## Notiziario Scientifico

**Notiziario dei seminari di carattere matematico**

a cura del Dipartimento di Matematica

*G. Castelnuovo*, Sapienza Università di Roma

Settimana dal 21-01-2019 al 27-01-2019

**Lunedì 21 gennaio 2019**

Ore 14:00, Aula 311, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo, 1, Pal. C

PhD Course

Roberto Fernandez (New York University Shanghai)
*Gibbs measures in classical statistical mechanics and stochastic processes*

Gibbs measures are the centerpiece of rigorous studies in classical statistical mechanics. Based on the initial ansatz of Boltzmann, Maxwell and Gibbs, these measures are at present ubiquitous probabilistic objects endowed with a rich mathematical theory and a wide range of applications. More recently, their theory has been put in correspondence with the theory of non-necessarily Markovian stochastic processes. This correspondence has exhibit common aspects but also important differences that could be exploited in the analysis of random sequences (or signals). The course will start with the precise definition of Gibbs measures and the description of their main properties. The limitations of Gibbsian theory will be subsequently explored, exposing a number of mechanisms leading to non-Gibbsian measures. The second part of the course will focus on one-dimensional lattices and compare Gibbs measures with discrete-time stochastic processes and other measures introduced in the theory of processes and symbolic dynamical systems (Bowen measures, g-measures).

**Lunedì 21 gennaio 2019**

Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Analisi Matematica

Thierry Paul (CMLS, Ecole Polytechnique, CNRS)
*Quantum Wasserstein*

I will define a quantum analogue to the Wasserstein distance of order two between density operators, namely positive trace one operators on Hilbert spaces. I will give first properties, in particular the link with usual Wasserstein distance between positive symbols of the quantum density operators and show how they define a kind of topology more adapted to the classical limit than the one defined by Schatten classes such as trace norm. I will present recent results obtained with E. Caglioti and F. Golse concerning a quantum version of the Brenier optimal transport Theorem and will finish by propagation estimates à la Gronwall using some quantum/classical analogue to the Wassertein metric measuring directly the "distance" between a quantum density operator and a classical probability density.

**Lunedì 21 gennaio 2019**

Ore 15:00, Aula D’Antoni, Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1

Corso di Dottorato

Prof. Han Peters (University of Amsterdam)
*Holomorphic dynamics: Wandering Fatou Components*

The iteration of rational functions, acting on the Riemann sphere, is a classical subject that has been studied for well over a century. It is remarkable that even the iteration of quadratic polynomials, a seemingly simple family of maps, has led to a surprisingly deep theory, with several important open questions still unsolved. Naturally the field of holomorphic dynamical systems has expanded into many directions. Since the late 1980's there has been considerable interest in the iteration of rational functions in higher dimensions. In recent years it has become clear that already in two complex variables phenomena arise that are unlike anything that can occur in one variable. In this course we will consider some of the most striking results in this direction of research. In particular we consider the construction of wandering domains, and we finish by discussing the most pressing open questions regarding the classification of invariant Fatou components. Programma 1. Crash course in 1D complex dynamics. Classification of invariant Fatou components and non-existence of wandering domains. Discussion of fixed points. 2. Parabolic bifurcations. Mane-Sad-Sullivan result. Lavaurs Theorem 3. Wandering domains in higher dimensions: skew products. Detailed proof of the construction of wandering domains. Discussion of very recent results. 4. Fatou components of polynomial automorphisms, and open questions.

**Lunedì 21 gennaio 2019**

Ore 16:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

Sam Gunnigham (University of Edinburgh)
*Quantum character theory*

I will give an overview of various approaches to studying character varieties (moduli spaces of local systems on manifolds) using tools of geometric representation theory and topological field theory. For example, in my work with Ben-Zvi and Nadler we show that the homology groups of character varieties (which are the subject of fascinating conjectures of Hausel and Rodriguez Villegas) are extracted from a certain topological field theory associated to the monoidal category of Harish-Chandra bimodules. A closely related topological field theory constructed by Ben-Zvi, Brochier, and Jordan defines canonical quantization of character varieties associated to the quantum group; In my ongoing work with David Jordan we are investigating how this theory computes invariants of knots and skeins in 3-manifolds via q-analogues of character sheaves and Harish-Chandra bimodules. I will not assume any prior familiarity with any of these concepts.

