Analyse des EDP, géométrie et physique

Liste des Contributions

19. A Weierstrass type representation of Constrained Willmore surfaces.

Idrisse Khemar (IECL - Université de Lorraine)

In a first part, we present a joint work with Josef Dorfmeister : a Weierstrass type representation for constrained Willmore surfaces in spheres. Using appropriates (moving) frames and a appropriate Lie algebra decomposition of so(1,n+3), we translate the PDE of constrained Willmore surfaces into the Lie algebra setting : namely we rewrite it as a Maurer-Cartan equation of an extended Maurer...

6. About Koszul-Tate resolutions

Prof. Camille Laurent-Gengoux (Université de Lorraine)

I will present several results and open problems about Koszul-Tate resolutions. Several topics will be addressed : how symmetries "closing" only on a singular subset naturally give a Z-graded Q-manifold. with Koszul-Tate negative part, how to get constructive Koszul-Tate resolutions. Then I will detail several open questions about affine varieties. Joints works with Hancharuk, Kotov, Salnikov, Strobl.

27. Area Variations under pointwize Lagrangian and Legendrian constraints

Prof. Tristan Riviere (ETH)

20. Asymptotics for two-dimensional elliptic Allen-Cahn systems

Prof. Fabrice Bethuel (Laboratoire Jacques-Louis Lions, Sorbonne Université)

The formation of codimension-one interfaces for multi-well gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the Allen-Cahn equation. The vectorial case in contrast is quite open. This lack of results and insight is to a large extent related to the absence of known monotonicity formula. I will focus on the ...

24. Bouncing Jacobi Fields and the Allen-Cahn equation on surfaces

Prof. Frank Pacard (Ecole polytechnique)

There is a strong parallel between the theory of minimal hypersurfaces and the solutions of the double-well phase transition Allen-Cahn equation on a manifold. In this talk, I will report some recent result on the relations between geodesics on surfaces and solutions of the Allen-Cahn equation with uniform bounds on the Morse Index and energy, as the phase transition parameter tends to 0. Our...

8. Darboux theorems for volume-valued symplectic forms

Prof. Leonid Ryvkin (Université Lyon 1)

We will discuss a Darboux type theorem for a certain class of multisymplectic (n+2)-form in a (n+2m)-dimensional manifold, generalizing the work for 3-forms in 5-dimensional space. In addition to closedness of the form, the involutivity of a certain distribution is a necessary condiition for flatness. When the distribution is zero or everything we recover the classical Moser and Darboux...

23. Direct connections on jet groupoids

Prof. Alessandra Frabetti (Université Lyon 1)

Gauge fields are the local expression of a principal connection on a principal bundle, and therefore encode the infinitesimal data of a parallel transport between the fibres along curves on the base manifold. One may wonder if there is a field interpretation for parallel transport. Reading principal connections as infinitesimal connections on the associated Atiyah Lie algebroid, this question...

5. Domain wall dynamics in notched ferromagnetic nanowires

Prof. Gilles Carbou (LMAP, UPPA)

Ferromagnetic nanowires have promising applications in data storage. In such devices, the information is encoded by Domain Walls (DW) which are thin zones of magnetization reversal. The magnetization behavior is described by the non linearLandau-Lifschitz model. In this talk, we investigate the stability of DW configurations. In particular we highlight DW pinning properties by notches...

10. Eigenfunctions and representation theory

Prof. Fran Burstall (University of Bath)

Originally discussed by Strichartz in the '80's, there has been some recent interest from the harmonic map community in eigenfunctions of the Laplacian on symmetric spaces whose squares are also eigenfunctions. The state of the art until recently has been the construction of local examples on classical symmetric spaces. In this talk, I shall show how some simple ideas from representation...

29. Formality theorem for differential graded manifolds

Prof. Mathieu Stiénon (Penn State University)

The Atiyah class of a dg manifold $(\mathcal{M},Q)$ is the obstruction to the existence of an affine connection on the graded manifold $\mathcal{M}$ that is compatible with the homological vector field $Q$. The Todd class of dg manifolds extends both the classical Todd class of complex manifolds and the Duflo element of Lie theory. Using Kontsevich's famous formality theorem, Liao, Xu and I...

14. Hilbert-Einstein Lagrangian on a Generalised Frame Bundle

Prof. Jérémie Pierard de Maujouy (UCLouvain)

Einstein's equation can be obtained as the Euler-Lagrange equation associated to the Hilbert-Einstein Lagrangian, which is essentially the scalar curvature. The curvature tensor, and therefore Einstein's equation, can be formulated and studied on the frame bundle of spacetime. We will introduce a Lagrangian defined on a 10-manifold such that the solutions to the Euler-Lagrange equations equip...

21. Morse Index Stability of Willmore Immersions

Prof. Alexis Michelat (EPFL)

The Morse index of a critical point of a Lagrangian L is the dimension of the maximal vector space on which the second derivative D2L is negative-definite. In the classical theory of Hilbert spaces, one shows that the Morse index is lower semi-continuous, while the sum of the Morse index and nullity (the dimension of the Kernel of the differential operator associated to the second derivative)...

11. Multiplicative kernels: from Bessel to Kontsevich, Buchstaber and Calabi-Yau

Prof. Volodya Roubtsov (LAREMA, UMR 6093 du CNRS Département de Mathématiques, Université d'Angers)

We discuss few very recent results of a work in progress (in collaboration with I. Gaiur and D. Van Straten and with V. Buchstaber and I. Gaiur) about interesting properties of multiplication Bessel kernels, which includes well-known Clausen and Sonin-Gegenbauer formulae of XIX century, special examples of Kontsevich discriminant loci polynomials, raised as addition laws for special...

