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Informazioni Generali

I seminari si svolgeranno online, tramite la piattaforma Zoom. Interverranno professori, ricercatori e dottorandi. Nel pomeriggio invece, sempre su Zoom, si apriranno le stanze virtuali dove gruppi di studenti incontraranno, in modo informale, gli studenti di dottorato per discutere di come si svolge la ricerca scientifica in SISSA, a livello accademico e sociale. Data l'internazionalità culturale della SISSA, è richiesta una buona conoscenza della lingua inglese: le lezioni della mattina si terranno in tale lingua.

Orario Dettagliato

Lunedì 14 dicembre

  • Ore 10:00, Prof. Gianluigi Rozza, 'Computational fluid dynamics challenges'

    Abstract: We will describe current challenges in computational fluid dynamics, the only branch of classical physics without a general theory and in great transformation thanks to recent developments in model reduction, data science, machine learning and high performance computing. Applications in several fields such that biomedicine, environmental sciences and industry will be presented. We will deal with current efforts carried out within the ERC project AROMA-CFD.

  • Ore 11:15, Prof. Roberto Trotta, 'Theoretical and Scientific Data Science and Applications to Cosmology'.

    Starting in October 2021, SISSA is delighted to be offering a brand new PhD course in Theoretical and Scientific Data Science, focusing on theoretical aspects of machine learning (including, for example, explainability, interpretability, connection with information theory and statistical physics) and applications to the natural sciences. I this talk I will give an overview of the programme, its structure and learning objectives. I will then present how some of these notions can be applied to frontiers research in cosmology.

  • Ore 12:15, Prof. Nicola Gigli, 'Optimal Transport'.

    Abstract: I will give an introduction to the world of optimal transport, that attracted the attention of several different research groups around the world in the last 30 years. I will start from basic definitions and end with the proof of the celebrated theorem of Brenier about optimal maps in the Euclidean space.

Martedì 15 dicembre

  • Ore 10:00, Prof. Antonio Lerario, 'Convex bodies and algebraic geometry'.

    Abstract: In this seminar I will discuss some interesting and unexpected connections between the problem of counting the number of solutions to a system of algebraic equations and computing the volume of a certain convex body associated to the system -- magically they turn out to be essentially the same problem!

  • Ore 11:00, Prof. Marcello Porta, 'Many-Body Quantum Mechanics'.

    Abstract: I will give an overview of selected recent developments in mathematical quantum mechanics, with a focus on many-body systems. In particular, I will discuss the derivation of effective nonlinear theories for large quantum systems, and the emergence of universality in condensed matter models.

  • Ore 12:00, Dott. Andrea Ricolfi, 'Some ideas in algebraic geometry'.

    Abstract: I will introduce some of the core ideas in algebraic geometry, and use them to present the field of modern enumerative geometry, via a few concrete examples. This field has deep connections with many other areas such as mathematical physics, string theory, combinatorics.

Mercoledì 16 dicembre

  • Ore 12:00, Dott. Carlo Scarpa, 'Canonical metrics in Kähler geom etry'.

    Abstract: Among the many metrics that one can define on a manifold, is it possible to canonically choose one? We will talk about possible answers to this question when the manifold carries some additional data, a complex structure.

Giovedì 17 dicembre

  • Ore 10:00, Prof. Alberto Maspero, 'Dynamical systems and water waves'.

    Abstract: Classical questions in dynamical systems regard the existence of stationary solutions, periodic and quasi-periodic orbits, long time stability or instability of invariant objects. I will describe how this questions are meaningful in the modern theory of dynamical systems for PDEs, bringing as example the dynamics of water waves equations.

  • Ore 11:00, Dott. Miruna-Stefana Sorea, 'The shapes of level curves of real polynomials near strict local minima'.

    Abstract: We consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries of convex disks. Otherwise, these level curves may fail to be convex. The aim of this talk is two-fold. Firstly, to study a combinatorial object measuring this non-convexity; it is a planar rooted tree. And secondly, we want to characterise all possible topological types of these objects. To this end, we construct a family of polynomial functions with non-Morse strict local minima realising a large class of such trees.

Venerdì 18 dicembre

  • Ore 11:00, Dott. Alessandro Rubin, 'What is a noncommutative geometry?'.

    Abstract: The term 'noncommutative geometry' carries with it a certain aura of mystery: When can we say that a geometry is commutative? How many commutative geometries are there? And why might we want to remove commutativity? In this talk we will answer these questions, passing through functional analysis, differential topology, Riemannian geometry, measure theory and (if time permits) some basic condensed matter physics.

  • Ore 12:00, Dott Guido Mazzuca, 'A gentle introduction to integrable systems'.

    Abstract: In my talk I will introduce you the “integrable systems” group of SISSA. After that I will explain to you our main object of study through some examples. Hopefully I will also be able to underline the connection between this and other fields of mathematics.

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