Archivio News

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.

(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.

Teacher: Prof. Andrea Appel (andrea.appel@unipr.it)

Title: Topics in Representation Theory

Syllabus:  
 The Yang-Baxter equation (YBE) is a fundamental symmetry in mathematics and physics arising from a system of particles moving along a line. The quest for constant solutions of YBE (R-matrices) is at the very origin of the theory of Drinfeld-Jimbo quantum groups and their universal R-matrix. In this course, we will review the role and the importance of the YBE in various areas of algebra, geometry, and topology. I will explain the interplay between quantum groups and R-matrices in its simplest case. Then, I will outline some recent and novel construction of R-matrices depending on a spectral parameter in the case of a quantum group of “higher order” known as the Yangian.

Schedule of the course  (24 hours / 6CFU)

Dates: 29/01/205 - 16/04/2025  - Lectures will be held every Wednesday 1:30pm-3:30pm at the University of Parma (Room C, Mathematics Building). Simultaneously, lectures will be streamed on a dedicated MS Teams Channel for online participation (link). 

Note: At the request of participants, it is possible to attend the lessons online.

Assessment method: The final exam will consist in a seminar on a topic related to the course.

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.

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.

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

Titolo (italiano): Teoria delle Decisioni per l’Intelligenza Artificiale
Docente: Prof. Federico Bergenti, Università degli Studi di Parma
Contenuti (inglese):
The course introduces the students to the topics of Decision Theory that are relevant to
Artificial Intelligence. In particular, the course discusses decision-theoretic planning
and learning through the following agenda: brief review of random variables and
stochastic processes (if needed), discrete-time Markov chains, Markov decision
processes, base algorithms for automated planning using Markov decision processes
(e.g., value iteration and policy iteration), base algorithms for machine learning using
Markov decision processes (e.g., Q-learning and SARSA), overview of additional topics
(e.g., partially-observable Markov decision processes, game-theoretic planning). The
course is delivered as a set of classes and exercise sessions tailored to the specific
needs of the enrolled students.
Contenuti (italiano):
Il corso introduce gli studenti agli argomenti della Teoria delle Decisioni che sono di
particolare rilevanza per l'Intelligenza Artificiale. In particolare, il corso discute la
pianificazione e l'apprendimento dal punto di vista della Teoria delle Decisioni con il
seguente programma: cenni su variabili casuali e processi stocastici (se necessario),
catene di Markov tempo discrete, processi markoviani di decisione, algoritmi di base
per la pianificazione mediante processi markoviani di decisione (ad esempio, value
iteration e policy iteration), algoritmi di base per l'apprendimento mediante processi
markoviani di decisione (ad esempio, Q-learning e SARSA), breve panoramica di
argomenti aggiuntivi (ad esempio, processi markoviani di decisione parzialmente
osservabili, pianificazione nella teoria dei giochi). Il corso è erogato mediante lezioni e
sessioni di esercizi pensati appositamente per le esigenze degli studenti iscritti.
Luogo:
Plesso di Matematica, aula B
Campus di Scienze e Tecnologie, Università degli Studi di Parma
Parco Area delle Scienze, 53/A
43124 Parma

Calendario:
• 14 gennaio, dalle 14 alle 18
• 15 gennaio, dalle 14 alle 18
• 16 gennaio, dalle 9 alle 17
• 17 gennaio, dalle 9 alle 17
Numero totale di ore: 24
Numero totale di CFU: 6
Verifica delle competenze:
Prova orale al termine del corso riguardante tutti gli argomenti trattati durante il corso.

Francesca Anceschi (f.anceschi@staff.univpm.it)
Mirco Piccinini (mirco.piccinini@dm.unipi.it)
Syllabus: The main goal of this course is to provide a useful toolbox for the study
of the weak regularity theory á la De Giorgi-Nash-Moser (DGNM) for fractional
kinetic operators. Firstly, we will analyze the local case of the Fokker-Planck operator
in order to introduce the non-Euclidean geometry required for the study of
these kinetic operators. Then, we will provide all the advanced necessary tools to
deal with the nonlocal case, and we will conclude the course with some interesting
applications to more complex physical models, as e.g. those involving the Boltzmann
operator, where the main diffusion non-symmetric kernel satisfies very weak
integrability and non-degeneracy conditions.
Credits & schedule: 20 hours, 5CFU
• November 8, 2024: 10:30 - 12:30
• November 15, 2024: 10:30 - 12:30
• November 22, 2024: 10:30 - 12:30
• November 29, 2024: 10:30 - 12:30
• December 6, 2024: 10:30 - 12:30
• December 13, 2024: 10:30 - 12:30
• January 8, 2025: 10:30 - 12:30
• January 16, 2025: 10:30 - 12:30
• January 20, 2025: 10:30 - 12:30 & 14:30 - 16:30
Venue: aula F, Dipartimento di Matematica, Fisica e Informatica, Università di
Parma and/or Teams platform
Final exam: Research seminar on a proper article related to the course topics (to
be chosen in accordance with the teachers).

