Programme

You may want to download the book of abstracts.
Room 01 = big auditorium = grand amphithéâtre
Room X = big hall of mathematics building

attention The session numbers, the room numbers and the order of the lectures are still subject to changes.
This page and the book of abstracts is regularly updated.
Current version: 31 December 2016

Mouse over the links below gives a summary. On click you are brought to the details.

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Therefore, by default, only plenary lectures are generated with abstracts.
To get the abstracts of the other sessions, click the link of the session you want to see (in the navigation bar above or in the schedule below). Your patience might still be tested though.

Wednesday June 6

Thursday June 7

The Godeaux lecture is organized at least once every two years during a BMS event. These lectures honoring the memory of Lucien Godeaux are organized with the assets of the Belgian Center for Mathematical Studies which were transferred to the BMS after the dissolution of this Center. Lucien Godeaux (1887-1975) was one of the world's most prolific mathematicians (with 644 papers published) and took many initiatives to encourage young mathematicians to communicate their research. He was the founder of the Belgian Center for Mathematical Studies in 1949.

Friday June 8

Titles and organizers of special sessions

Poster sessions

  • For titles and abstracts see here


see below


see below

Abstracts of plenary lectures

P1: Plenary Lecture by Pierre-Emmanuel Caprace (room 01)

[We 6/6 10h00-11h00] Pierre-Emmanuel Caprace (Institut de Recherche en Mathématiques et Physique, Un. catholique de Louvain, Louvain-la-neuve, Belgium)
Locally compact groups beyond Lie theory
abstract in pdf

   The theory of locally compact groups stretches out between two extremes. The first one is the class of connected groups. It is well understood since the solution of Hilbert's fifth problem in the 1950's, which describes how to approach it using Lie theory. The opposite case is the class of totally disconnected groups, i.e. locally compact groups all of whose connected components are reduced to singletons. Although this case is much wilder than the connected one and has long been considered as intractable, unexpected developments from the last two decades suggest that the very existence of a non-discrete locally compact group topology yields important restrictions on the underlying algebraic structure. The goal of this talk is to provide a friendly invitation to this field.

authors: Pierre-Emmanuel Caprace


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P2: Plenary Lecture by Gilles Godefroy (room 01)

[Th 7/6 09h30-10h30] Gilles Godefroy (Université Paris 6, Institut de Mathématiques de Jussieu, Paris, France)
The free Banach space over a metric space, and some of its uses
abstract in pdf

   Let $M$ be a metric space. The space $Lip_0(M)$ of all real-valued Lipschitz functions which vanish at some distinguished point is a Banach space for its natural norm, and the closed linear span $\frak{F}(M)$ of all the Dirac measures is actually a predual of $Lip_0(M)$.
   This Banach space $\frak{F}(M)$, called the free space over $M$, reflects pretty well the properties of the metric space $M$.But although free spaces are simple to define, their structure is far from being well-understood.
   We will display some examples where such free spaces are crucially used, some recent results relevant to Grothendieck's approximation property and extension operators for Lipschitz maps, and some simply stated open questions.

authors: Gilles Godefroy


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P3: Plenary Lecture by Giovanni Peccati (room 01)

[Th 7/6 11h00-12h00] Giovanni Peccati (Unité de Recherche en Mathématiques, Université de Luxembourg, Luxembourg, Luxembourg)
On probabilistic approximations
abstract in pdf

   Probabilistic approximations are mathematical statements allowing one to measure the distance between the laws of two generic random elements. In this talk, I will explore some new analytic aspects of probabilistic approximations involving functionals of infinite-dimensional Gaussian fields, and point out several connections with the following topics: universality, limit theorems on homogeneous spaces, variance estimates and concentration inequalities.

authors: Giovanni Peccati


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P4: Plenary Lecture by Stefaan Vaes (room 01)

[Th 7/6 12h00-13h00] Stefaan Vaes (Deptartment of Mathematics, KU Leuven, Heverlee (Leuven), Belgium)
On the classification of von Neumann algebras arising from free groups acting on probability spaces
abstract in pdf

   A famous problem of Murray and von Neumann (1943) asks whether the group von Neumann algebras $L(\mathbb{F}_n)$ associated with the free groups with $n$ generators, $\mathbb{F}_n$, are non-isomorphic for distinct $n$'s. While this problem is still open, its ``group measure space'' version, showing that the crossed product von Neumann algebras $L^\infty(X) \rtimes \mathbb{F}_n$, arising from ergodic probability measure preserving actions $\mathbb{F}_n \curvearrowright X$ are non-isomorphic for $n = 2, 3, ...$, independently of the actions, has been recently settled by Sorin Popa and myself in [2,3]. I will comment on this, as well as on related classification results for von Neumann algebras established within Popa's deformation/rigidity program (see [1,4]).

