birkhoff-Witt theorem and the Quillen quasi-isomorphism C ---> BU. We then show how to produce a natural generalization of our result for dg operads, and prove a novel ''derived'' Poincaré-Birkhoff-Witt theorem for homotopy Lie algebras, which unifies the work of several authors on the universal envelopes of homotopy Lie algebras. Along the way, we will also mention other interesting applications of the theory. The talk is based on joint work with V. Dotsenko and on work in progress with A. Khoroshkin. -
Vendredi 28 février 2020
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10:00
Vladimir Dotsenko, Université de Strasbourg
Variations on the pre-Lie theme
The goal of this talk is to present several new results concerning the operad controlling pre-Lie algebras, a truly remarkable algebraic structure that appears in many different contexts including combinatorics, differential geometry, homotopy theory and mathematical physics. In particular, I will discuss my recent work with O. Flynn-Connolly on universal enveloping pre-Lie algebras of Lie algebras, and about the connections of Markl's theorem from 2005 on Lie elements in free pre-Lie algebras to Willwacher's theory of operadic twisting.