# Calendar

## November 2019

### Relations between the Schrödinger problem and the optimal transport theory and their applications

#### Luigia RIPANI (Université Cergy-Pontoise)

### Relations between the Schrödinger problem and the optimal transport theory and their applications (mini-course following seminar).

#### Luigia RIPANI (Université Cergy-Pontoise)

The Schrödinger problem is an entropy minimization problem with marginal constraints and a fixed reference process. In the past few years it enjoys an increasing popularity in different fields, thanks to this relation to optimal transport, smoothness of solutions and other well performing properties in numerical computations.

After introducing the Schrödinger problem and reviewing some classical results of optimal transport, we will present some application to the study of functional inequalities, curvature-dimension condition and applied problems.

### Feynman integrals associated to elliptic curves

#### S. Weinzierl (THEP, Mainz)

Feynman integrals are indispensable for precision calculations in quantum field theory. But they are notoriously difficult to calculate. While we do have methods to compute any one-loop Feynman integral analytically, already at two-loops there are Feynman integrals for which the known methods fail. The first obstruction one encounters is related to elliptic curves, and for this reason the Feynman integrals not tractable by standard methods are known as ``elliptic’’ Feynman integrals. In this talk I will review our current knowledge about Feynman integrals associated to elliptic curves.

### QED corrections to hadronic decays on the lattice

#### Nazario Tantalo

QED radiative corrections to hadronic observables are generally rather small but they become phenomenologically relevant when the target precision is at the percent level. This is the case of leptonic and semileptonic decays of light and heavy pseudoscalar mesons. On the one hand, QED radiative corrections to hadronic observables can be calculated with the required non-perturbative accuracy by using lattice techniques. On the other hand, the inclusion of electromagnetic interactions in a lattice calculation is a challenging problem because QED is a long-range unconfined interaction and numerical simulations necessarily require a finite volume. The problem is particularly delicate in the case of QED radiative corrections to decay rates because of the appearance of infrared divergences (proportional to the logarithm of the lattice volume) at intermediate stages of the calculations. In this talk I will briefly review the recent theoretical advances that opened the way to realistic non-perturbative simulations of QCD+QED, discuss a method that allows to calculate QED radiative corrections to hadronic decay rates and present the results of a non-perturbative calculation of the leptonic decay rates P-> l nu (gamma) in the case of light (P=pi,K) and charmed (P=D,Ds) pseudoscalar mesons.

### Number-theoretic spin chains

#### Vojkan Jaksic, UCP-IEA and McGill

The number theoretic spin chains were introduced in 1993 by A. Knauf in an influential paper.

In this talk I will describe a research program that connects:

(1) Statistical mechanics of number theoretic spin chains.

(2) Large deviation principle

(3) Multi-fractal analysis of Bernoulli convolutions

(4) Theory of repeated quantum measurements.

### Mapping single molecule dynamics in living cells

#### Christian Vestergaard (Institut Pasteur)

Single molecule tracking in live cells is providing unprecedented insights into the nano- and micro-scale dynamics underlying cellular function. By accessing the full distribution of molecular properties, rather than simply their average values, the great advantage of single molecule measurements is their ability to identify static and dynamic heterogeneities as well as rare behaviors.

Thanks to photoactivatable dyes, millions of individual molecule trajectories can now be acquired using techniques such as PALM or uPAINT at the scale of entire cells and over time intervals lasting many hours. As SM experiments generate more and more data, the development of a principled and unifying statistical framework becomes ever more necessary. While the large amounts of data open up new research venues for understanding biological processes, the wealth of information also come with more variability and noise. Statistically robust tools are needed to handle the complex structure of the large datasets and to account for the various sources of experimental and systemic noise and variability.

I will here give an overview of the different sources of noise and variability in single molecule tracking data and how they affect recorded data. I will next present a global probabilistic framework for inferring spatially and temporally varying physical parameters from experimentally recorded biomolecule motion. I will in particular show how to account for the noise and variability of recordings. Finally, I will demonstrate links between inferred physical maps and the underlying biology.

The probabilistic inference framework is being developed as an open source Python library: TRamWAy.readthedocs.io

### Testing for the environmental dependence of the growth rate

#### Ixandra Achitouv

The growth rate of cosmic structures is a powerful quantity to probe gravitational interactions and dark energy.

In the late-time Universe the growth rate becomes non-linear, making it more difficult to probe, but also makes it in principle a source of additional cosmological information than its linear counterpart. In this talk, I will discuss why it becomes interesting to probe the growth rate in regions of different density, as well as recent developments in measuring the growth rate using RSD around voids.

### PHYSICS and ASTROPHYSICS of COSMIC RAYS

Cosmic rays (CR) have a central position in many major astrophysical issues, from the solar system to galaxy clusters. They stand for a testimony on the conditions in the most extreme objects in the Universe and plays a key role in the physics and chemistry of the interstellar medium (ISM), with consequences ranging from star formation and galactic magnetic fields to the production of light elements. Moreover, the CR could carry information on Dark Matter.

The results of observations, accumulated during the past decade, have considerably transformed our knowledge of the CR physics. The level of detail and precision achieved in the direct measurements of CR by the PAMELA, AMS-02, Fermi or Voyager space missions bring remarkable constraints on the propagation models of Galactic CR. The observations from Kaskade-GRANDE and Auger from 10^*15* to 10^*20* eV enabled us to improve our knowledge on the Galactic-extragalactic transition and on the extreme energy particles. Moreover, if CR generates an incompressible background to neutrino astronomy experiments, the latter have in turn enabled us to measure an anisotropy in the flow of cosmic rays at small and large scales. Such a feature, that still remains to be understood, could notably be connected the microphysics of transport and the properties of the interstellar magnetic field. Finally, the observations of possible high-energy acceleration sites, from X-rays to gamma-rays of high and very high energy, have brought many elements supporting the theories of acceleration. At the same time, several works of numerical simulations have made progress on the microphysics of acceleration. Notwithstanding, several crucial questions still remain, including the exact origin of particles with energy ≥10^*15* eV.

### On the semiclassical spectrum of the Dirichlet-Pauli operator

#### Loïc Le Treust (AMU Marseille)

This talk is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we establish the simplicity of the eigenvalues and provide accurate asymptotic estimates involving Bergman-Hardy spaces associated with the magnetic field.