Information on courses

• The space BV: definition and examples
• BV functions in one variable
• Sets of finite perimeter
• Embedding theorems and isoperimetric inequalities
• Fine properties of BV functions
• SBV functions: definition and examples

• There will be NO lectures in the week 1-4 April 
• The lecture of Tuesday 25^th March will be in "aula F"
• Interested students should contact the teacher

Teachers: Marzia Bisi and Maria Groppi (University of Parma)
Syllabus:
The course is intended to provide an introduction to classical kinetic Boltzmann approach to rarefied gas dynamics, and some recent advances including the generalization of kinetic models to reactive gas mixtures and to socio-economic problems.
Main topics:
- distribution function and Boltzmann equation for a single gas: collision operator, collision invariants, Maxwellian equilibrium distributions;
- kinetic theory for gas mixtures: extended Boltzmann equations and BGK models;
- kinetic models for reacting and/or polyatomic particles;
- hydrodynamic limits, Euler and Navier-Stokes equations;
- Boltzmann and Fokker-Planck equations for socio-economic phenomena, as wealth distribution or opinion formation.
Period and venue:
Lectures will be delivered online on Teams platform in February-March 2025 in the following dates:
- Tuesday, 25 February at 2.30 - 4.30 pm;
- Wednesday, 26 February at 11.00 am - 1.00 pm;
- Tuesday, 4 March at 3.30 - 5.30 pm;
- Thursday, 6 March at 10.30 am - 0.30 pm;
- Wednesday, 12 March at 11.00 am - 1.00 pm;
- Thursday, 13 March at 11.00 am - 1.00 pm;
- other lectures will be scheduled in the week 17-21 March upon agreements with participants.
Verification of the acquired skills: students will give a talk on a topic related to the arguments of the course.

Syllabus: The course is principally focused on Boundary Element Methods (BEMs).
Lectures involve: Boundary integral formulation of elliptic, parabolic and hyperbolic problems
- Integral operators with weakly singular, strongly singular and hyper-singular kernels
- Approximation techniques: collocation and Galerkin BEMs - Quadrature formulas for
weakly singular integrals, Cauchy principal value integrals and Hadamard finite part
integrals - Convergence results - Numerical schemes for the generation of the linear system
coming from Galerkin BEM discretization.
Knowledge of basic notions of Numerical Analysis and, in particular, of numerical
approximation of partial differential equations is required.
References will be provided directly during the course.
Exercises, given at the end of every lecture, will be discussed by the students in the following
lecture, in order to assess the comprehension of the subject.
Dates: Lectures will be delivered online on Teams platform in the following Tuesdays, from
9 am to 12 am:
11/03/2025; 18/03/2025; 25/03/2025; 01/04/2025; 08/04/2025; 15/04/2025; 29/04/2025; 06/05/2025

Docente: Paolo Baroni
Syllabus: The course aims at analyzing the basic elements of the theory of nonlinear elliptic equations having signed measures as data. In particular, the following topics will be studied:
- Existence of solutions for linear and nonlinear equations with measure data. Comparison between SOLAs, entropy and renormalized solutions.
- Consequence of density conditions on the measure. Linear and nonlinear potentials.
- Characterization of dual energy spaces in terms of Wolff potentials.
- Bounds of solutions in terms of Wolff potentials.
- Bounds of the gradient of solutions in terms of Riesz potentials.
Calendar: March and April 2025, Tuesday, 14:30-16:30, 4 (March 4, 11, 18, 25)+4 (April 1, 8, 15, 22) two-hour lessons
Venue: Microsoft teams meetings if participants from Modena or Ferrara will participate, building of Mathematics of the University of Parma otherwise (in the case, the precise room will be fixed after the schedule for the second semester classes will be finalized)
Verification of the acquired skills: an oral presentation of an in-depth analysis on a topic developed throughout the course, lasting approximately one hour.
Notes: interested participants are required to contact the teacher in advance, so to organize the first meetings.

