Event Details


Thursday 3th

Sala de Conferencias, IMAG

Talk 1: 10:00 - 11:00 am

Speaker: Alessandro Savo (Università di Roma, Sapienza, Italy)

Title: Heat content, exit time moments and isoparametric foliations.
Abstract: We derive the first variation formula for the heat content of a smooth bounded domain in an analytic Riemannian manifold, and see how stationary domains force the existence of an isoparametric foliation on the domain. The same happens for the sequence of exit-time moments \(T_1(\Omega),T_2(\Omega),\dots\) which generalize the torsional rigidity \(T_1(\Omega)\). The purpose of the talk is to show the role of isoparametric foliations in the theory of overdetermined PDE's; in some respect they generalize the properties of the foliation of \(\mathbf R^n\) by concentric spheres


Coffee Break: 11:00 - 11:30


Talk 2: 11:30 - 12:30


Speaker: José M. Espinar((Universidad de Cádiz)

Title:Characterization of free boundary minimal surfaces with dihedral symmetry.
Abstract: Let \(\sigma _1\) be the first Steklov eigenvalue on an embedded free boundary minimal surface in \(b ^3\). The show that the family of embedded free boundary minimal surfaces \(\Sigma_{\bf g}\) of genus \(1 \leq {\bf g} \in \mathbb{N}\), one boundary component and dihedral symmetry constructed by Carlotto-Franz-Schulz satisfy \(\sigma_1 (\Sigma _{\bf g}) =1\).


Talk 3: 12:30 - 13:30


Speaker: Alvaro Pelayo (Complutense University of Madrid, Spain)

Title: Hamiltonian dynamics and spectral theory of integrable systems.
Abstract: This talk is an introduction to finite dimensional classical and quantum integrable systems. We will briefly review some classical results on toric integrable systems by Atiyah, Delzant, Guillemin and Sternberg, and then discuss recent local and global results concerning symplectic and spectral properties of integrable systems, focusing on those of toric and semitoric type.


Friday 4th

Sala de Conferencias, IMAG

Online access: Sala Einstein (virtual)
Password: 938641


Talk 4: 12:00 - 13:00 am

Speaker: Antonio L. Martínez-Triviño (Universidad de Granada)

Title: A Weiertrass type representation for translating solitons and singular minimal surfaces.
Abstract: In this talk, we present a Weierstrass representation formula for translating solitons and singular minimal surfaces in \(\mathbb{R}^{3}\). As application, we study when the euclidean Gauss map has harmonic argument and solve a general Cauchy's problem in this class of surfaces.