## Colloquia di dipartimento

**Mercoledì 16 Ottobre 2024**

Ore 16:30 - 17:30, Aula Picone

**Corinna Ulcigrai**, Institut für Mathematik - Universität Zürich

### Flows on surfaces: dynamics and rigidity

*Flows on surfaces are one of the most studied examples of dynamical systems, starting from the work of Poincaré at the end of the 19th century. Many models of systems of physical origin are described by ﬂows on surfaces, e.g. in celestial mechanics, polygonal billiard dynamics, or solid-state physics.
While the topological structure of trajectories has been well understood already in the last century, the ergodic theory and the fine chaotic properties of flows which preserve area have been an active area of research in the last decades. In this talk, we will survey some of the results, as well as recent breakthroughs on linearisation and rigidity questions in higher genus.*

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**Giovedì 16 Maggio 2024**

Ore 16:00 - 17:00

**Laure Saint Raymond**, Institut des Hautes Études Scientifiques, Université Paris-Saclay

### Internal waves in a domain with topography

*Stratification of the density in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting properties. In particular, in 2D these waves concentrate on attractors for some generic frequencies of the forcing. At the mathematical level, this behaviour can be analyzed in the inviscid case with tools from geometry, spectral theory and micro local analysis.*

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**Martedì 9 Gennaio 2024**

Ore 16:30 - 17:30

**Gigliola Staffilani**, Abby Rockefeller Mauze Professor Massachusetts Institute of Technology

### The Schrödinger equations as inspiration of beautiful mathematics

*In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.*

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**Martedì 27 Giugno 2023**

Ore 16:30 - 17:30

**Laure Saint Raymond**, Institut des Hautes Études Scientifiques, Université Paris-Saclay

### Internal waves in a domain with topography

*Stratification of the density in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting properties. In particular, in 2D these waves concentrate on attractors for some generic frequencies of the forcing. At the mathematical level, this behaviour can be analyzed in the inviscid case with tools from geometry, spectral theory and microlocal analysis.*

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**Evento annullato causa motivi personali dell'oratrice**

**Giovedì 26 Marzo 2020**

Ore 16:30 - 17:30

**Martin Hairer**, Imperial College, London

### Geometric Stochastic PDEs

*We will give a quick review of Parisi and Wu's stochastic quantisation procedure and apply it to the non-linear sigma model as well as the Yang-Mills model. We then review a number of recent results on the resulting equations, which in particular sheds new light on an old controversy. *

**A causa della situazione sanitaria dovuta alla pandemia di Covid-19 l'evento è stato annullato**

**Martedì 29 ottobre 2019**

Ore 16:30 - 17:30

**Jean-Benoît Bost**, Université Paris-Sud Orsay

### Theta invariants of Euclidean lattices

*Euclidean lattices have been studied for a long time, because of their role in crystallography and in arithmetics. More recently, they have also been studied in computer science, because of their application to cryptography. During the last decades, new invariants of Euclidean lattices defined in terms of the associated theta series have become increasingly important to investigate them from these diverse perspectives. In this talk, I will give a gentle introduction to the theory of Euclidean lattices, and try to explain the significance of their theta invariants from various points of view. *

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**Martedì 25 giugno 2019**

Ore 16:30 - 17:30

**Tristan Rivière**, ETH Zürich

### Looking at 2 spheres in R^{3} with a Morse theoretic perspective

*The so called Willmore Lagrangian is a functional that shows up in many areas of sciences such as conformal geometry, general relativity, cell biology, optics... We will try first to shed some lights on the universality of this Lagrangian. We shall then present the project of using the Willmore energy as a Morse function for studying the fascinating space of immersed 2-spheres in the euclidian 3 space and relate topological obstructions in this space to integer values and minimal surfaces.*

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**Lunedì 6 maggio 2019**

Ore 16:30 - 17:30

**Caucher Birkar**, University of Cambridge

### Birational geometry of algebraic varieties

*Birational geometry has seen tremendous advances in the last two decades. This talk is a gentle introduction to some of the main concepts and recent advances in the field. *

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**Martedì 11 Dicembre 2018 **

Ore 16:30 - 17:30

**Christian Lubich**, Universität Tübingen

### Dynamics, numerical analysis and some geometry

*Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic integrators for Hamiltonian ordinary and partial differential equations, of dynamical low-rank approximation of time-dependent large matrices and tensors, and its use in numerical integrators for Hamiltonian tensor network approximations in quantum dynamics.*

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