Institut Camille Jordan, UMR 5208

Séminaire de Physique Mathématique

Vendredi à 14h30

en salle Fokko du Cloux, bâtiment Braconnier, la DOUA (Plan d'accès)

• Contact: Johannes Kellendonk (kellendonk at math.univ-lyon1.fr) 

• 26 septembre 2014 : Joseph BEN GELOUN (Perimeter Institute) 

• 17 octobre 2014 : Pavel Mnev (Bonn)
  A perturbative cellular TQFT with Segal-like gluing
  We will discuss the BF theory on cobordisms endowed with cellular decompositions in BV-BFV formalism, its quantization and gluing properties. Partition functions are expressed in terms of the Reidemeister torsion and the propagator connecting the in- and out- boundary components, and also contain a mod 16 phase. As a side result we also obtain the gluing formula for propagators.

• 24 octobre 2014 : Daniel Prins
  Flux vacua on manifolds with SU(5)-structure in terms of generalized complex geometry.
  The supersymmetry equations are a set of Killing spinor equations that determine flux vacua of d=10 type II supergravity. On certain manifolds of the type R^{1, 9-2n} \times M_2n, these equations have been recast to resemble integrability conditions of generalized almost complex structures. In all such cases, an SU(n)-structure is present. This begs the question to what extent this equivalence holds when considering n=5. An obvious obstacle to overcome is that this can only work for Riemannian, rather than Lorentzian manifolds. I will demonstrate that, by making use of complex supergravity, one can show that a necessary but not quit sufficient condition for solutions to the supersymmetry equations on manifolds with SU(5)-structure can indeed be given in terms of generalized almost complex structures.

• 7 novembre 2014 : Adrian Tanasa (Paris)
  3D random tensor models
  Random tensor models, seen as quantum field theoretical (QFT) models, represent a natural generalization of the celebrated matrix models. From this QFT point of view, one of the main results of the study of matrix models is that their perturbative series can be reorganized in powers of 1/N (N being the matrix size). The leading order in this expansion is given by planar graphs (which are dual to triangulations of the 2-dimensional sphere S^2). In this talk I will present such a 1/N asymptotic expansion for some particular class of 3-dimensional random tensor models (called multi-orientable models). The leading order (and hence the dominant graphs, dual to particular triangulations of the three-dimensional sphere S^3), the next-to-leading order and finally some results on the combinatorics of the general term of this asymptotic expansion will be given.

• 14 novembre 2014 : Camille Laurent-Gengoux (Metz)
  Classe d'Atiyah, structures L-infini et géométrie complexe.
  La classe d'Atiyah d'une paire d'algébroides de Lie est l'obstruction à l'existence d'une bonne application exponentielle, c'est-à-dire un "bon" Poincaré-Birkhoff-Witt, qui linéarise une certaine action de groupoide de Lie. Quand elle n'est pas nulle, cette classe encode des structures L-infini toutes canoniquement isomorphes entre elles. Nous donnerons une construction explicite de celles-ci et montreront comment utiliser cela en géométrie feuilletée ou complexe. Cet exposé est basé sur deux travaux communs avec Mathieu Stiénon, Yannick Voglaire et Ping Xu.

• 6 decembre 2014 : Samuel Monnier (Zurich)
  Anomalies and extended field theories
  In the framework of the Atiyah-Segal axioms of field theories, a field theory is a functor between a bordism category and a category of Hilbert spaces. We will present a recent and elegant point of view on anomalous field theories, where they are pictured as natural transformations between two field theory functors in one dimension higher. One of the field theories can be taken to be the trivial one, while the other is an "anomaly field theory" that characterizes completely the anomaly. We will show how several surprising facts about anomalous field theories find a natural explanation in this framework, like for instance the fact that the partition function is an element of a Hermitian line instead of a complex number, or that the state space is a gerbe rather than a honest Hilbert space. We will also discuss how this formalism explains features of chiral rational conformal field theories in 2 dimensions, such as the existence of a vector of conformal blocks instead of a unique partition function.

• 13 decembre 2014 : Chiara Esposito (Wuerzburg)
  Quantization of Poisson-Hamiltonian systems
  In this talk we will introduce the concept of Hamiltonian system in the canonical and Poisson settings and we will present some of the recent results about momentum maps in Poisson geometry. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and propose a non-formal approach of the Poisson-Hamiltonian spaces for triangular Poisson Lie groups.

