TIME SERIES ANALYSIS

1. We will recall the basic principles of applied and numerical Fourier analysis: Fourier series and transform, energy and power spectrum, mutual and autocorrelation and their numerical computation.
2. Impulse and harmonic response of a system.
3. Filtering of a time series.
4. Time series as sampling of a continuous signal.

ADVANCED TOPICS IN ANALYSIS (JOINT COURSE WITH SAPIENZA AND TOR VERGATA)

Title: Linearization of flows and maps in Rnand C
Teachers:  Luigi Chierchia - Michela Procesi -
Duration: 20 h
Period: TBA

Program
- Stable and unstable manifolds. Linearization of holomorphic maps and small divisors (Siegel)
- Diffeomorphisms of holomorphic vector fields; Poincaré-Dulac Theorem in resonant and non-resonant cases

 

ADVANCED TOPICS IN LOGIC, HISTORY AND PEDAGOGY( JOINT COURSE WITH SAPIENZA AND TOR VERGATA)

Module  1:  Laboratorio di Didattica:
Teacher: Prof. Benedetto Scoppola  (Univ. Tor Vergata)
Period: TBA
Program:
- algoritmo di euclide in aritmetica (massimo comun divisore) e nella teoria dei numeri
(frazioni continue)
- proporzioni ad elementi interi: i risultati del libro VII
- potenze e proporzioni continue
- incommensurabili.

Modulo 2. Logica:

Teacher: Prof. Lorenzo Tortora De Falco  (Univ. Roma Tre)
Period: TBA
Program:
- Soddisfacibilità e dimostrabilità. Il teorema fondamentale dell'analisi canonica.
- Gentzen e l'eliminazione del taglio
- Dimostrazioni e programmi: la corrispondenza di Curry-Howard
- Introduzione alla Logica Lineare.

Modulo 3. Storia:

Teacher: Prof. Enrico Rogora  (Univ. la Sapienza)
Period: TBA
Program:
- Lagrange
- Il teorema di Ruffini Abel
- Il lavoro di Abel sulle equazioni e sulle funzioni ellittiche
- Il contributo di Galois
- Le soluzioni analitiche delle equazioni di quinto grado
- La teoria di Galois-Klein

ADVANCED TOPICS IN ALGEBRA AND GEOMETRY (JOINT COURSE WITH SAPIENZA AND TOR VERGATA)

Title : Special projective varieties in Algebraic Geometry
Teacher: Alessandro Verra (Univ. Roma Tre)

Duration: 20h
Period: April-May 2026
Program

• Geometry of linear systems of quadrics
• Determinantal equations of planar curves
• Vector bundles on curves, Picard group
• Surfaces in $P^3$

ADVANCED TOPICS IN MATHEMATICAL PHYSICS (JOINT COURSE WITH SAPIENZA AND TOR VERGATA)

Title: Supersymmetric approach to quantum disordered systems
Teacher: Luca Fresta ( Univ. Roma Tre)
Duration: 20h
Period: Feb: 10,12,24; Mar 11,13,16,18,20,23.

Program

• Complex and Grassmann Gaussian integration (Efetov’s supersymmetric method)

• Random Schrödinger operators: Wegner and Lifshitz tail estimates

• Random matrix theory: Wigner's semicircle law for GUE matrices

• Gaussian random band matrices (RBM)

• Supersymmetric Hn|m non-linear sigma models and probabilistic connections

• non-linear sigma models and probabilistic connections