Content: introduction to differential model problems for option pricing in the Black-Scholes framework, analysis of peculiar troubles and advantages in application of standard numerical methods for partial differential problems: Finite Difference, Finite Element, Boundary Element, Binomial, Monte Carlo.

Period: 01/11/2024 - 31/03/2025
Calendar: 12 hours scheduled upon agreement with participants
CFU: 3
Assessment Method: production of a short paper/discussion on a significant follow-up topic.

(20 hours, 5 CFU)  Michela Eleuteri, Maria Giulia Lugaresi

Syllabus: The course aims to describe some methods of research in the history of mathematics, showing how the study of different themes and historical sources requires different approaches and tools of inquiry.
In the first part of the course (10 hours) we will present elementary methods of historical research that can be applied in the critical examination of printed mathematical texts of the past. We will provide examples of critical reading taken from some important Italian mathematical works of the 18th and 19th century devoted to the foundations of infinitesimal calculus.
In the second part of the course (10 hours) we will introduce some unpublished original sources in the history of mathematics in order to explain how to approach the critical reading, transcription and analysis of them. In particular, we will focus on some pure and applied mathematical works by Paolo Ruffini.

Interested students are invited to contact the teachers.

Date:
Friday, 28/02/2025, ore 10-13; 14-16. Modena. The early period of the Calculus of Variations.
Tuesday, 11/03/2025, ore 10-13; 14-16. Ferrara. Mathematics applied to the study of the fluid-dynamics during the 18th century.
Tuesday, 18/03/2025, ore 10-13; 14-16. Modena. The Calculus of Variations after Lagrange.
Tuesday, 25/03/2025, ore 10-13; 14-16. Ferrara. The manuscripts by Teodoro Bonati at the Ariostea Library of Ferrara.

Verification of the acquired skills: presentation of a written paper regarding one of the themes
developed during the course.

Docenti: Alessandro Benfenati, Elena Morotti
Syllabus: Scientific research drives the development of new and improved medical technologies. The progress of medical imaging, in particular, contributes to the enhancement of diagnostic tools with a significant impact on global health. In this context, the interplay among Physics, Math and Computer Science plays a crucial role in developing algorithms that enable computers to reconstruct and interpret medical images, leading to faster and more accurate diagnoses.
Medical imaging is also a key area where AI and deep learning are making significant strides, but the use of such cutting-edge tools must meet normatives and legislative constraints.
Topics:
- introduction to computational imaging as an inverse problem, with a special focus on tomographic reconstruction;
- optimization algorithms for image reconstruction and their applicability;
- inspection of real medical images and their analysis;
- deep learning for medical imaging and different possible approaches involving convolutional neural networks;
- explainable AI with examples on imaging

Calendar:
Wednesday 12/02/2025 09:30-13:00, 14:00-17:30. Aula: Laboratorio Zironi - [MO 18] - Via Campi 213/B (Matematica),
Thursday 13/02/2025 09:30-13:00, 14:00-17:30. Aula M2.3 - [MO 18] - Via Campi 213/B (Matematica)
Friday 14/02/2025, 09:30-12:30, 14:00-17:00. Aula: Laboratorio Zironi - [MO 18] - Via Campi 213/B (Matematica)

Verification of the acquired skills: Oral presentation on the topics of the course.

Ore totali: 20, CFU 5

Esame: Oral presentation on the topics of the course

Course Title: Group actions on manifolds
Day and Time:
i) Monday 25th November 10:30am – 13:30am Aula A, Department of Mathematics
ii) Monday 2th December 10:30am – 13:30am Aula A, Department of Mathematics
iii) Monday 9th December 11:30am – 12:30am Aula A, and Sala Riunioni e Seminari 12:30am – 13:30am
iv) Monday 16th December 11:30am – 12:30am Aula A, and Sala Riunioni e Seminari 12:30am – 13:30am
v) Thuesday 4th February Sala Riunioni e Seminari 10:30am – 13:30am
vi) Wendsday 5th February Sala Riunioni e Seminari 10:30am – 13:30am