28. New variations on old themes

Prof. Thierry Lévy (Sorbonne Université)

In a first part, I will report on an ongoing collaboration with Adrien Kassel (CNRS, ENS Lyon) where we elaborate on a classical theorem of G. Kirchhoff (1847). In a second part, I will present recent developments due to Frédéric Hélein on an early work of W.A. Mozart (1762).

15. Non-perturbative renormalisation group from algebraic quantum field theory

Prof. Kasia Rejzner (University of York)

In this talk I will present recent results obtained in collaboration with Brunetti, Duetsch and Fredenhagen, concerning the construction of a net of C*-algebras for interacting quantum field theories. Using these construction one can discuss features like the time-slice axiom, action of the appropriate version of the renormalisation group and anomalous Nother theorem.

18. On the understanding of the Jacobian determinant

Prof. Dong Ye (East China Normal University, Université de Lorraine)

I will talk about the problem to prescribe the Jacobian determinant or the volume form, I
will present some old and more recent results on this problem, and mention the link with the
density problem in Sobolev spaces.

1. openning

16. Periodic Darboux transforms

Prof. Katrin Leschke (University of Leicester)

In classical differential geometry, geometric transformations have been used to create new curves and surfaces from simple ones: the aim is to solve the underlying defining compatibility equations of curve or surface classes by finding solutions to a simpler system of differential equations arising from the transforms. Classically, the main concern was a local theory. In modern theory,...

13. Pinching theorems via Ricci flow

Prof. Peter Topping (University of Warwick)

There is a long tradition in Differential Geometry of results that deduce topological consequences from pointwise positive curvature hypotheses. In this talk we consider the consequences of pinched curvature of various types and explain how recent developments in Ricci flow have proved to be decisive in establishing results along these lines.
Joint work with ManChun Lee (CUHK)

25. Q-Curvature and the Positive Mass Theorem

Prof. Paul Laurain (IMJ)

After a brief review of the classical Positive Mass Theorem and a short introduction to Q-curvature, I will present a theorem on the positive mass for Q-curvature and discuss some applications.

9. Regularity for solutions of H-systems and n-harmonic maps with n/2 square integrable derivatives

Prof. Pawel Strzelecki (University of Warsaw)

Over 30 years ago Frédéric Hélein proved that all harmonic maps from surfaces into compact Riemannian manifolds are smooth. Despite the existence of several partial results, for $n>2$ the counterpart of this theorem is wide open. In a recent work with two coauthors, Michał Miśkiewicz and Bogdan Petraszczuk, we prove regularity of $n$-harmonic maps into compact Riemannian manifolds and weak...

26. Singularities of degenerate complex Monge-Ampère equation, according to Alireza Bahraini

Prof. Daniel Bennequin (IMJ)

Conjugating a variety of methods, analytic series, Schauder a priori estimates, global continuity, Alireza Barhaini obtained recently a precise description of the singular behavior of the solution of a complex Monge-Ampère equation, degenerating along a smooth divisor in a compact Kähler manifold. Applications are given to the Bogomolov-Miyaoka-Yau inequality and to the Kodaira-Hodge theory on...

12. Stability and Boundary stabilization of 1-D hyperbolic systems

Prof. Jean-Michel Coron (Sorbonne Université)

Hyperbolic systems in one-space dimension appear in various real-life applications (navigable rivers and irrigation channels, heat exchangers, chemical reactors, gas pipes, road traffic, chromatography, ...). This presentation will focus on the stabilization of these systems by means of boundary control. Stabilizing feedback laws will be constructed. This includes explicit feedback laws that...

22. The loop group method for harmonic maps with applications to Willmore surfaces

Prof. Josef F. Dorfmeister (Technical University of Munich)

The first part of the talk gives a review of the loop group method for harmonic maps from Riemann surfaces to (semisimple) symmetric spaces. Applications of this will be illustrated by pointing out the relation between certain types of harmonic maps and certain classes of surfaces. In the second part we will describe in some detail the discussion of Willmore surfaces in spheres along the...

17. The physical origin of the Batalin-Vilkovisky approach

Christian Brouder (Sorbonne Université)

This talk describes a (hypothetical) historical path that lead Batalin and Vilkovisky to the discovery of their (wonderful) approach, starting from the quantization of scalar fields, to the quantization of electrodynamics and non-Abelian gauge fields.

7. Tight Best-Lipschitz Maps from Surfaces to Surfaces

Prof. Karen Uhlenbeck (IAS)

In honor of the contributions of Frederic Helein to analysis, I pose several new problems rather than present solutions. George Daskalopoulos and I have been studying best Lipschitz maps from surfaces to surfaces. While this is motivated by Thurston’s distance function in Teichmuller space, it has connections with older ideas. I will give a bit of the history about Lipschitz extensions, define...

3. Undecidably semilocalizable metric measure spaces and Radon-Nikodymification of arbitrary measure spaces

Prof. Thierry De Pauw (Université Paris Cité)

The questions raised here grew from the desire to give an integral representation for members of the dual of $BV$, the Banach space of functions of bounded variation. This potentially has application to the calculus of variations since $BV$ dual contains subgradients of energy functionals to be minimized. The question quickly links to that of identifying the dual of...