# Seminars

**A list of past seminars is avalaible ****here****: **

## List of upcoming seminars

Our seminars are scheduled on Monday, at 5.30 pm (Italian time), unless specified. For the list of upcoming seminars, expand the menu ticking on the arrow.

October 19, 2022 - -

**Giulia Carigi**(University of L'Aquila)

**Title: ** **Ergodic properties of a stochastic model for geophysical fluid dynamics**

Room C.1.16, Coppito 2, Univaq ( via Vetoio 1 )

October 26, 2022 -

**Robin Reuvers**(Roma Tre University)

**Title: ** **Ground state energy of dilute Bose gases in 1D**

Main Lecture Hall, ex-isef GSSI

** **(University of L'Aquila) ** ** ** **

**(University of L'Aquila)**

**Ergodic properties of a stochastic model for geophysical fluid dynamics**** **

** **

Date : October 19, 2022 at 14:30 (italian time)

The seminar will be held in presence and streamed through zoom:

**onsite: **Room C.1.16, Coppito 2, Univaq ( via Vetoio 1 )

**zoom: **The seminar will be also streamed through zoom at the link

https://zoom.us/j/87571297606?pwd=dEhQdlcwZERZbXp4TElmcUI3Tk1YZz09

ID riunione: 875 7129 7606

Passcode: 618838

## Abstract

A two-layer quasi-geostrophic (2LQG) model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. We will discuss the problem of unique ergodicity and exponential convergence of transition probabilities as well as response theory for stochastic partial differential equations like the 2LQG model.

** **(University of Rome 3) ** ** ** **

**(University of Rome 3)**

**Ground state energy of dilute Bose gases in 1D **** **

** **

Date : October 26, 2022 at 14:30 (italian time)

The seminar will be held in presence and streamed through zoom:

**onsite: **Main Lecture Hall, ex-isef GSSI

**zoom: **The seminar will be also streamed through zoom at the link

https://zoom.us/j/87571297606?pwd=dEhQdlcwZERZbXp4TElmcUI3Tk1YZz09

ID riunione: 875 7129 7606

Passcode: 618838

## Abstract

In 1963, Lieb and Liniger formulated an exactly solvable model for interacting bosons in 1D. Thanks to its exact Bethe ansatz solution, the model and its generalizations soon became popular objects of study in mathematical physics. Later, when new techniques allowed for the creation of (quasi-)1D systems in the lab, Lieb and Liniger's model found experimental use and became even better known.

In the meantime, the mathematical physics community had moved on and was rigorously studying interacting bosons in 2 and 3D. Without the availability of exact solutions, rigorous results were much more difficult to obtain, and a popular goal was the derivation of the ground state energy of Bose gases in various settings in 2 and 3D. Many of these efforts focused on the dilute limit, in which the density of the gas is very low.

Somehow, Bose gases in 1D were not studied in this way, probably because the Lieb-Liniger model provides an exactly solvable set-up. Nevertheless, we can use insights from the 2 and 3D approaches to prove results about the ground state energy of dilute Bose gases in 1D. In the talk, I will review the developments above and explain the new results.