Past Seminars: (see also GSSI Academic Calendar)



Speaker: Gianmarco Caldini (University of Trento)

Title: On regularity theory for generalized surfaces

Abstract: The natural question of how much smoother integral currents are with respect to their initial definition goes back to the late 1950s and to the origin of the theory with the seminal article of Federer and Fleming. In this seminar I will explain how closely one can approximate an integral current representing a given homology class by a smooth submanifold. Part of what will be discussed is derived from a joint study with William Browder and Camillo De Lellis, and builds on earlier preliminary work by the former author together with Frederick Almgren.



Speaker: Mahdi Haghshenas (Imperial College London)

Title: Boundedness and decay of waves on decelerated FLRW spacetimes

Abstract: After outlining the stability problem for Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes, we study the wave equation—as a proxy for the Einstein equations—on decelerated FLRW spacetimes with non-compact, flat spatial sections. We demonstrate how dispersion and expansion affect the long-time behaviour of waves. In particular, we present uniform energy bounds and integrated local energy decay estimates across the full decelerated expansion range. Furthermore, we describe a hierarchy of r-weighted energy estimates, in the spirit of the Dafermos–Rodnianski method, which lead to energy decay estimates.



Speaker: Gianluca Crippa (University of Basel)

Title: Anomalous dissipation in fluid dynamics

Abstract: The celebrated Kolmogorov's K41 theory of fully developed turbulence attempts to explain and quantify "wild, but typical" behaviors of "chaotic" fluids, most notably the lack of conservation of the total energy. The loss of energy is not due to friction between fluid molecules, but rather to the limited regularity of the flow. Kolmogorov's theory is numerically and experimentally validated to a very large extent, however, very little is known in rigorous mathematical terms. In my lecture, I will present some aspects of Kolmogorov's theory, and illustrate recent results on a related question for the linear advection equation.