Information on courses

(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

(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In the second part of the course (10 hours) we will introduce some unpublished original sources in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, 31/01/2025, ore 10-13; 14-16. Ferrara.
Friday, 28/02/2025, ore 10-13; 14-16. Modena.
Tuesday, 11/03/2025, ore 10-13; 14-16. Ferrara.
Tuesday, 25/03/2025, ore 10-13; 14-16. Modena.

Verification of the acquired skills: presentation of a written paper regarding one of the themes
developed during 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 Decembre 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 Febraury Sala Riunioni e Seminari 10:30am – 13:30am;
vi) Wendsday 5 th Febraury 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 by 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:
i) Theorem: A closed subgroup of a Lie group is an embedded Lie group. Article: Palais and Terng `` general Theory of canonical forms’’
ii) Theorem: If a transformation of a Riemannian manifold preserves the distance, then it is an isometry. Article: Karsten Grove and Chaterine Searle ``Global G-manifold reductions and resolutions’’
iii) Theorem: If the G action on a connected manifold is proper, then there exists a Riemannian metric such that the G action on M is isometric. Article: Huckleberry and Wurzbacher ``Multiplicity-free complex manifolds’’
iv) Theorem: The Hopf-Rinow Theorem. Article: Sjamaar and Lerman `` Stratified Symplectic Spaces and Reduction’’.

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

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.

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).