Du 7 au 9 juin 2012
IRMA
La 89ème rencontre entre physiciens théoriciens et mathématiciens aura pour thème : Invariants quantiques des 3-variétés en mathématiques et en physique
The 89th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on June 7--9, 2012. The theme will be : "Quantum invariants of 3-manifolds in Mathematics and in Physics".
Organizers : Athanase Papadopoulos and Vladimir Turaev
Invited speakers :
- Norbert A'Campo (Basel)
- Joergen Ellegaard Andersen (Aarhus)
- Anna Beliakova (Zürich)
- Francesco Costantino (Strasbourg)
- Lizhen Ji (Michigan)
- Etera Livine (ENS Lyon)
- Julien Marché (Ecole Polytechnique)
- Rinat Kashaev (Genève)
- Thomas Krajewski (CPT Marseille)
- Sergei Matveev (Cheliabinsk)
- Gwenael Massuyeau (Strasbourg)
- Majid Narimannejad (Basel)
The talks will be in English. Some of the talks will be survey talks intended for a general audience.
Graduate students and young mathematicians are welcome. Registration is required (and free of charge), at the following link Hotel booking can be asked for through the registration link.
For practical and other questions please contact the organizers :
- Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr
- Vladimir Turaev : vladimir.turaev@math.unistra.fr
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Jeudi 7 juin 2012
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09:15
Accueil -
09:30
Norbert A'campo, Basel
Khovanov homology
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10:30
Pause -
11:00
Sergei Matveev, Cheliabinsk
Roots of low-dimensional objects
Abstract : --- We develop a new version of the famous Diamond Lemma [1] and we describe several results on prime decompositions of different geometric objects. All results are obtained by using that version and the standard technics for removing intersections of surfaces. 1. The Kneser-Milnor prime decomposition theorem of 3-manifolds into connected sums of prime factors (new proof). 2. A similar theorem of Swarup for decompositions into boundary connected sums (new proof). 3. A prime decomposition theorem for knotted graphs in 3-manifolds containing no non-separating 2-spheres. 4. Counterexamples to prime decomposition theorems for knots in 3-manifolds and for 3-orbifolds. 5. A new theorem on annular splittings of 3-manifolds, which is independent of the JSJ-splitting theorem. 6. An existence and uniqueness theorem for prime decompositions of homologically trivial knots in thick surfaces. 7. Prime decomposition theorem for virtual knots. Reference: [1] M. H. A. Newman, On theories with a combinatorial definition of "equivalence", Ann. Math. 43 (1942), 223-243. -
14:00
Gwenael Massuyeau, Strasbourg
Splitting formulas for the LMO invariant
Abstract. --- For rational homology 3-spheres, there are two universal finite-type invariants: the Le-Murakami-Ohtsuki invariant and the Kontsevich-Kuperberg-Thurston invariant. These invariants take values in the same space of "Jacobi diagrams", but it is not known whether they are equal. In 2004, Lescop found some relations satisfied by the variations of the KKT invariant when one replaces embedded rational homology handlebodies by others. In this talk, we shall review the LMO invariant and show that it satisfies exactly the same relations. Our proof is an application of the LMO functor, which is a kind of TQFT extending the LMO invariant. -
15:00
Pause -
15:30
Julien Marché, Paris
Semi-classical description of the colored Jones polynomials
Abstract.--- The "knot state" is the vector associated to a knot complement by the topological quantum field theory of level k and group SU_2. I will recall how this state is defined by the colored Jones polynomials and what is its expected semi-classical description when k goes to infinity. Then, I will given some elements of the proof for the figure eight knot and give some consequences as the Witten conjecture for the Dehn fillings of the knot. This is joint work with Laurent Charles (IMJ). -
17:00
Boat Trip Offered To All Participants By The Mayor Of Strasbourg
We shall all leave together from IRMA at 16h30
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18:30
Dinner Offered To All Participants
At the restaurant "Le Petit Bois vert" (2 quai de la Bruche, Petite France quarter)
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Vendredi 8 juin 2012
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09:30
Rinat Kashaev, Genève
Volume Conjecture for Teichmüller TQFT
Abstract.--- Within the context of Teichmuller TQFT, I will describe a definition of a knot invariant by using the combinatorics of one-vertex Hamiltonian triangulations, and formulate a version of the Volume conjecture for it (joint work with Joergen Ellegaard Andersen). -
10:30
Pause -
11:00
François Costantino, Strasbourg
Nilpotent Reshetikhin-Turaev invariants of 3-manifolds and the Volume Conjecture
Abstract.--- Joint work with Nathan Geer and Bertrand Patureau-Mirand. The goal of the talk is to review the construction of non-semi simple surgery invariants of three manifolds in the case of sl_2. After recalling the axiomatic properties of ADO invariants of links and their extensions to graphs we will outline the construction of the "non semi-simple Reshetikhin-Turaev invariants" through surgery presentations and discuss some of its key points. Attention will be payed on the key differences with the standard case of Reshetikhin-Turaev invariants of closed three-manifolds. In the last part of the talk we will provide examples of topological applications of these invariants and in particular to the study of the Volume Conjecture. -
14:00
Joergen Elleggard Andersen, Aarhus
TBA
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15:00
Pause -
15:30
Thomas Krajewski, Marseille
Group field theory models of quantum gravity
Abstract.--- Group field theories are generalizations of matrix models defined on D copies of a group whose perturbative expansion generates the spin foam amplitudes of BF-theories and/or quantum gravity in D dimensions. After a basic review of their construction, we will review some recent advances in the field as well as open problems. -
16:30
Anna Beliakova, Zürich
Towards the categorification of the universal sl(2) link invariant
Abstract.--- The aim of the talk is to define a bicomplex categorifing the ribbon element of U_q(sl(2)) and to discuss it properties. This is joint work with K. Habiro. -
18:00
Reception By The Mayor Of Strasbourg At The City Mayor Hall
Place Broglie (we shall leave together from IRMA after the last talk)
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Samedi 9 juin 2012
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09:30
Vladimir Turaev
Quantum invariants
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10:30
Pause -
11:00
Lizhen Ji, Michigan
Invariants and groups in the spirit of the Erlangen program
This lecture will make a relation with the topic of the next Encounter Between Mathematicians and Theoretical Physicists (September 2012), and it will be an invitation to that conference. Abstract : According to the Erlangen program, the geometry of a space is the study of invariants of the symmetries of the space, and hence an important part of the geometry of a group is to find good spaces when it acts, which often give rise to interesting invariants of the group. We will discuss several examples of groups from such a perspective, including arithmetic groups, mapping class groups, the outer automorphism group of free groups. For the last groups, tropical geometry, a singular deformation of the usual geometry, will play an important role.