Instructor Name: Leonardo Biliotti
Course Description: In this course, we will develop several modern techniques in Lie group acting on manifolds. We focus ourselves on the proper actions proving the Slice Theorem, The Tubular Neighborhood Theorem and the Principal orbit type Theorem. We also describe the orbit type of the manifold and the orbit space. Finally, we study maximal Torus of a
compact connected Lie group and we that the centralizer of a Torus is connected. As an application we prove that an Adjoint orbit of a compact connected Lie group is simply connected.
CFU: 6
Number of hours: 18 hours of class + 8 hours of self-study studying one of the following topics: Theorem of Slice and the article: Diaz Ramos and Kollross “Polar actions with a fixed point’’
Tubular Neighborhood Theorem and the article Karsten Grove and Chaterine Searle “Global G-manifold reductions and resolutions’’ Principal Orbit Theorem and the article: Huckleberry and Wurzbacher “Multiplicity-free complex manifolds’’

Stratification by orbit types and the article Sjamaar and Lerman ``Stratified Symplectic Spaces and Reduction’’.
Maximal Torus and the article Milnor “Curvatures of Left Invariant metrics on Lie groups C’’

Final exam: the student chooses one of the above topics and give a talk of one hour.

The final exam can take a place on-line.

Prof.ssa Simona Bonvicini (UNIMORE), Prof. Giuseppe Mazzuoccolo (UNIMORE), Dott. Davide Mattiolo (KU Leuven Belgium).
Calendar: 15th January 2025 – 25th February 2025
Lectures: 15/1, 16/1, 22/1, 23/1, 29/1, 31/1, 5/2, 7/2,12/2,14/2, 17/2, 18/2, 24/2, 25/2.
Further Notes: The lectures may be conducted online
Assessment Method: A seminar on a course topic
Topics: Basic Definitions for Graphs: Connectivity on the vertices and edges of a graph, Menger's Theorem, vertex and edge colorings of a graph, Brooks' Theorem, Vizing's Theorem.
Matching Theory: Matchings in bipartite graphs (König's and Hall's Theorems) and matchings in arbitrary graphs (Tutte's Theorem).
Flows: Nowhere-zero k-flows, definition of flow number, and Tutte's Conjectures. 4-flow Theorem, 8-flow Theorem and 6-flow Theorem.
Discharging Method in Graph Theory: Examples and applications.
Introduction to Ramsey Theory.

(6 CFU)

January 20-24, 2025 -  

Palazzo Manfredini (University of Ferrara), via Ludovico Muratori 9, 44121, Ferrara

https://sites.google.com/view/advancednumericalmethods4mldl/home?authuser=0

The purpose of the event on Advanced Numerical Methods for Machine and Deep Learning is to offer a research-oriented introduction to stochastic numerical optimization algorithms, randomization in numerical linear algebra, regularization

techniques, uncertainty quantification, and their applications in engineering and inverse imaging problems.

The program includes four theoretical blocks, each taught by a different lecturer. Each of the 4 blocks (5 hours each) is complemented by a lab session (2 hours) and/or exercise session (2 hours).

Lecturers

• Giovanni S. Alberti - MaLGa & University of Genoa, Italy

Machine Learning for Inverse Problems

• Elena Celledoni - Norwegian University of Science and Technology (NTNU), Norway

Deep learning from the point of view of numerical analysis

• Nataša Krklec Jerinkić - University of Novi Sad, Serbia

First order methods in stochastic optimization

• Joel A. Tropp- Caltech, USA

Randomized matrix computations: themes and variations

Computational Lab

• Federica Porta, University of Modena and Reggio Emilia
• Luca Ratti, University of Bologna

Invited speakers

• Stefania Bellavia, University of Florence
• Sandra Pieraccini, Polytechnic University of Turin
• Silvia Villa, MaLGa & University of Genoa

Organizing and Scientific Committee

Tatiana A. Bubba  (University of Ferrara)

Valeria Ruggiero  (University of Ferrara)

The event is sponsored by FAIR (Future Artificial Intelligence Research) and by INdAM - GNCS