28Apr15:0018:00Semiari Proff. Da Lio - Riviere15:00 - 18:00(GMT+02:00)
dettagli dell'evento
I professori Francesca Da Lio e Tristan Riviere dell'ETH di
dettagli dell'evento
I professori Francesca Da Lio e Tristan Riviere dell’ETH di Zurigo martedì 28 aprile 2026 nella sala riunioni del primo livello del DMA terranno i seguenti seminari:
ore 15.00 Professoressa Francesca Da Lio:
Title: Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfaces
Abstract:
In joint work with Matilde Gianocca and Tristan Rivière, we introduce a new method to establish the upper semicontinuity of the extended Morse index–the number of negative and zero eigenvalues–for conformally invariant variational problems in two dimensions, including harmonic maps. The approach proves robust and extends to several settings in geometric analysis, such as biharmonic maps, Willmore surfaces, Yang–Mills connections, Ginzburg–Landau energies, and constant mean curvature surfaces.
A key ingredient is the use of conservation laws in the bubble tree analysis of critical points of conformally invariant Lagrangians from closed surfaces into closed smooth manifolds. We apply this framework to problems of energy quantization, necklessness, and Morse index stability. Furthermore, we extend the analysis to sequences of maps defined on degenerating domains converging to a punctured Riemann surface, under the assumption that the lengths of the images of the associated collars remain below a critical threshold.
ore 16.00 Professore Tristan Riviere
Title : Area Variations with Differential Constraints
Abstract : The study of the variation of the area of sub-manifolds under pointwize constraints on the tangent plane has numerous motivation from various branches of mathematics such as control theory, elasticity, symplectic and calibrated geometry or minimal surface theory. We will explain the difficulties for developing the analysis of the PDEs such variational problems are generating and expose various regularity results obtained in this direction so far. We will then come to a recent work in collaboration with Alessandro Pigati in which we are proving that surfaces which are critical points of the area under Legendrian constraint, that is surfaces which are tangent to a non integrable plane distributions and critical point of the area under this sub-riemannian constraint, are smooth away from isolated conical singularities. We will then come to the still mysterious problem relative to the location of these conical singularities and explain why it is relevant to fundamental questions in differential geometry which have to do with the realization or not of special homology classes by calibrated surfaces.
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Orario dell'evento
28/04/2026 15:00 - 18:00(GMT+02:00)
Posizione
Sala Professori al I Livello del Dipartimento di Matematica ed Applicazioni Renato Caccioppoli