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, 2026. 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, 2026.

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 2026..

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  “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 2025/2026

• Advances in algebra 1:  Categorical and geometric methods in representation theory _ Georgios Dalezios 
• Advances in algebra 2: An introduction to rank functions _ Lidia Angeleri 
• Graphs, algebras and representations _ Daniel Labardini Fragoso, Jorge Vitória 
• Advances in Algebra: Generalised Buchberger and Schreyer Algorithms for Coherent Rings _ Ihsen Yengui 
• Advances in Algebra, Geometry and Mathematical Physics: Tensors and their applications _ Jeroen Zuiddam 
• Advances in Numerical Analysis and Mathematical Modelling: exponential integrators for evolutionary equations _ Marco Caliari, Fabio Cassini
• Advances in Numerical Analysis and Mathematical Modelling: Multi-agent interaction models, from control to learning across scales _ G. Albi, Dr. M. Bonafini
• Advances in Numerical Analysis and Mathematical Modelling: Short Course on Advances Numerical Methods for Hyperbolic Equations 2026 _ Michael Dumbser, Olindo Zanotti
• Advances in Geometry: Abelian Coverings of Algebraic Varieties _ Federico Fallucca 
• Advances in cryptography and codes: fully homomorphic encryption _ Dott. Chiara Marcolla
• Advances in Mathematical Analysis: an introduction to scalar conservation laws _ Paolo Bonicatto, Elio Marconi 
• Advances in Mathematical Analysis: selected topics in Geometric Measure Theory _ Andrea Marchese 

Additional courses borrowed from the Master Degree in Mathematics

• Mathematical Physics - Quantum Relativistic Theories _ Valter Moretti
• Spatial Models in Biology and Epidemiology _ Cinzia Soresina 
• Graphical Models and Network Science _ Veronica Vinciotti
• Advanced Statistical Methods _ Claudio Agostinelli
• Bayesian Statistics _ Pier Luigi Novi Inverardi, Claudio Agostinelli
• Interactive Theorem Proving _ Roberto Zunino 
• Tensor Decomposition for big data analysis _ Alessandra Bernardi, Stefano Canino 
• Geometric Measure Theory _ Paolo Bonicatto, Andrea Marchese
• Optimal Transport _ Paolo Bonicatto, Andrea Marchese
• Optimization _ Mauro Bonafini 
• Geometric analysis _ Lorenzo Mazzieri

 

• 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:

1.  Promotion of transdisciplinary research in the Doctoral Course
2.  Training of PhD candidates with transdisciplinary competences
3.  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@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.