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
 

Tentative schedule

• Chierchia: 30/03 (14-16), 01/04 (9-11), 08/04 (9-11), 10/04 (9-11), 13/04 (14-16);
• Procesi: 27/04 (14-16), 29/04 (14-16), 04/05 (14-16), 06/05 (14-16), 11/05 (14-16).

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)
               Prof. Lionel Vaux                        (Aix-Marseille Université)
 

Period: The “Logic” module (12 hours) of the institutional PhD course “Didactics, Logic and History of Mathematics” will be held at the Department of Mathematics and Physics of Roma Tre University (room to be determined) during the month of April 2026, following the provisional program attached below.

 

The course will consist of 4 meetings of 3 hours each, either on a weekly basis (from Monday 30 March to Friday 24 April) or on a biweekly basis (from Monday 13 April to Friday 24 April).

The instructors will be Lorenzo Tortora de Falco (Roma Tre University) and Lionel Vaux (Aix-Marseille Université).

Call for Interested Students

 

In order to better determine both the dates and the content of the course, interested students are asked to come forward, briefly presenting their academic background (with particular reference to any Logic courses they have already taken) by sending an email to:

tortora@uniroma3.it

Program:
 

part 1 (6h): general proof theory

• Satisfiability and provability. Fundamental theorems of first order logic (Canonical Analysis)
• Gentzen and cut-elimination theorem
• Proofs and programs: Curry-Howard’s correspondence

part 2 (6h): logical proofs as graphs (linear logic)

• Graphs and colorings: Yeo’s theorem and variants
• Proof nets: a graphical language for Linear Logic proofs
• Graph theory meets proof theory: correctness criteria
• Cut elimination as graph rewriting

Modulo 3. Storia:

Teacher: Prof. Enrico Rogora  (Univ. la Sapienza)

Schedule

• November: Tuesday 11, 11:00-13:00; Wednesday 12, 11:30-13:30; Tuesday 18, 11:00-13:00; Wednesday 19, 11:30-13:30;
• December: Tuesday 2, 11:00-13:00; Wednesday 3, 11:30-13:30.

All lectures will take place in Room F at the Department of Mathematics "Guido Castelnuovo", Sapienza.

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