• 30 Janvier 2015 : Axel de Goursac (Univ. catholique Louvain)
  Supergéométrie non-commutative
  Nous décrirons les récents progrs en supergéométrie non-commutative, en particulier concernant son application en analyse harmonique de supergroupes, ainsi que les supergroupes quantiques topologiques.

• 6 Fevrier 2015 : Viet Dang Nguyen (Lille)
  Front d'onde de puissances complexes de fonctions analytiques et régularisation méromorphe en Théorie quantique des champs.
  Soit f une fonction réelle analytique, je vais tout d'abord donner des majorations du front d'onde de la famille méromorphe de distributions (f+i0)^\lambda. Ensuite je vais décrire un analogue de la régularisation dimensionnelle en théorie quantique des champs sur une variété réelle analytique qui donne des amplitudes de Feynman dépendant de faon méromorphe d'un paramtre \lambda. Puis je vais montrer comment soustraire les poles de ces amplitudes de Feynman de faon compatible avec la causalité ˆ la manire d'Epstein--Glaser et Brunetti--Fredenhagen. Enfin je vais discuter des avantages de cette approche par rapport ˆ l'approche de Brunetti--Fredenhagen s'appuyant sur le prolongement des distributions.

• 27 Fevrier 2015 : Marcello Porta (ETH)
  Universality in interacting graphene models
  Graphene is a recently discovered material, which can be considered as the first realization of a two-dimensional crystal. Its unique physical properties attracted a lot of interest in the condensed matter physics community, both from a theoretical and an experimental point of view. Remarkably, few interesting features of graphene can be understood from a mathematically rigorous viewpoint. In this talk, I will present results on models for interacting electrons on the honeycomb lattice, describing graphene. In particular, I will present a rigorous proof of the universality of the optical conductivity, which agrees with recent experiments. Also, I will report about recent progress in the understanding of the universality of the Hall conductivity in a related model, the interacting Haldane model. The results are based on a rigorous formulation of the Wilsonian renormalization group, and on Ward identities. This is joint work with A. Giuliani and V. Mastropietro.

• 6 mars 2015 : Vladimir Salnikov (Caen)
  GŽomŽtrie graduŽe en thŽories de jauge
  Dans cet exposŽ je vais prŽsenter quelques constructions issues de la gŽomŽtrie gŽnŽralisŽe et de la gŽomŽtrie graduŽe qui apparaissent naturellement dans le contexte des thŽories de jauge. Je vais rappeler la notion des Q-variŽtŽs qui se rŽvle trs commode pour la description des symŽtries des modles sigma. InspirŽ par la relation connue entre le jaugeage et la cohomologie Žquivariante on gŽnŽralise cette dernire notion pour le cas d'une Q-variŽtŽ arbitraire. Le concept de la Q-cohomologie Žquivariante permet donc de remplacer la procŽdure habituelle de jaugeage dans le cadre plus gŽnŽral. On va considŽrer les exemples des modles sigma de Poisson et de Dirac: on peut les obtenir en appliquant la procŽdure proposŽe ˆ l'action du groupe liŽ aux structures n-plŽctiques; passant par les algebroides on peut Žgalement dŽcrire leurs symŽtries en termes de la gŽomŽtrie diffŽrentielle classique. Si le temps le permet je vais mentionner quelques autres sujets proches, notamment l'universalitŽ du modle sigma de Dirac ainsi que les thŽories de jauges supersymŽtriques.

• 13 Mars 2015 : Sylvain Carrozza (CPT Marseille)
  Renormalization of 3d group field theories
  Group Field Theories (GFTs) are non-local quantum field theories of a specific type, which lie at the crossroad of tensor models and loop quantum gravity. The recent generalization of the 1/N expansion from matrix to tensor models opened the way to the application of standard renormalization techniques in the GFT context. Focusing on 3d models with so-called gauge invariance condition, which are directly motivated by loop quantum gravity, I will illustrate the variety of results obtained so far. Particular attention will be given to the UV fixed points of such GFTs, the properties of which differ from that of ordinary scalar field theories.

