Page 58 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 58
INVITED SPEAKERS
Uniqueness results for discrete Schrodinger evolutions
Eugenia Malinnikova, eugeniam@stanford.edu
NTNU, Norway, and Stanford, United States
I will give a survey of some recent results on uniqueness for (semi)-discrete Schrödinger equa-
tion and their connections to classical uncertainty principle.
Some Recent Developments on the Geometry of Random Spherical
Eigenfunctions
Domenico Marinucci, marinucc@mat.uniroma2.it
University of Rome Tor Vergata, Italy
A lot of efforts have been devoted in the last decade to the investigation of the high-frequency
behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e.,
Gaussian eigenfunctions for the spherical Laplacian ∆S2. In this talk we shall review some of
these results, with particular reference to the asymptotic behaviour of variances, phase transi-
tions in the nodal case (the Berry’s Cancellation Phenomenon), the distribution of the fluctua-
tions around the expected values, and the asymptotic correlation among different functionals.
We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-
Chaos expansions and with recent developments in the derivation of Quantitative Central Limit
Theorems (the so-called Stein-Malliavin approach).
Looking at Euler flows through a contact mirror: Universality and Turing
completeness
Eva Miranda, eva.miranda@upc.edu
Universitat Politècnica de Catalunya-CRM-Observatoire de Paris, Spain
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is gov-
erned by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the
global existence problem for the Euler and Navier-Stokes equations based on the concept of
universality. Inspired by this proposal, we show that the stationary Euler equations exhibit sev-
eral universality features, in the sense that, any non-autonomous flow on a compact manifold
can be extended to a smooth stationary solution of the Euler equations on some Riemannian
manifold of possibly higher dimension [1]. A key point in the proof is looking at the h-principle
in contact geometry through a contact mirror, unveiled by Etnyre and Ghrist in [4] more than
two decades ago.
We end up this talk addressing a question raised by Moore in [5] : “Is hydrodynamics capa-
ble of performing computations?". The universality result above yields the Turing completeness
of the steady Euler flows on a 17-dimensional sphere. Can this result be improved? In [2] we
construct a Turing complete Euler flow in dimension 3. Time permitting, we discuss this and
other generalizations contained in [3].
This talk is based on several joint works with Cardona, Peralta-Salas and Presas.
56
Uniqueness results for discrete Schrodinger evolutions
Eugenia Malinnikova, eugeniam@stanford.edu
NTNU, Norway, and Stanford, United States
I will give a survey of some recent results on uniqueness for (semi)-discrete Schrödinger equa-
tion and their connections to classical uncertainty principle.
Some Recent Developments on the Geometry of Random Spherical
Eigenfunctions
Domenico Marinucci, marinucc@mat.uniroma2.it
University of Rome Tor Vergata, Italy
A lot of efforts have been devoted in the last decade to the investigation of the high-frequency
behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e.,
Gaussian eigenfunctions for the spherical Laplacian ∆S2. In this talk we shall review some of
these results, with particular reference to the asymptotic behaviour of variances, phase transi-
tions in the nodal case (the Berry’s Cancellation Phenomenon), the distribution of the fluctua-
tions around the expected values, and the asymptotic correlation among different functionals.
We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-
Chaos expansions and with recent developments in the derivation of Quantitative Central Limit
Theorems (the so-called Stein-Malliavin approach).
Looking at Euler flows through a contact mirror: Universality and Turing
completeness
Eva Miranda, eva.miranda@upc.edu
Universitat Politècnica de Catalunya-CRM-Observatoire de Paris, Spain
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is gov-
erned by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the
global existence problem for the Euler and Navier-Stokes equations based on the concept of
universality. Inspired by this proposal, we show that the stationary Euler equations exhibit sev-
eral universality features, in the sense that, any non-autonomous flow on a compact manifold
can be extended to a smooth stationary solution of the Euler equations on some Riemannian
manifold of possibly higher dimension [1]. A key point in the proof is looking at the h-principle
in contact geometry through a contact mirror, unveiled by Etnyre and Ghrist in [4] more than
two decades ago.
We end up this talk addressing a question raised by Moore in [5] : “Is hydrodynamics capa-
ble of performing computations?". The universality result above yields the Turing completeness
of the steady Euler flows on a 17-dimensional sphere. Can this result be improved? In [2] we
construct a Turing complete Euler flow in dimension 3. Time permitting, we discuss this and
other generalizations contained in [3].
This talk is based on several joint works with Cardona, Peralta-Salas and Presas.
56
