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Dr Grégory Ginot (Paris 6)10/21/15, 9:00 AMTopAlgMini-coursLecture I: Factorization homology is a bifunctor from (structured) manifolds of dimension n and algebras over the little n-cubes operad. We will explain the axioms it satisfies and how it can be thought of as a kind of (derived) generalization of Eilenberg-Steenrod usual axioms of Homology of spaces. We will also give some examples .Go to contribution page
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Dr Rosona Eldred (Münster)10/21/15, 10:40 AMTopAlgExposé de recherche sur propositionIn the 90s, Goodwillie developed a calculus of homotopy functors of spaces/spectra, which gave rise to other variants, such as the orthogonal calculus of Weiss for functors of real inner product spaces. I will report on joint work with David Barnes wherein we formalize the comparison of these two theories, which involves making rigorous the folk result that n-excisive implies n-polynomial.Go to contribution page
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Prof. Stéphane Baseilhac (Montpellier)10/21/15, 11:40 AMTopAlgExposé de recherche sur invitationI will explain how the 2-3 triangulation move, in the context of hyperbolic polyhedra, gives rise to an essentially unique sequence of (2+1)-dimensional QFT, including the Chern-Simons functional of sl(2,C)-connections (as the classical case), quantum Teichmüller theory, and the quantum hyperbolic invariants of 3-manifolds.Go to contribution page
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Dr Diarmuid Crowley (Aberdeen)10/21/15, 2:20 PMTopAlgExposé de recherche sur invitationI shall report on joint work with Johannes Nordström in which we identify a new invariant of the rational homotopy type of a space X, which we call the Bianchi-Massey tensor. The Bianchi-Massey tensor is a linear map on the degree (4n-1) rational cohomology of X taking values in a subspace of the 4-fold tensor product of the degree n cohomology of X. We use the Bianchi-Massey tensor to...Go to contribution page
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Anthony Blanc (MPI Bonn)10/21/15, 3:40 PMExposé de recherche sur propositionThis is work in progress with Ludmil Katzarkov, Pranav Pandit and Bertrand Toën. I will explain how to use the theory of formal moduli problems of Lurie to obtain a better understanding of the deformation theory of a dg-category up to Morita equivalence, based on previous work by Preygel. This leads to a finiteness result about any formal deformation of a smooth and proper dg-category.Go to contribution page
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Dr Greg Stevenson (Bielefeld)10/21/15, 4:40 PMTopAlgExposé de recherche sur invitationOne can frequently interpret universal coefficient theorems as computations of hom-sets in some triangulated category T via morphisms and extensions between certain cohomological functors. The relevant cohomological functors are obtained by restricting the hom-functors of T to a "suitably nice" subcategory C. I'll discuss joint work with Ivo Dell'Ambrogio and Jan Stovicek which explains when C...Go to contribution page
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Dr Grégory Ginot (Paris 6)10/22/15, 9:00 AMTopAlgMini-coursLecture II: we will explain how factorization homology (as defined in the first lecture) can be computed from a triangulation using higher Hochschild type homology.Go to contribution page
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Martin Palmer (Université Paris 13)10/22/15, 10:40 AMTopAlgExposé de recherche sur propositionUnordered configuration spaces of points (or particles) on connected manifolds are basic objects that appear in many different areas within topology. When the manifold M is non-compact, a theorem of McDuff and Segal states that these spaces are homologically stable, with integral coefficients, as the number of points goes to infinity. When M is closed, however, these spaces are in general...Go to contribution page
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Thomas Ehrhard (Paris 7)10/22/15, 11:40 AMTopAlgExposé de recherche sur invitationOn verra comment les notions de catégorie monoïdale, d'adjonction et de monade/comonade sont intimement liées à la sémantique des langages de programmation fonctionnels et à l'interprétation calculatoire des preuves. Ce lien se comprend bien à travers la logique linéaire, un raffinement de la logique intuitionniste et de la logique classique introduit par Jean-Yves Girard dans les années 1980.Go to contribution page
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Dr Urtzi Buijs (UCL Louvain/ Malaga)10/22/15, 2:20 PMTopAlgExposé de recherche sur invitationStarting from the study of the rational homotopy type of mapping spaces under Quillen's approach, we develop homotopy techniques in order to connect rational homotopy theory with a wide range of areas such as deformation theory and number theory.Go to contribution page
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Mr Andrea Cesaro (Université Lille 1)10/22/15, 3:40 PMTopAlgExposé de recherche sur propositionLes algèbres preLie apparaissent naturellement dans plusieurs domaines des mathématiques, notamment dans la théorie de la déformation des structures algébriques. Le but de cet exposé est d'expliquer la construction de structures à puissances divisées, $\Lambda(PreLie,−)$- et $\Gamma(PreLie,−)$-algèbres associées aux algèbres preLie et ses applications. La définition de ces structures à...Go to contribution page
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Dr Yaël Frégier (Lens)10/22/15, 4:40 PMTopAlgExposé de recherche sur invitationLes symétries des systèmes Hamiltoniens sur une variété symplectique peuvent être, dans les bons cas, exprimés en termes d'application moment. D'autre part il existe une généralisation de la mécanique Hamiltonienne pour des formes fermées de degré supérieur à deux. Ceci apparait par exemple lorsque l'on considère des structures symplectiques sur des espaces de lacets. Le rôle des crochets de...Go to contribution page
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Dr Grégory Ginot (Paris 6)10/23/15, 9:00 AMTopAlgMini-coursLecture III: we will review some applications of factorization homology as an invariant of little n-cubes algebras. In particular, we will give an overview of Bar constructions for little n-cubes algebras and state non-abelian Poincaré duality, which computes factorization homology with values in iterated loop spaces.Go to contribution page
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Ramzi Ksouri (Sousse)10/23/15, 10:40 AMTopAlgExposé de recherche sur propositionNous définissons la notion de foncteur à dualité dans la catégorie $\mathcal{C}\mathrm{-mod}$ des foncteurs covariants d'une catégorie $\mathcal{C}$ vers $k\mathrm{-mod}$. On donne une caractérisation pour l'existence d'un foncteur à dualité. Nous illustrons cette notion par des exemples.Go to contribution page
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Dr Claudia Scheimbauer (Max Planck Institute for Mathematics, Bonn)10/23/15, 11:40 AMTopAlgExposé de recherche sur invitationA relative (also called twisted) quantum field theory should be some transformation between quantum field theories, which themselves are symmetric monoidal functors out of a space-time category. In examples, the notion of natural transformation turns out to be too strong, making it necessary to relax it. In joint work with Theo Johson-Freyd we provide a framework for both lax and oplax...Go to contribution page
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Bertrand Toën (CNRS et Toulouse)10/23/15, 2:00 PMTopAlgExposé de recherche sur invitationThis is a report on a work in progress with Robalo and Vezzosi. I will present the construction of a motivic realization of (dg-)categories over base of arbitrary characteristics, based on some previous work by A. Blanc. This will be used in order to define various realizations of categories, l-adic, de Rham, Betti etc, recovering the usual realizations when applied to the derived category of...Go to contribution page
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