**Lunedì 21 gennaio 2019**

Ore 9:00, Sala Convegni, CNR, Piazzale Aldo Moro 7, Roma

Conferenza
*Conferenza DIITET-CNR, Area Strategica “Matematica Applicata”*

- 9:00 Saluti di Benvenuto: Ing Emilio Fortunato Campana, Direttore DIITET
- 9:15 Introduzione alla giornata: Matematica Applicata nel DIITET: Roberto Natalini, Giovanni Rinaldi, Michela Spagnuolo
- 9:30-10:45 Scientific Computing

* New CHallenges for (adaptive) PDE solvers: the interplay of ANalysis and GEometry, Micol Pennacchio (IMATI, Pavia and Genova)

* Computational techniques for uncertainty quantification of partial differential equations with random parameters, Lorenzo Tamellini (IMATI, Pavia)

* Scalable preconditioners for sparse and large linear systems, Pasqua D’Ambra (IAC, Napoli)

* On the role of numerical viscosity in the approximation of systems of conservation laws, Laura Spinolo (IMATI, Pavia)

* Innovative methodologies in applied mathematics: the developments of Particle Methods for fluid mechanics at CNR, Andrea Colagrossi (INM, Roma) - 10:45-11:15 Coffee Break
- 11:15 Invited Talk: Hard Sciences: Separating Hype from Fundamentals Prof. Alberto L. Sangiovanni-Vincentelli (The Edgar L. and Harold H. Buttner Chair, Department of EECS, University of California, Berkeley)
- 12:15-13:15 Optimization

* Optimization-based Decision Support Tools to Promote Sustainable Freight Transport in Urban Contexts, Antonino Sgalambro (IAC, Roma)

* The Perspective Reformulation in Mixed-Integer Nonlinear Optimization Claudio Gentile, (IASI, Roma)

* Robust Optimization, Sara Mattia (IASI, Roma)

* Optimization under uncertainty, Fabrizio Dabbene (IEIIT, Torino) - 13:15 -14:15 Lunch Break & Poster Session
- 14:15 -14:30 Matematica e Imprese - l’esperienza dello SPORTELLO MATEMATICO
- 14:30 -15:45 Mathematical Modelling

* Modelling the Immune Response, Filippo Castiglione (IAC, Roma)

* Mathematical Modeling in Systems Biology and Biomedical Application, Pasquale Palumbo (IASI, Rome)

* Optimal spatio-temporal control of invasive plants in protected areas, Carmela Marangi (IAC, Bari)

* Computational topology methods for reasoning on shape analysis and similarity, Silvia Biasotti (IMATI, Genova)

* Persistent homology for data analysis and machine learning: past, present, and future challenges, Daniela Giorgi (ISTI, Pisa) - 15:45-16:15 Coffee Break
- 16:15-17:30 Data Science

* Industrial statistics: between tradition and innovation, Antonio Pievatolo (IMATI, Milano)

* SAR Meteorology: is it a new perspective in the atmospheric remote sensing with space geodesy and high precision Numerical Weather Prediction (NWP) models?, Giovanni Nico (IAC, Bari)

* Advancing the frontiers of earthquake science through statistical seismology, Elisa Varini (IMATI, Milano)

* Traffic Data Classification for Police Activity, Stefano Guarino (IAC, Roma)

* Network-Based Data Analysis Paola Paci (IASI, Roma)

**Martedì 22 gennaio 2019**

Ore 10:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma

Esame Finale di Dottorato

Stefano Iovieno (Dipartimento di Matematica, Sapienza Università di Roma)
*Soliton representations and Sobolev diffeomorphism symmetry in CFT*

We construct an uncountable family of proper soliton representations using a particular class of non smooth diffeomorphisms and we show that any soliton representation has positive energy. In addition, we extend any irreducible unitary projective positive energy representation of \( Diff_+(S^1) \) to the group of fractional Sobolev diffeomorphisms \( D^s(S^1) \), with \( s>3 \). We show that the positive energy vacuum representations of \( Diff_+(S^1) \) with integer central charge can be extended to the group \( D^s(S^1) \) with \( s>2 \).

