SISSA Mathematics Colloquia

[Emanuele Tuillier Illingworth]

*SISSA Mathematics Colloquia*

*Wednesday, February 7, 2018 - 16:00,  room A-128*
Speaker: David Evans, Cardiff  University
Title: Exotic quantum symmetries
Abstract: Groups act as symmetries of physical systems and on their 
mathematical models - such as actions on algebras of operators on 
Hilbert spaces. Symmetries beyond those arising from groups or their 
deformations as quantum groups, loop groups are feasible but hard to 
locate and realise. The accepted position was that the Haagerup system 
was exotic and surely could not be constructed from group like 
symmetries. We discuss work with Terry Gannon that this should be 
considered as misconception. We start with some elementary background 
from von Neumann algebras and show how conformal quantum field theory 
can shed light on this issue.
*
*
*Monday the 12th of March  2018, 4.00pm,  rm 128*
Speaker: Carlangelo Liverani, Universita’ di Roma Tor Vergata
Title: Beyond averaging
Abstract: Averaging theory allows to effectively describe the motion of 
a system with fast and slow components for a moderately long time. Yet, 
in applications it is often necessary to have information on the 
behaviour of the system for times much longer than the time for which 
averaging holds true. It is then natural to try to explore what happens 
for longer times. I will discuss some results pertaining the case in 
which the fast degrees of freedom perform a chaotic motion and will 
emphasise the similarities with the case in which the fast variables are 
described by a random process.
*
*
*Thursday the 17th of May 2018, 4.00pm rm 128*
Speaker: Camillo De Lellis, Institut fuer Mathematik, Universitat Zurich
Title: Boundary regularity of area-minimizing surfaces and a question of 
Algren
Abstract: The theory of integral currents, developed by Federer and 
Fleming in the 60s,
gives a powerful framework to solve the Plateau's problem in an 
arbitrary Riemannian manifold and for every dimension and codimension. 
The interior and boundary regularity theories for the codimension one 
case are rather well understood since the end of the seventies. In 
higher codimension a far-reaching interior regularity theory was 
developed by Almgren in his celebrated Big Regularity Paper (originally 
a typewritten manuscript of more than 1700 pages), whereas the current 
literature fails to provide even a single regular point at the boundary 
unless we require rather restrictive assumptions on the ambient space. 
In a joint work with Guido de Philippis, Annalisa Massaccesi and Jonas 
Hirsch we provide a first general boundary regularity result, which also 
allows to answer to a question of Algren on the connectivity of the 
minimiser.