Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

host: Willemien

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Massot and Theillière showed how one can prove the holonomic approximation lemma using convex integration in the case of first-order jet bundles. In this talk we will discuss a generalization of this idea to higher-order jet bundles using the simplest non-trivial case as a leading example. We will discuss the problems one encounters when trying to generalize this approach and how to solve them. In particular, we will touch upon extending sections of a jet bundle holonomically from a submanifold to an open neighbourhood thereof and a mixed-order version of convex integration.

On gas giant planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: The boundary is at a finite distance.

We consider the acoustic wave and the acousto-gravitational equations of gas giants. The geometry of acoustic waves is modeled by the above mentioned singular Riemannian, "gas giant" metric. We give an overview of the basic properties of the geometry, including properties of geodesics near the boundary, the Hausdorff dimension of the boundary, and the discreteness of the (acoustic) spectrum of the Laplace–Beltrami operator. We present the spectral analysis of this operator and derive the Weyl law. The involved exponents depend on the Hausdorff dimension, which, in the supercritical case (the relevant case for Jupiter and Saturn), is larger than the topological dimension. The Weyl asymptotics determines the blow-up in the supercritical case.

We then consider various inverse problems for simple gas giant planets, proving that the metric is uniquely determined by its boundary distance data and that the geodesic ray transform is injective. We study the determination of a conformal factor of the metric from boundary data (rigidity) using methods involving singular microlocal analysis of the normal operator corresponding to the geodesic ray transform. Moreover, we present the boundary observability of acoustic waves given full and local observations and show how the resulting observability inequality can be turned into a scanning protocol where the observation set moves in time. We conclude with some remarks on inertia-gravity modes on gas planets forming the essential spectrum.

Joint research with Y. Colin de Verdìère, C. Dietze, J. Ilmavirta, A. Kykkänen, R. Mazzeo and E. Trélat.

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Title: Quantitative uniform-in-time propagation of chaos for stochastic particle systems interacting through L^p kernels

Abstract: Deriving macroscopic evolution equations from interacting particle systems is a classical problem in mathematical physics. In the mean-field regime, such systems are expected to converge, as the number of particles tends to infinity, to solutions of nonlinear Fokker-Planck equations. One particular challenge is to establish whether this convergence holds uniformly in time, especially for systems with singular interaction kernels.
In this talk, we first briefly review recent results establishing uniform-in-time propagation of chaos. We then introduce the framework of mollified interacting particle systems. Finally, we discuss recent work establishing quantitative uniform-in-time propagation of chaos for interaction kernels in L^p (p>d). The approach is based on a mild formulation of the limiting equation together with semigroup estimates.

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Speaker morning (11-12.45): Elena Agliari (U Rome)

Title: TBA

Abstract: TBA




Speaker afternoon (14.15 - 16.00): Edan Lerner (UvA)

Title: Mechanical Criticality in Jamming Transitions

Abstract: Jamming transitions include a broad class of nonequilibrium mechanical phenomena in which material systems transition abruptly between floppy or fluid to rigid or solid phases. In my lecture I will review some of the recent theoretical and computational advancements towards understanding jamming transitions in soft matter systems. Starting from the simplest system of disordered spring networks, I will then describe the mechanics of soft-sphere packings, the rheology of dense non-Brownian suspensions, and finally the stiffening of biopolymer networks subjected to large deformations. I will show how the scaling behavior near the respective jamming transitions of these systems can be obtained by perturbing their respective critical states.

TBA

TBA

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

TBA

TBA

TBA

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

TBA

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Further details and meeting link: https://www.uu.nl/staff/TManopulo/Extra2

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

TBA

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!

Named after the Dutch god of formalization, in the Loki meetings we formalize diverse areas of math. Newcomers welcome!