Talks in mathematical physics

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Date / Time

Speaker

Title

Location

17 March 2025
13:30-14:30

Alex Takeda
Uppsala University

Details

Title	Formality of Y-infinity algebras and operations in string topology
Speaker, Affiliation	Alex Takeda, Uppsala University
Date, Time	17 March 2025, 13:30-14:30
Location	Y27 H 25
Abstract	I will define a certain type of properadic algebra called a Y-infinity algebra, which is an A-infinity algebra together with higher structure maps encoding a certain type of Poincaré duality structure. In particular, the algebra of chains on the based loop space of any oriented manifold is canonically endowed with this type of structure. By using the formalism of properadic Kaledin classes, we can study these algebraic structures and detect their formality, or lack thereof. I will also explain the relation between these algebraic structures and string topology operations, and how Y-infinity formality plays a role in understanding these operations. This talk is about joint works with M. Rivera, Z. Wang and C. Emprin.

Formality of Y-infinity algebras and operations in string topologyread_more

7 April 2025
13:30-14:30

Coline Emprin
Ecole Normale Supérieure de Paris

Details

Title	Kaledin classes and formality criteria
Speaker, Affiliation	Coline Emprin, Ecole Normale Supérieure de Paris
Date, Time	7 April 2025, 13:30-14:30
Location	Y27 H 25
Abstract	A differential graded algebraic structure A (e.g. an associative algebra, a Lie algebra, an operad, etc.) is formal if it is related to its homology H(A) by a zig-zag of quasi-isomorphisms preserving the algebraic structure. Kaledin classes were introduced as an obstruction theory fully characterizing the formality of associative algebras over a characteristic zero field. In this talk, I will present a generalization of Kaledin classes to any coefficients ring, to other algebraic structures (encoded by operads, possibly colored, or by properads), and to address a more general problem: the existence of homotopy equivalences between algebraic structures. I will prove new formality criteria based on this obstruction theory, presenting applications in several domains such as algebraic geometry, representation theory and mathematical physics.

Kaledin classes and formality criteriaread_more

Y27 H 25

14 April 2025
13:30-14:30

Marvin Dippel
University of Salerno

Details

Title	DeformationTheory for generalized Coisotropic Reduction
Speaker, Affiliation	Marvin Dippel, University of Salerno
Date, Time	14 April 2025, 13:30-14:30
Location	Y27 H 25
Abstract	Reduction of Poisson manifolds by coisotropic submanifolds formalizes symmetry reduction of classical mechanical systems, and therefore plays an important role in Poisson geometry. Constraint algebras encode the additional structure on the algebra of functions needed for reduction and their deformations yield (formal) star products compatible with reduction. I will discuss the deformation theory of these constraint algebras and present some results about an adapted Hochschild-Kostant-Rosenberg Theorem computing the cohomology controlling this deformation theory.

DeformationTheory for generalized Coisotropic Reductionread_more

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