Du 28 au 30 mai 2015
IRMA
La 95ème rencontre entre mathématiciens et physiciens théoriciens aura pour thème : "Géométrie, arithmétique et physique: autour des motifs".
The 95th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on May 28-30, 2015. The theme will be: "Geometry, arithmetic and physics: around motives".
Organizers : Florence Lecomte and Athanase Papadopoulos (Strasbourg)
The invited speakers include :
- Norbert A'campo (Basel)
- Joseph Ayoub (Zürich)
- Pierre Cartier (IHES)
- Hélène Esnault (Berlin)
- Annette Huber (Freiburg)
- Bruno Kahn (Paris)
- Dirk Kreimer (Berlin)
- Pierre Lochak (Paris)
- Olav Arnfinn Laudal (Oslo)
- Hiroaki Nakamura (Osaka)
- Leila Schneps (Paris)
- Christophe Soulé (IHES)
- Walter van Suijlekom (Nijmegen)
- Pierre Vanhove (IHES)
- Jörg Wildeshaus (Paris)
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 this link. Hotel booking can be asked for through the registration link.
For practical matters and other questions please contact the organizers:
- Florence Lecomte : lecomte@math.unistra.fr
- Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr
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Jeudi 28 mai 2015
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09:00
Pierre Cartier, IHES
Cosmic Galois group
Il y a vingt ans , j'ai constaté de forts liens entre la théorie des multi-zetas , et les calculs par Connes et Kreimer sur la théorie de la renormalisation . J'ai introduit -- provisoirement - l'idée d'un groupe de symétrie d'un genre nouveau en Physique des Particules Elémentaires , commutant aux groupes de symétries connus (géométrique et de jauge) . Ma conjecture , basée sur les informations numériques disponibles vers 2000 , était trop optimiste . Après une première tentative de Connes et Marcolli , Francis Brown , déjà bien connu pour ses travaux sur les multizetas , au vu de nouveaux résultats "expérimentaux" , vient de proposer une version révisée de mon rêve . C'est ce que je me propose d'expliquer dans mon exposé . -
10:00
Coffee Break
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10:30
Lizhen Ji, University of Michigan, Ann Arbor
Toric varieties vs. Finsler metrics
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11:30
Walter Van Suijlekon, Nijmegen
Semigroup of inner perturbations in noncommutative geometry
Starting with a *-algebra, we define a semigroup which extends the group of unitary elements in that algebra. As we will explain, this semigroup describes inner perturbations of noncommutative manifolds, and has applications to gauge theories in physics. We will present some elementary examples of the semigroup associated to matrix algebras, and to (smooth) functions on a manifold. Joint work with Ali Chamseddine and Alain Connes. -
14:00
Joseph Ayoub, Zürich
The foliated topology and the conservativity of the classical realisations
I'll describe parts of an approach to the conservativity of the de Rham realisation of Voevodsky motives based on a new Grothendieck topology called the foliated topology. -
15:00
Coffee Break
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15:30
Anette Huber, Freiburg
Periods and Nori motives
Periods are number obtained by integrating rational differential. They define a countable subalgebra of the complex numbers containg many interesting elements like log(2), \pi, \zeta(n), but also Feynman integrals. We explain an insight of Kontsevich how the formal properties of the period algebra can be explained by the theory of motives. -
16:30
Christophe Soulé, IHES
Weight complexes
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19:30
Dinner
Restaurant "Au Petit Bois vert", quartier Petite France. Everybody is invited. We shall leave IRMA at 19:00
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Vendredi 29 mai 2015
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09:00
Dirk Kreimer, Berlin
Variations of Feynman Integrals
We discuss Feynman graphs and their associated integrals. In their simplest incarnation, the are a source of periods. In general, as functions of the momenta and masses of particles whose scattering they describe, they have monodromy under variation of such parameters. We discuss how to understand this monodromy. -
10:00
Coffee Break
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10:30
Hélène Esnault, Freie Universität Berlin
Simply connected varieties in algebraic geometry
We pose the problem of the relation between the étale fundamental group and various categories of crystals and discuss some known cases. -
11:30
Jörg Wildeshaus, LAGA, Villetaneuse
Relative motives of Abelian type and conservativity of realizations
The first part of the talk will introduce the category of relative motives (or motivic sheaves) of Abelian type over a base. In the second part, a recent result on conservativity of realizations, when restricted to motives of Abelian type, will be explained. Depending on how much time is left, a considerably stronger version of this result will be mentioned: the realization of a motive of Abelian type not only respects, but detects the weights present (or absent) in the motive. -
14:00
Bruno Kahn, Institut Mathématique de Jussieu, Paris
Towards motives with modulus
I will explain work in progress with S. Saito and T. Yamazaki in which we try to emulate Voevodsky’s construction of triangulated categories of motives, replacing smooth varieties over a field by « modulus pairs ». The relationship between these new categories and Voevodsky’s categories connects with the notion of reciprocity sheaf that we introduced one year ago. -
15:00
Coffee Break
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15:30
Hiroaki Nakamura, Osaka
Topology and arithmetic on the profinite Eisenstein quotient
In this talk, we discuss some aspect of monodromy action on the profinite fundamental group of once-punctured torus, calling new attentions in number theory, arithmetic geometry and topology. We focus on Eisenstein periods encoded in the meta-abelian monodromy with an exhibition of elementary arithmetic of various Dedekind sums trading levels for weights. -
16:30
Arnfinn Laudal, Oslo
Noncommutative phase spaces, deformations and algebraic geometry
In this talk I shall show that the non-commutative phase space functor P h() defined for associative algebras, introduced in (WS): Geometry of Time Spaces, World Scientific, (2011), gives rise to a co-simplicial resolution P h (A) of the algebra A, and induces a de Rham complex that fits with the standard one in the commutative case. Let U be the 4-dimensional real affine algebra of a point with a 3-dimensional tangent space, in A3 . The versal family of deformation of U , as associa- R tive R-algebras, contains, in a natural way, the 6-dimensional moduli space, 2 (R3 ), which is my Toy Model for a Big Bang-scenario in cosmology, H := Hilb introduced in (WS). The study of the corresponding family of derivations of the 4-dimensional algebras, leads to a natural way of introducing an action of the gauge Lie algebras of the Standard Model, in H. Introducing the notion of quotient spaces in non-commutative algebraic geometry, we obtain a geometry that seems to fit well with the set-up of the Standard Model. These subjects are all treated within the set-up of (WS). -
18:00
Reception, Mairie (City Hall, Place Broglie). Everybody is invited. We shall leave IRMA at 17:30
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Samedi 30 mai 2015
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09:00
Pierre Vanhove, IHES
A Feynman integral via higher normal functions
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10:00
Coffee Break
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10:30
Norbert A'campo, Basel
Early examples of motifs and motifs in knot theory