Joint work with S. Carpi, S. Del Vecchio, Y. Tanimoto.

**Martedì 22 gennaio 2019**

Ore 15:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Modellistica Differenziale Numerica

J. Melou (IRIT e Mikros Image)
*A splitting-based algorithm for multi-view shape-from-shading*

Shape-from-shading is a classic ill-posed technique for 3D-reconstruction, which suffers from the well-known concave/convex ambiguity. However, if may recover thin details of the 3D-shape. On the other hand, multi-view stereo is not satisfactory either: if the overall 3D-shape is reasonable, thin details are missing and artefacts appears in the textureless areas. We propose a simple yet effective strategy for combining the advantages of both techniques.

**Mercoledì 23 gennaio 2019**

Ore 10:00, Aula D’Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

Corso di Dottorato

Andrey Piatnitski (Arctic University of Norway)
*Partial differential equations on singular or thin structures*

**Mercoledì 23 gennaio 2019**

Ore 14:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

Seminario per il Dottorato di Ricerca in Matematica

Edoardo Sernesi (Università Roma Tre)
*Curves on K3 Surfaces I*

- Generalities on Brill-Noether theory. Lazarsfeld's proof of Petri's conjecture.

- Gaussian maps, ribbons and extendability. Results of Wahl and Beauville-Merindol.

- The problem of characterizing K3 curves: some results.

[Lecture series in the framework of the Research Project "Families of curves: their moduli and their related varieties" - Mission Suistanability Tor Vergata, CUP: E81|18000100005, P.I.: F. Flamini]

**Mercoledì 23 gennaio 2019**

Ore 16:00, Aula F, Dipartimento di Matematica e Fisica, Largo San Leonardo Murialdo, 1, Edificio Aule, primo piano

Colloquium di Matematica

Ugo Dal Lago (Università di Bologna)
*Differential Program Semantics*

Giving meaning to programs through axiomatic, denotational, and
operational semantics is one of the main goals of theoretical computer
science since its early days. Traditionally, program semantics is
built around notions of program equivalence and refinement, based on
which verification and transformation techniques can be justified.
More and more often, however, programs are substituted with
approximately equivalent programs, or verified against imprecise
specifications. Program semantics has started dealing with program
differences only in recent years, through the interpretation of
programs in metric spaces. We give a brief survey about the state of
the art on metric program semantics, and on the inadequacy of metrics
as a way to deal with program differences. We thus point at a few
preliminary results on a new kind of differential program semantics,
which a soon-to-start ERC project plans to investigate along four
axes: logical relations, bisimilarity, game semantics, and linear
logic.

**Mercoledì 23 gennaio 2019**

Ore 14:00, Aula Dal Passo (1201), Dipartimento di Matematica, Università di Roma Tor Vergata

Mini-workshop
* A 1/2-day of IDEAS about the Dynamics of Plasmas in Tokamaks and their Numerical Simulations*

- 14:00 Cristel CHANDRE (Institut de Mathématiques de Marseille, CNRS/Aix-Marseille Université/Centrale Marseille, France), Title: "A brief introduction to gyrokinetics"
- 15:00 Philippe GHENDRIH (CEA-IRFM (Commissariat à l'Energie atomique - Institut de Recherche sur la Fusion par confinement Magnétique), Cadarache, France), Title: "Kinetics and gyrokinetics to understand turbulent heat transport in burning thermonuclear plasmas"
- 16:00 Coffee BREAK
- 16:30 Ahmed RATNANI (Max Planck Institute for Plasma Physics, Garching, Germany), Title: "Challenges in the numerical simulation of MHD"

