**Abstract:**

This is the last conference of the semester and will be of a more general nature than the earlier more specialized conferences and workshops of the program. It will cover broad aspects of descriptive set theory and its connections with other areas of mathematics.

09:30 • EPF Lausanne, Salle BI A0 448

Peter Zograf (Steklov Institute and Universtiy of St. Petersburg)

Families index for orbifold Riemann surfaces abstract

**Abstract:**

We present a local index theorem for families of Cauchy-Riemann operators on orbifold Riemann surfaces that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. The curvature of the determinant line bundle with Quillen\'s metric is explicitly expressed as a linear combination of natural symplectic forms on the moduli spaces of orbifold Riemann surfaces. In particular, each conical point gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new Kähler metric on the moduli space.

14:00 • Université de Genève, Villa Battelle, 7 route de Drize, 1227 Carouge

Francesco Amoroso (Université Caen Normandie)

Height on Galois extension abstract

**Abstract:**

In a recent joint paper with D. Masser we prove that the Weil height of a non-zero algebraic number, not a root of unity, which generates a Galois extension, can be bounded from below "essentially" by a positive constant. We further analyse Galois extension with full symmetric group. We prove that two classical constructions of generators give always algebraic numbers of "big" height. These results answer a question of C. Smyth and provide some evidence to a conjecture which asserts that the height of such a generator growth to infinity with the degree of the extension.

14:15 • Universität Basel, Fachbereich Mathematik, Spiegelgasse 5, Room 05.002

Prof. Dr. Boris Gralak (Université de Marseille)

Frequency disp ersion in electromagnetism abstract

**Abstract:**

Frequency dispersion plays a central role in electromagnetism, and many applications in optics are based on its engineering. The basic principles (inertia, causality, passivity) creating and governing frequency dispersion in standard optical media will be presented. Then, the vital role of frequency dispersion in metamaterials will be shown, notably in the cases of the flat lens and invisible systems. Several models of frequency dispersive permittivity will be given, including an extended version of Kramers-Kronig relations and an effective medium description of a multilayered system.

In the second part, an augmented formulation of Maxwell equations [A. Tip, Linear absorptive dielectrics, Phys. Rev. A 57 (1998)] will be introduced in order to transform the time-dependent and non-selfadjoint Maxwell operator (with frequency dispersion) into a time-independent and selfadjoint augmented operator. In addition, a simple frequency linearization procedure, leading to a time-independent but non-selfadjoint operator, will be considered. This linearization has been implemented in the finite element method, and the computation of complex band structures will be shown for 2D photonic crystals made of Drude metal rods. Finally, the modal analysis of wave propagation in dispersive media will be presented, leading to a revisited version of Sommerfeld precursor.

14:15 • EPF Lausanne, Salle MA A1 12

Fei Pu (EPF Lausanne)

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

17:15 • EPF Lausanne, Salle MA A1 10