References
  1. S. Popa, Deformation and rigidity for group actions and von Neumann algebras. Proceedings of the International Congress of Mathematicians (Madrid, 2006), Vol. I, European Mathematical Society Publishing House, 445-477, 2007.
  2. S. Popa, S. Vaes, Unique Cartan decomposition for II$_1$ factors arising from arbitrary actions of free groups. arXiv:1111.6951
  3. S. Popa, S. Vaes, Unique Cartan decomposition for II$_1$ factors arising from arbitrary actions of hyperbolic groups. arXiv:1201.2824
  4. S. Vaes, Rigidity for von Neumann algebras and their invariants. Proceedings of the International Congress of Mathematicians (Hyderabad, 2010), Vol. III, Hindustan Book Agency, 1624-1650, 2010.

authors: Sorin Popa, Stefaan Vaes


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P5: Plenary Lecture by Julio Rubio García (room 01)

[Fr 8/6 09h30-10h30] Julio Rubio García (Dept. Matemáticas y Computación, Univ. La Rioja, Logroño, La Rioja, Spain)
The Role of Formalization in Computational Mathematics
abstract in pdf

   Computer-aided theorem proving is now mature enough to tackle challenging mathematical problems (as the Four Color Theorem or the Kepler Conjecture). In the talk, we will report on our project to apply formalization techniques to the correctness verification of software systems for Computational Mathematics, in particular in Computational Algebraic Topology. This project is partially supported by the ForMath (Formalisation of Mathematics) European project.

authors: Julio Rubio García


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P6: Plenary Lecture by Michel Van den Bergh (room 01)

[Fr 8/6 11h00-12h00] Michel Van den Bergh (Dept. WNI, Universiteit Hasselt, Diepenbeek, Belgium)
Caldararu's conjecture
abstract in pdf

   In 2005 Andrei Caldararu made a fundamental conjecture connecting commutative and non-commutative algebraic geometry.
   Caldararu's conjecture states that the classical Hochschild-Kostant-Rosenberg map which relates differential forms and vector fields to Hochschild (co)homology is compatible with product provided it is twisted by the square root of the Todd genus.
   Despite the fact that Caldararu's conjecture is elementary to state it remained open for quite sometime. But recently Damien Calaque, Carlo Rossi and myself managed to complete its proof using techniques from deformation quantization.
   In the lecture I will explain Caldararu's conjecture as well as the ingredients that go into its proof.

authors: Michel Van den Bergh


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P7: Godeaux Lecture by Ana Vargas Rey (room 01)

[We 6/6 11h30-12h30] Ana Vargas Rey (Dept. Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain)
Multilinear Restriction, Multipliers and Waves
abstract in pdf

   In the seventies, C. Fefferman [4] proved that the spherical partial Fourier integrals of an $L^p$ function in $\mathbb{R}^n$ ($n\ge2$) do not converge in norm to the function, unless $p=2.$ After that, the study of other summation methods, such us Céesaro or Bochner-Riesz sums, became the object of very active research in Harmonic Analysis. Those are examples of oscillatory integrals. After almost forty years, the problem of their boundedness is still open. Other examples of oscillatory integral are the adjoint Fourier restriction operators.
   The problem of restriction of the Fourier transform to hypersurfaces (or more generally to submanifolds in $\mathbb{R}^n$ was posed by Stein in the seventies. This operator (in its adjoint form) gives the solution of dispersive equations (Schrödinger, wave, etc...) in terms of the Fourier transform of the initial data. Somehow the restriction operator is simpler than the Bochner-Riesz multiplier operators, and can be studied a model case. Moreover, there are many open problems about dispersive equations for which it can be used a powerful tool. As an example of those, we will introduce the problem of smoothing of the solution of the equations after local integration in time. In the case of the wave equation, it is a strong form of a version of the Bochner-Riesz sumns, known as the cone multiplier.
   The $L^2$ restriction estimates were proven on the seventies. It was Bourgain in the nineties who was first able to deal with other exponents. After his work there was a big development of the theory via the so-called bilinear method (Lee, Moyua, Tao, V. Vega, Wolff...). Bennett-Carbery-Tao [1] proved a sharp multilinear version of the restriction theorem. Quite recently, Bourgain and Guth [3] used their result to improve on the restriction problem. Their method can be also used to deal with multiplier operators. In particular, it has being used to obtain new bounds for the multiplier of the cone. This is a joint work with Sanghyuk Lee ([5]).

References
  1. J. Bennett, A. Carbery and T. Tao, On the multilinear restriction and Kakeya conjectures, Acta Math. 196 (2006), 261-302.
  2. J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), 147-187.
  3. J. Bourgain and L. Guth, Bounds on oscillatory integral operators based on multilinear estimates, Geom. Funct. Anal. 21 (2011), 1239-1295.
  4. C. Fefferman, The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330-336.
  5. S. Lee and A. Vargas, On the Cone Multiplier in $\mathbb R^3,$ preprint.
  6. G. Mockenhaupt, A note on the cone multiplier, Proc. Amer. Math. Soc. 117 (1993), 145-152.
  7. T. Tao, A Sharp bilinear restriction estimate for paraboloids, Geom. Funct. Anal. 13 (2003), 1359-1384.
  8. T. Tao, A. Vargas and L. Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), 967-1000.
  9. T. Wolff, A sharp cone restriction estimate, Annals of Math. 153 (2001), 661-698.
  10. E. M. Stein, Problems in harmonic analysis, Proc. Sympos. Pure Math. 35, Amer. Math. Soc, Providence, RI, 1979, pp. 3-19.

authors: Sanghyuk Lee, Ana Vargas


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