• 20 Mars 2015 : Jens Kaad (Nijmegen)
  Unbounded Kasparov products by differentiable Hilbert C*-modules
  In this talk I will give an introduction to the current developments in unbounded KK-theory. The starting point for these investigations is to find explicit unbounded representatives for interior Kasparov products in bounded KK-theory. An example would here be to represent a K-homology class by an explicit spectral triple. This turns out to be deeply linked to the understanding of differentiable structures in Hilbert C*-modules. After having reviewed the general framework I will focus on a situation of particular interest for the theory: One could consider an ideal in a C*-algebra which already carries a spectral triple (for example an open subset in n-dimensional Euclidean space). The problem of computing the unbounded Kasparov product then amounts to (the highly non-trivial task of) restricting the spectral triple to the ideal in question.

• 27 mars 2015 : Vladimir Dotsenko (Imperial College, Dublin)
  Gauge symmetries in pre-Lie algebras
  I shall talk about a recent work with Sergey Shadrin and Bruno Vallette, where we develop calculus to handle gauge symmetries of Maurer-Cartan elements in (differential graded) pre-Lie algebras. Basically, in a general dg Lie algebra gauge symmetries are complicated because the Baker-Campbell-Hausdorff formula is involved. In a dg Lie algebra coming from a dg associative algebra, the gauge action is very easy to write down, as it was done, for instance, by Schlessinger and Stasheff. The dg pre-Lie case, very important for homotopy theory of operads, is somewhere in between, and it turns out that there is a remarkable formula for gauge symmetries utilising combinatorics of rooted trees. Time permitting, I shall discuss some applications as well.

• 3 avril 2015 : Pierre Martinetti (Trieste)
  Triplet spectral tordu pour le modle standard
  On donnera un Žtat de lÕart de la description du modle standard des particules ŽlŽmentaires en gŽomŽtrie non-commutative. On verra en particulier comment une action non-triviale sur les spineurs de lÕalgbre des fonctions lisses sur une variŽtŽ, combinŽe ˆ un Ç twist È a la Connes-Moscovici, permet de gŽnŽrer le champ scalaire supplŽmentaire (nŽcessaire ˆ la stabilisation du vide Žlectrofaible) de faon cohŽrente avec la condition du premier ordre. Par ailleurs ce champ scalaire rend le calcul de la masse du boson de Higgs en gŽomŽtrie non-commutative compatible avec la valeur expŽrimentale.

• 10 avril 2015, salle 112 : Michele Cirafici (Lisbon)
  Framed quivers, line defects and BPS invariants
  I will discuss a particular class of framed quivers. The motivation to study these quivers comes from physics, where they describe so-called line defects in supersymmetric quantum field theories. Physicists are interested in understanding certain BPS states associated with these line defects. I will give a precise description of these quantities in terms of certain enumerative invariants associated with the framed quivers. The computation of these invariants can be reduced to a purely combinatorial problem. If time permits, I will also describe a connection with the theory of cluster algebras and with certain integrable systems.

• 24 avril 2015 : Amaury Freslon
  Aspects analytiques des dŽformations de SU(2)
  Le formalisme des groupes quantiques topologiques permet de gŽnŽraliser de nombreux aspects de l'analyse au cadre des dŽformations de groupes de Lie compacts. On peut en particulier s'intŽresser ˆ des questions d'analyse harmonique, notamment concernant la convergence des sŽries de Fourier. Je montrerai comment, en s'inspirant de la thŽorie gŽomŽtrique des groupes, on peut obtenir des propriŽtŽs d'approximations pour les dŽformations de SU(2) qui s'interprtent comme des affaiblissements de la notion de moyennabilitŽ. Cet exposŽ est basŽ en partie sur un travail en commun avec K. De Commer et M. Yamashita.

• 25 septembre 2015 : Christophe Sabot (ICJ)
  Marches renforcées, sigma-modèles et un opérateur de Schrödinger aléatoire
  L'exposé donnera un aperçu des avancées récentes sur deux modèles de marches en auto-interaction, la marche renforcée par arête (ERRW) et le processus de saut renforcé par sites (VRJP), et présentera leur relations avec un sigma modèle supersymétrique étudié par Disertori, Spencer, Zirnbauer, et un opérateur de Schrödinger aléatoire avec un potentiel 1-dépendent. Nous montrerons comment les informations sur le sigma-modèle les propriétés spectrales de l'opérateur de Schrödinger au bas du spectre sont reliées aux propriétés probabilistes du ERRW et du VRJP.

• 2015 :
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• 2015 :
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