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Kathryn Hess Bellwald (EPFL)26/10/2021 10:30
Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies, to automatic detection of network dynamics, to understanding the neural representation of natural auditory signals, and to demonstrating that the population activity of grid cells...
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Noémie Combe26/10/2021 14:00
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Martin Palmer-Anghel26/10/2021 14:45
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Hugo Pourcelot26/10/2021 16:00
Étant donnée une ∞-opérade cohérente O, on peut munir l’espace des extensions de l’identité d’une structure canonique de O-algèbre, à valeurs dans la catégorie des cocorrespondances. Cette action a été introduite par Toën puis adaptée par Mann–Robalo en vue d’applications aux invariants de Gromov–Witten. J’exposerai une généralisation de cette construction, couvrant le cas des ∞-opérades...
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Sebastian Cea26/10/2021 16:45
Intersection (co)homology is a way to enhance classical (co)homology, allowing us to use a famous result called Poincaré duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive at intersection (co)homology by a classifying sheaves that satisfy what are called the Deligne axioms.
Parallel to this, it is common knowledge in...
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Najib Idrissi (Université Paris Diderot / IMJ-PRG)27/10/2021 09:00
The usual Swiss-Cheese operad encodes triplets (A,B,f), where A is an algebra over the little disks operad in dimension n (i.e., an \mathsf{E}n-algebra), B is an \mathsf{E}{n-1}-algebra, and f : A \to Z(B) is a central morphism of E_n-algebras.
The Swiss-Cheese operad admits several variants and generalizations. In Voronov's original version, the morphism is replaced by an action A...
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Kathryn Hess Bellwald (EPFL)27/10/2021 10:30
Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies, to automatic detection of network dynamics, to understanding the neural representation of natural auditory signals, and to demonstrating that the population activity of grid cells...
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Alexander Berglund27/10/2021 14:00
For a simply connected finite CW-complex X, we construct a tractable model for the rational homotopy type of the classifying space Baut(X) of the topological monoid of self-homotopy equivalences of X, aka the classifying space for fibrations with fiber X.
The space Baut(X) is in general far from nilpotent, so one should not expect to be able to model its rational homotopy type by a dg Lie...
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Bruno Vallette27/10/2021 15:30
This talk will cover the recent complete treatment of the long-term research programme between Lie theory, deformation theory, and rational homotopy theory that originates in the works of Quillen, Deligne, and Sullivan. I will settle the integration theory of homotopy Lie algebras with algebraic infini-groupoids that give rise to explicit higher Baker—Campbell—Hausdorff formulas. A direct...
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Victor Roca Lucio27/10/2021 16:20
The integration procedure which associates an infinity-groupoid to a (complete) homotopy Lie algebra dates back to Hinich and Getzler. Recently, a new method was developed by Robert-Nicoud and Vallette: it relies on the representation of the Getzler functor with a universal object and the use of the recent progresses of the operadic calculus. The goal of this talk is to generalize their...
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Joana Cirici28/10/2021 09:00
Dolbeault cohomology is a fundamental cohomological invariant for complex manifolds. This analytic invariant is connected to de Rham cohomology by means of a spectral sequence, called the Frölicher spectral sequence. In this talk, I will explore this connection from a multiplicative viewpoint: using homotopy-theoretical methods, I will describe how products (and higher products) behave in the...
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Thibaut Mazuir28/10/2021 10:30
In this talk, I will introduce the notion of n-morphisms between two A-infinity algebras. These higher morphisms are such that 0-morphisms corresponds to A-infinity morphisms and 1-morphisms correspond to A-infinity homotopies. I will then prove that the set of higher morphisms between two A-infinity algebras provide a satisfactory framework to study the higher algebra of A-infinity algebras :...
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Guillaume Laplante-Anfossi28/10/2021 11:20
Nous présentons une nouvelle famille de réalisations des opéraèdres, une famille de polytopes qui codent les opérades à homotopie près comprenant l'associaèdre et le permutoèdre. En se servant des techniques récemment développées par N. Masuda, A. Tonks, H. Thomas et B. Vallette, nous définissons une approximation cellulaire de la diagonale pour cette famille de polytopes de même que le...
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Sinan Yalin28/10/2021 14:00
Since the Newlander-Nirenberg integrability theorem in 1957, the description of complex manifolds through integrable almost complex structures provided many far reaching applications ranging from deformation theory to Hodge theory for example.With the rise of derived geometry during the last decade, and more recently of derived analytic geometry, comes naturally the following question: is...
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Jérôme Scherer28/10/2021 15:30
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Cristina Costoya29/10/2021 09:00
An oriented closed connected d-manifold is inflexible if it does not admit selfmaps of unbounded degree. In addition, if for every oriented closed connected d-manifold M ′ the set of degrees of maps M′ → M is finite, then M is said to be strongly inflexible. The first examples of simply connected inflexible manifolds have been constructed by Arkowitz and Lupton using Rational Homotopy Theory....
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Mariam Pirashvili29/10/2021 10:30
Crossed modules are algebraic models of homotopy 2-types and hence have \pi_1 and \pi_2 . We propose a definition of the centre of a crossed module whose essential invariants can be computed via the group cohomology H^i (\pi_1, \pi_2). This definition therefore has much nicer properties than one proposed by Norrie in the 80’s.
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Sarah Whitehouse (University of Sheffield)29/10/2021 11:10
Model categories give an abstract setting for homotopy theory, allowing study of different notions of equivalence. I'll discuss various categories with associated functorial spectral sequences. In such settings, one can consider a hierarchy of notions of equivalence, given by morphisms inducing an isomorphism at a fixed stage of the associated spectral sequence. I'll discuss model structures...
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Jovana Obradovic
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