Title and Credits: Galois Theory: from groups and forms to descent theory and extensions

Teacher: Prof. Daniel Bulacu, University of Bucarest

Syllabus:  The classical Galois theory dates back to 1830, but it took more than 100 years for it to be reformulated (by Artin) in the language of module theory. Artin's criterion that decides when a field extension K/k is Galois allows to extend the classical Galois theory to Hopf algebras. This was initiated by Chase and Sweedler in 1969 in the commutative case, the general case being considered by Kreimer and Takeuchi in 1981. Today Hopf-Galois extensions appear in various branches of mathematics and physics, being also known as dual algebraic versions of non-commutative fiber spaces (the notion of quantum fiber space can be introduced as a module associated with a Hopf-Galois extension).

The purpose of this course is to make the transition from the classical Galois theory to the Hopf-Galois theory and to present some directions of study for the latter. Briefly, the content of the course is as follows:

• Classical Galois theory.
• Extensions of fields, extensions of separable Galois fields without groups, strongly graded rings, cross products, affine group schemes.
• Relevant examples of Hopf algebras.
• Hopf-Galois extensions and examples.
• Descent theory.
• Hopf-Galois theories in various categories.

Dates 2022/2023: 4, 6, 11, and 13 July 2023, 16:00-18:00 (4 lectures, 8 hours).

Main lecturer
Special speaker
Professor Patrizio Bianchi  Chair Holder of the UNESCO Chair on Education, Growth and Equality
Professor Valentina Mini   Adjunct Professor of Statistics, Advanced Statistics and Statistics for Economics and Business
Location
Department of Mathematics and Computer Science
University of Ferrara, Palazzo Manfredini
Via Muratori 8 / 9 - 44121 Ferrara

Lecture 1. Global Vision and Globalization
Global economic, political, and cultural integration: benefits and drawbacks. Interdisciplinary approaches to contemporary challenges.
27 September 2024 | 09:00 – 12:00 | Classroom B1 | Professor Patrizio Bianchi
Lecture 2. Geopolitics: Focus on Africa and Europe
Geopolitical dynamics of Africa and Europe: historical contexts, contemporary challenges, and global ramifications.
30 September 2024 | 15:00 – 18:00 | Classroom C1 | Manfo Zangmo
Lecture 3. Introduction to Transdisciplinarity Theory
Transdisciplinarity: theoretical foundations, basic concepts, and principles.
02 October 2024 | 15:00 – 18:00 | Classroom C1 | Professor Valentina Mini
Lecture 4. Quantitative Methods for Transdisciplinary Approaches
Theoretical competencies in mathematics and statistics for interpreting scientific literature, bridging interdisciplinary gaps, and enhancing organizational capabilities.
04 October 2024 | 15:00 – 18:00 | Classroom C1 | Professor Valentina Mini
Lecture 5. Qualitative Methods for Transdisciplinary Approaches
Qualitative research methods for data collection, analysis, and interpretation in interdisciplinary research.
07 October 2024 | 15:00 – 18:00 | Classroom C1 | Professor Valentina Mini
Lecture 6. Long-Term Projection and Temporal Vision
Temporal perspective and scenario planning for understanding long-term implications in transdisciplinary studies.
09 October 2024 | 15:00 – 18:00 | Classroom C1 | Professor Patrizio Bianchi and Professor Valentina Mini
Lecture 7. Round Table Lab
Collaborative discussions with entrepreneurs to apply theoretical knowledge to realworld interdisciplinary issues.
11 October 2024 | 15:00 – 18:00 | Classroom C1 | Professor Patrizio Bianchi, Professor Valentina Mini and Guest Entrepreneurs