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José São João21/10/2024 10:00
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Benachir El Allaoui21/10/2024 11:00
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Tommy-Lee Klein21/10/2024 14:00
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Nicolas Guès21/10/2024 15:00
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Paul Laubie21/10/2024 16:30
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21/10/2024 17:30
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Clément Dupont (Université de Montpellier)22/10/2024 10:15
Various maps arising in topology look like they should come from algebraic geometry, if only one could allow them to take values « at infinity ». This is the case for the little disks operad, whose underlying spaces have the homotopy type of the configuration spaces of points on the affine line, but whose operadic maps are not algebraic in any obvious way. I will explain how to solve this...
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Viktoriya Ozornova22/10/2024 11:15
The main objective of this series is to discuss the relationship of strict and (various variants of) weak higher categories. The beginning is the case of usual categories being embedded into $(\infty,1)$-categories. We will discuss this embedding in different models for $(\infty,1)$-categories, alongside with a reminder on these models. Once the case $n=1$ is somewhat understood, we will move...
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Jean Douçot22/10/2024 14:30
Via the Riemann-Hilbert correspondence, character varieties
can be seen as moduli spaces of monodromy data of meromorphic
connections with regular singularities on a Riemann surface. Varying the
curve with marked points, this leads to isomonodromic deformations and
to the well-known mapping class group actions on character varieties.This story admits a far-reaching generalization if we...
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Inbar Klang22/10/2024 15:30
I will give an introduction to topological Hochschild homology via free loop spaces and configuration spaces, and talk about its relationship with algebraic K-theory. I will then discuss what happens in the presence of a finite group action. This will touch upon joint work with Adamyk, Gerhardt, Hess, and Kong, and joint work in progress with Chan and Gerhardt.
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Oisin Flynn Connolly22/10/2024 16:45
In this talk, I will present joint work with José Moreno-Fernández and Felix Wierstra on coalgebras in topological spaces. We will construct the comonad associated to a topological operad and we will sketch the proof of a recognition principle for iterated suspensions as coalgebras over the little cubes operad. These statements are Eckmann-Hilton dual to May's foundational results on iterated...
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Mario Fuentes23/10/2024 09:00
The rational homotopy type of simply connected spaces is fully captured by its Quillen model, a differential graded Lie algebra constructed from the space. Conversely, any positively graded differential Lie algebra can be "realized" as a topological space, with rational homotopical and homological invariants preserved by these two functors.
However, these constructions are inherently...
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Mohamed Ayadi23/10/2024 10:00
In this presentation, I will discuss the classification method for finite topological quandles for a given cardinality n. As an application, we classify finite topological quandles with up to 4 elements. Then in a second step, I will talk about twisted bialgebra structures within the realm of finite topological quandle species, one of the first kind and one of the second kind. The obstruction...
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Viktoriya Ozornova23/10/2024 11:30
The main objective of this series is to discuss the relationship of strict and (various variants of) weak higher categories. The beginning is the case of usual categories being embedded into $(\infty,1)$-categories. We will discuss this embedding in different models for $(\infty,1)$-categories, alongside with a reminder on these models. Once the case $n=1$ is somewhat understood, we will move...
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Samuel Lerbet (Institut Fourier, Université Grenoble Alpes)23/10/2024 14:30
Unimodular rows are fundamental objects in algebraic K-theory as they classify stably free projective modules. Geometrically, they correspond to morphisms to punctured affine space and may thus be thought of as an algebro-geometric analogue of maps to spheres in topology. The latter give rise to Borsuk's cohomotopy groups, a counterpart to which was constructed purely algebraically by van der...
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Clover May23/10/2024 15:30
Cohomology with $\mathbb{Z}/p$-coefficients is represented by a stable object, an Eilenberg--MacLane spectrum $H\mathbb{Z}/p$. Classically, since $\mathbb{Z}/p$ is a field, any module over $H\mathbb{Z}/p$ splits as a wedge of suspensions of $H\mathbb{Z}/p$ itself. Equivariantly, cohomology and the module theory of $G$-equivariant Eilenberg--MacLane spectra are much more complicated.
