# Manifesto and Courses

There are several courses organised by the School that students may attend depending on their individual curriculum.

All courses will be held at the Department of Mathematics except where differently indicated.

**Manifesto of Studies**

According to art. 6 of the "Regolamento interno del corso di dottorato in Matematica", the document "Manifesto of Studies Doctoral School in Matematics" (see the download box at the bottom) contains the list of courses, along with the rules that must be respected. As goes for rules not included here, we refer to the "Regolamento interno del corso di dottorato in Matematica".

According to the "Manifesto of Studies of the Doctoral School in Mathematics" we recall the following rules.

A candidate for the Ph.D. Degree in Mathematics must complete three courses, relevant to their research topic and taken from those presented in the Manifesto of Studies.

Doctoral students must present their study plan, in accordance with their advisor, no later than January 31, 2024. Possible other courses of interest, not listed in the Manifesto of Studies, can be introduced in the study plan if accompanied by a motivation for their choice and in agreement with the student’s supervisor.

Any modification to the study plan, agreed with the supervisor, must be submitted no later than April 30, 2024.

Generally, all examinations must be completed within the end of July. In case of failure to do so, the student must present a motivation letter requesting for an extension. This must be submitted to the Director of the Doctoral School in Mathematics by 31 July 2024 (Doctoral School Committee dated 13/10/2021).

The School Committee, in accordance with the advisor, can ask for the presence in a student’s study plan of any specific course which is regarded of particular interest for the scientific education of the student.

Doctoral students are required to participate in the “Math Bites” and “Doc in Progress” seminars, organized by the research groups of the Doctoral School, and to other activities (such as workshops, summer schools, and others) as proposed by their advisors.

Students of the curriculum “**e. Mathematical applications to Quantum Science and Technologies**” may choose their courses also among those in the Manifesto of the Q@TN Interdisciplinary Ph.D. School.

**Courses for the academic year 2023/2024**

**Advances in Mathematical Logic. Homotopy Type Theory**_Iosif Petrakis**Advances in Mathematical Analysis: Rigidity phenomena for PDE problems arising in geometry and mathematical physics**_Virginia Agostiniani, Stefano Borghini**Advanced in Theory of distributions and applications**_Brunetti Romeo**Advances in Mathematical Analysis: ODE with rough vector fields**_Andrea Marchese, Paolo Bonicatto**Advances in Mathematical Analysis and Applications. Euscotha: Euregio School on Control Theory and Applications**_Mauro Garavello, Frederic Jean, Marco Frego, Angelika Peer, Karl von Ellenrieder, Lucia Pallottino.**Advances in Mathematical Applications to Biology and Medicine: Stability analysis of dynamical systems in mathematical biology**_Stefania Ottaviano, Mattia Sensi**Advances in Numerical Analysis and Mathematical Modelling: Multi-agent interaction models, from control to learning across scales**_Giacomo Albi, Marco Bonafini**Advances in Numerical Analysis: Computational aspects of complex engineering systems**_Chiara Piazzola, Franco Zivcovich**Advances in Operation Research**_Romeo Rizzi**Advances in Cryptography and Codes: Cryptanalysis of Code-Based Cryptosystems and beyond**_Paolo Santini, Marche Polytechnic University (lecturer), Marco Calderini (examiner)

### Additional courses borrowed from the Master Degree in Mathematics

**Model Theory**_Stefano Baratella**Methods in Representation Theory**_Lidia Angeleri**Tensor Decomposition for big data analysis**_Alessandra Bernardi**Advanced Cryptography**_Edoardo Ballico**An Introduction to Symplectic Geometry**_Alessia Mandini**Geometry and Topology for Data Analysis**_ Alessandro Oneto**Advanced Geometry**_Roberto Pignatelli**Toric Geometry**_Elisa Postinghel, Luis Eduardo Solá Conde**Optimal Transport**_Andrea Marchese, Andrea Pinamonti**Geometric Measure Theory**_Andrea Marchese, Paolo Bonicatto**Geometric Analysis**_Lorenzo Mazzieri**Markov Decision Processes and Reinforcement Learning**_Luigi Amedeo Bianchi and Francesco Cordoni- Mathematical Physics of Quantum Relativistic Theories_Valter Moretti
**Mathematical Physics – Differential Geometric Methods**_Enrico Pagani, Valter Moretti, Nicolò Drago**Scientific Machine Learning for Biomedical Applications**_Sahli Costabal, Pezzuto**Graphical Models and Network Science**_Veronica Vinciotti**Advanced Statistical methods**_Claudio Agostinelli

The schedule of PhD courses will be available in the download box.

Information for courses borrowed from the master's degree: Lessons timetable

For more information about the courses, see the Manifesto in the download box below.

#### Transdisciplinary programme in Quantum Science and Technologies

A transdisciplinary programme in Quantum Science and Technologies** **is a secondary programme that gives to the PhD candidate didactic and research traning on a complementary discipline.

The specific aims are:

- Promotion of transdisciplinary research in the Doctoral Course
- Training of PhD candidates with transdisciplinary competences
- Increase of the external collaborations

PhD students can apply for the program within 2 months of enrolling in the PhD program by sending an e-mail to phd.maths [at] unitn.it and attaching as required by the "TRANS-DISCIPLINARY PROGRAM IN SCIENCE AND QUANTUM TECHNOLOGY (TPQST)":

- A motivation letter (other than the one presented for applying to the Ph.D., if any), specifying the reasons why the candidate deems her / his research project of interest for the field of QST.
- A brief research proposal, formally approved by the student's tutor or advisor.