**Giovedì 24 gennaio 2019**

Ore 11:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Corso breve

Annalisa Buffa (EPFL, Svizzera)
*The interplay of geometric modelling and numerical analysis of PDEs - I *

http://www.mat.uniroma2.it/~dott/Buffa.htm

**Giovedì 24 gennaio 2019**

Ore 12:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

Seminario di Analisi Numerica

Isabella Furci (Università degli Studi dell'Insubria)
*Spectral analysis and fast methods for structured matrix sequences and PDE discretizations*

When simulating phenomena in applied sciences, often one has to deal with functional equations that do not admit an analytical solution. Describing real situations is however possible resorting to numerical approximations. The general purpose is to furnish useful tools aimed at solving computational issues, stemming from such approximation techniques.
In this talk we focus on the case where the resulting matrix sequences \( \{A_n\}_{n} \) possess a structure, that is they belong to the class of Toeplitz matrix sequences or to the more general class of *Generalized Locally Toeplitz (GLT)* matrix sequences. Consequently, the spectral analysis of the coefficient matrices plays a crucial role for an efficient and fast resolution.

The convergence properties of iterative methods are strictly related to the notion of symbol, a function which asymptotically provides an approximation of the eigenvalues of \( A_n \) by its evaluations of an uniform grid. We provide new tools for computing the spectrum of preconditioned banded symmetric Toeplitz matrices, Toeplitz-like matrices, \( n^{-1}K_n^{[p]} \), \( nM_n^{[p]} \), \( n^{-2}L_n^{[p]} \), coming from the B-spline IgA approximation of \( -u''= \lambda u \), plus its multivariate counterpart for \( -\Delta{u}= \lambda u \) [2], and block and preconditioned block banded symmetric Toeplitz matrices, [1,3]. For all the above cases we propose new algorithms based on the classical concept of symbol, but with an innovative view on the errors of the approximation of eigenvalues by its uniform sampling.

The algorithms devised are special interpolation-extrapolation procedures performed with a high level of accuracy and only at the cost of computing of the eigenvalues of a moderate number of small sized matrices.

[1] Ahmad, F., Al–Aidarous E. S., Alrehaili D. A., Ekström S.-E., Furci I., Garoni C., and Serra-Capizzano S. Are the eigenvalues of preconditioned banded symmetric Toeplitz matrices known in almost closed form?, Numer. Algorithms 78(3), 867–893 (2018).

[2] Ekström, S.-E., Furci, I., Garoni, C., Manni, C., Serra-Capizzano, S., and Speleers, H. Are the eigenvalues of the B-spline IgA approximation of −∆u = λu known in almost closed form?, Numer. Linear. Algebra Appl. 25(5), (2018). Early version by Ekström S.-E., Furci I., and Serra-Capizzano S. with the same title in Technical report, 2017-016, Department of Information Technology, Uppsala University (2017).

[3] Ekström S.-E., Furci I., and Serra-Capizzano S., Exact formulae and matrix–less eigensolvers for block banded Toeplitz-like matrices, BIT Numer. Math. 58(4), 937–968 (2018).

**Giovedì 24 gennaio 2019**

Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Corso breve

Annalisa Buffa (EPFL, Svizzera)
*The interplay of geometric modelling and numerical analysis of PDEs - II*

http://www.mat.uniroma2.it/~dott/Buffa.htm

**Venerdì 25 gennaio 2019**

Ore 10:30, Aula Dal Passo, , Dipartimento di Matematica, Università di Roma Tor Vergata

Corso breve

Annalisa Buffa (EPFL, Svizzera)
*The interplay of geometric modelling and numerical analysis of PDEs - III*

http://www.mat.uniroma2.it/~dott/Buffa.htm

**Venerdì 25 gennaio 2019 (*annullato*)**

Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma

Seminario per Insegnanti (Piano Lauree Scientifiche)

Emiliano Ippoliti (Dipartimento di Filosofia, Sapienza Università di Roma)
*L'arte della rappresentazione matematica. Le 'rappresentazioni matematiche' e il loro ruolo per l'avanzamento della conoscenza.*

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