Hiroyasu Izeki
Harmonic maps and random walks on countable groups abstract
Abstract:
Let Y be a proper CAT(0) space and G a countable group acting on Y. The main result of this talk says that if the action of G does not fix a point in the boundary at infinity of Y and its rate of escape is zero, then there is a flat subspace in Y left invariant by the action of G. The key ingredient of the proof is an equivariant harmonic map from G into Y. Some consequences of this result will be also discussed.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Mini-workshop on Stochastic Dynamics and Stochastic Equations abstract
Abstract:
The workshop will be held at the Bernoulli center, EPFL, March 25 (Monday) -March 27 (Wed), 2024. It is anticipated to start at 2pm on Monday and concludes 12:30 on Wednesday. The focus will be on SDEs, SPDEs, stochastic dynamics of stochastic equations, and related topics.
14:00 • EPF Lausanne, Bernoulli Center
Sebastien Loisel (Heriot-Watt University)
Solving convex optimization problems in function spaces
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Mitchell Taylor
Stable phase retrieval in function spaces abstract
Abstract:
Let $(\\Omega,\\Sigma,\\mu)$ be a measure space and $1\\leq p\\leq \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do \\emph{stable phase retrieval (SPR)} if there exists a constant $C\\geq 1$ such that for any $f,g\\in E$ we have \\begin{equation} \\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\||f|-|g|\\|. \\end{equation} In this case, if $|f|$ is known, then $f$ is uniquely determined up to an unavoidable global phase factor $\\lambda$; moreover, the phase recovery map is $C$-Lipschitz. Phase retrieval appears in several applied circumstances, ranging from crystallography to quantum mechanics.In this talk, I will present some elementary examples of subspaces of $L_p(\\mu)$ which do stable phase retrieval and discuss the structure of this class of subspaces. In particular, I will explain how SPR connects to $\\Lambda(p)$-set theory, which is a classical topic in the intersection of number theory and harmonic analysis. The material in this talk is based on joint work with M.~Christ and B.~Pineau as well as with D.~Freeman, T.~Oikhberg and B.~Pineau.
14:15 • EPF Lausanne, MA A1 10
Prof. Dr. Anuj Kumar (UC Berkeley)
Nonunique solutions of the transport equation for Sobolev vector fields abstract
Abstract:
We construct nonunique solutions of the transport equation in the class $L^\\infty$ in time and $L^r$ in space for divergence free Sobolev vector fields $W^{1, p}$. We achieve this by introducing two novel ideas: (1) In the construction, we interweave the scaled copies of the vector field itself. (2) Asynchronous translation of cubes, which makes the construction heterogeneous in space. These new ideas allow us to prove nonuniqueness in the range of exponents beyond what is available using the method of convex integration and sharply matchwith the range of uniqueness of solutions from Bruè, Colombo, De Lellis ’21.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Isabelle Gallagher
On the dynamics of dilute gases abstract
Abstract:
Abstract: The evolution of a gas can be described by different models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. On the one hand Lanford showed in 1974 that the Boltzmann equation appears as a law of large numbers in the low density limit of a gas of hard spheres, at least for very short times. On the other hand, fluid mechanics equations such as the Navier-Stokes equations can be derived from the Boltzmann equation in the limit of when the mean free path tends to zero. Reconciling both approaches in order to derive fluid mechanics equations from Newton\'s laws for the system of particles is to this day an open question.In this talk we shall explain these different limiting procedures, their difficulties and some recent advances in Hilbert\'s program.
16:30 • UZH Zentrum, Building KO2, Room F 150