Dr
Grégory Ginot
(Paris 6)
21/10/2015 09:00
TopAlg
Mini-cours
Lecture 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
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Dr
Rosona Eldred
(Münster)
21/10/2015 10:40
TopAlg
Exposé de recherche sur proposition
In 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.
Prof.
Stéphane Baseilhac
(Montpellier)
21/10/2015 11:40
TopAlg
Exposé de recherche sur invitation
I 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.
Dr
Diarmuid Crowley
(Aberdeen)
21/10/2015 14:20
TopAlg
Exposé de recherche sur invitation
I 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...
Anthony Blanc
(MPI Bonn)
21/10/2015 15:40
Exposé de recherche sur proposition
This 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.
Dr
Greg Stevenson
(Bielefeld)
21/10/2015 16:40
TopAlg
Exposé de recherche sur invitation
One 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...
Dr
Grégory Ginot
(Paris 6)
22/10/2015 09:00
TopAlg
Mini-cours
Lecture II: we will explain how factorization homology (as defined in the first lecture) can be computed from a triangulation using higher Hochschild type homology.
Martin Palmer
(Université Paris 13)
22/10/2015 10:40
TopAlg
Exposé de recherche sur proposition
Unordered 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...
Thomas Ehrhard
(Paris 7)
22/10/2015 11:40
TopAlg
Exposé de recherche sur invitation
On 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.
Dr
Urtzi Buijs
(UCL Louvain/ Malaga)
22/10/2015 14:20
TopAlg
Exposé de recherche sur invitation
Starting 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.
M.
Andrea Cesaro
(Université Lille 1)
22/10/2015 15:40
TopAlg
Exposé de recherche sur proposition
Les 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, - et -algèbres associées aux algèbres preLie et ses applications. La définition de ces structures à...
Dr
Yaël Frégier
(Lens)
22/10/2015 16:40
TopAlg
Exposé de recherche sur invitation
Les 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...
Dr
Grégory Ginot
(Paris 6)
23/10/2015 09:00
TopAlg
Mini-cours
Lecture 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.
Ramzi Ksouri
(Sousse)
23/10/2015 10:40
TopAlg
Exposé de recherche sur proposition
Nous définissons la notion de foncteur à dualité dans la catégorie des foncteurs covariants d'une catégorie vers . On donne une caractérisation pour l'existence d'un foncteur à dualité. Nous illustrons cette notion par des exemples.
Dr
Claudia Scheimbauer
(Max Planck Institute for Mathematics, Bonn)
23/10/2015 11:40
TopAlg
Exposé de recherche sur invitation
A 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...
Bertrand Toën
(CNRS et Toulouse)
23/10/2015 14:00
TopAlg
Exposé de recherche sur invitation
This 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...