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For the... -
Niels Feld23/10/2024 16:45
In the nineties, Voevodsky proposed a radical unification of algebraic and topological methods. The amalgam of algebraic geometry and homotopy theory that he and Fabien Morel developed is known as motivic homotopy theory. Roughly speaking, motivic homotopy theory imports methods from simplicial homotopy theory and stable homotopy theory into algebraic geometry and uses the affine line to...
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Hugo Pourcelot (LAGA)24/10/2024 09:00
Given a monoidal adjunction and a certain orientation datum on the right adjoint F, I will explain how to transport gebras over dioperads along F, via endowing this functor with a shifted Frobenius monoidal structure. This procedure generalizes so-called integration along the fiber, which is for instance the case when F is the pushforward of a projection X x M --> X, with M a closed oriented...
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Marvin Verstraete24/10/2024 10:00
An important result in deformation theory over a field of characteristic 0 asserts that every deformation problem can be controlled by a differential graded Lie algebra. More precisely, every solution of a deformation problem over a field of characteristic 0 can be seen as a Maurer-Cartan element in some dg lie algebra $L$. The isomorphisms classes of deformation problems are also in...
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Viktoriya Ozornova24/10/2024 11:30
The main objective of this series is to discuss the relationship of strict and (various variants of) weak higher categories. The beginning is the case of usual categories being embedded into $(\infty,1)$-categories. We will discuss this embedding in different models for $(\infty,1)$-categories, alongside with a reminder on these models. Once the case $n=1$ is somewhat understood, we will move...
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Léo Hubert24/10/2024 14:30
Grothendieck's theory of test categories allows to characterize small categories with the property that an appropriate localization of their categories of presheaves modelize the homotopy category of spaces. Any test category then allows to do homotopy theory just as well as traditional simplicial sets can.
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However, simplicial sets exhibit other niceties. Among them is the Dold-Kan... -
Francesca Pratali (Université Sorbonne Paris Nord)24/10/2024 15:30
By a result of Heuts-Moerdijk, the oo-category of simplicial diagrams on the nerve of a discrete category A is equivalent to that of left fibrations over the nerve of A. This is an instance of the well known Grothendieck-Lurie straightening-unstraightening theorem.
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In this talk, we will explain how one can generalize this result to the operadic case. More specifically, by working with the... -
Morgan Rogers24/10/2024 16:45
My work revolves around monoids acting on things, especially in the context of (1-)topos theory. As such, it is through this lens that I view the ingedients of algebraic geometry, and I will tell you about this perspective. From a research perspective, this work hasn't gone very far yet; I merely intend to sketch out for you a different way of setting up the big picture.
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Since (Grothendieck)... -
Léonard Guetta25/10/2024 09:15
In this talk, I will present a joint work with Lyne Moser where we prove that double categories model (oo,1)-categories. More precisely, we equip the category of double categories with a model category structure and show that it is Quillen equivalent to the Rezk model category structure on bisimplicial sets.
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I will also explain how this model of (oo,1)-categories is related to other... -
Paula Verdugo25/10/2024 10:15
Equipments, a special kind of double categories, have shown to be a powerful environment to express formal category theory. We build a model structure on the category of double categories and double functors whose fibrant objects are the equipments, and combine this together with Makkai’s early approach to equivalence invariant statements in higher category theory via FOLDS (First Order Logic...
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Éric Hoffbeck25/10/2024 11:40
Using two different subcategories A and R of Omega (the category of trees), we first define linear infinity-operads as some presheaves (over A with values in chain complexes) with additional structure maps inducing a "composition up to homotopy"). We then define algebras over such an infinity-operad X as presheaves (over R with values in chain complexes) with structure maps encoding an "action...
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