General information
The seminars will take place online, using the platform Zoom. They will be held by professors, researchers and PhD students. During the afternoon, always on Zoom, we will open the virtual rooms where groups of students will meet PhD students to talk not only about their research, but also about their experience in Trieste and at SISSA.
Schedule
Monday december 14th
 10:00 AM, 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 AROMACFD.
 11:15 AM, Prof. Roberto Trotta, 'Theoretical and Scientific Data Science and Applications to Cosmology'.
Abstract: 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. In 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.
 12:15 AM, 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.
Tuesday december 15th
 10:00 AM, 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!
 11:00 AM, Prof. Marcello Porta, 'ManyBody Quantum Mechanics'.
Abstract: I will give an overview of selected recent developmrnts in mathematical quantum mechanics, with a focus on manybody systems. In particular, I will discuss the derivation of effective nonlinear theories for large quantum systems, and the emergence of universality in condenses matter models.
 12:00 AM, 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.
Wendsday december 16th
 12:00 AM, Dott. Carlo Scarpa, 'Canonical metrics in Kähler geometry'.
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.
Thursday december 17th
 10:00 AM, Prof. Alberto Maspero, 'Dynamical systems and water waves'.
Abstract: Classical questions in dynamical systems regard the existence of stationary solutions, periodic and quasiperiodic 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.
 11:00 AM, Dott. MirunaStefana 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 nonzero 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 twofold. Firstly, to study a combinatorial object measuring this nonconvexity; 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 nonMorse strict local minima realising a large class of such trees.
Friday december 18th
 11:00 AM, Dott. Alessandro Rubin, 'What is a noncommutative geometry?'.
Abstract: The term 'noncommutative geometry' carries with it a certain aura of mistery: 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, mesure theory and (if time permits) some basic condensed matter physics.
 12:00 AM, 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.

