Research areas
The research topics of each student are agreed upon by the student, the supervisor and the Doctoral Board. Topics may be of an institutional or a specific nature. Institutional topics can be inferred from the activity of the members of the Doctoral Board, from the research areas present at the DMA and from the list of DMA faculty members.
Techniques for Communicating and Popularising Mathematics
The course, taught by university lecturers, CNR researchers and science journalists, consists of 8 meetings, each devoted to a different topic: from stop motion to podcasts, from comics to radio and interviews, newsletters, exhibitions and mathematical artefacts, and the writing of scientific articles. To book your place, send an e-mail to cmusella@unina.it with the subject “prenotazione Corso di Comunicazione”, stating your first name, surname, student ID number and year of study.
Training activities
The training programme includes courses designed specifically for the PhD:
| Course title | Hours | Period | Notes |
|---|---|---|---|
| An Introduction to Computational Algebra and Computational Algebraic Geometry | 20 | Wednesday 7 January (10:00-12:00 and 14:00-16:00), room E - Friday 9 January (10:00-12:00), room F - Monday 12 January (10:00-12:00), room C - Tuesday 13 January (10:00-12:00 and 14:00-16:00), room C - Wednesday 14 January (10:00-12:00 and 14:00-16:00), room C - Thursday 15 January (10:00-12:00 and 14:00-16:00), room F | Taught by Prof. Francesca Cioffi |
| Symmetrization methods for local and nonlocal operators | 20 | 26/1, 2/2, 4/2, 25/2, 2/3, 4/3, 9/3, 11/3, 18/3, 25/3: room E (3rd level) Time: 15:00 - 17:00 | Taught by Prof. Vincenzo Ferone |
| An introduction to the fractional p-Laplacian | 6 | Tuesday, 20 January 2026⋅ 15:00 -17:00 Sala Professori, 2nd level Wednesday, 21 January 2026⋅ 15:00 -17:00 Sala Professori, 2nd level Thursday, 22 January 2026⋅ 15:00 -17:00 Sala Professori, 2nd level | Taught by Prof. Antonio Iannizzotto (Cagliari) |
| Algebra and Geometry of Rank-Metric Codes | 20 | - Monday 19 January, 10:00-13:00 (room D); - Wednesday 21 January, 10:00-12:00 (room D) and 14:00-16:00 (room D); - Friday 23 January, 10:00-13:00 (room D); - Monday 26 January, 10:00-13:00 (room E); - Tuesday 27 January, 10:00-13:00 (room E); - Thursday 29 January, 10:00-12:00 (room E) and 14:00- 16:00 (room E). | Taught by Prof. Gianira N. Alfarano (University of Rennes) and Alessandro Neri |
| Noncommutative Geometry | 20 | every Thursday, 16:00-18:00, room G, starting 15 January | Taught by Prof. Francesco D'Andrea |
| Differential Geometry | 24 | November–December 2025 – COMPLETED | Taught by Prof. Alessandro Zampini |
| Shape Optimization | 20 | September – December 2026 | Taught by Prof. Cristina Trombetti |
| Lefschetz properties | 20 | 8 January 20 January 22 January 27 January 3 February 5 February 10 February 12 February 17 February 24 February, always 14:00-16:00. | Taught by Prof. Giovanna Ilardi |
| Numerical treatment of Partial Differential Equations | 24 | February 2026 – COMPLETED | Taught by Prof. Calabrò |
| AI Paradigms for Scientific Machine Learning | 24 | September – December 2026 | Taught by Prof. Francesco Piccialli, Prof. Salvatore Cuomo and Prof. Fabio Giampaolo |
| From Individual-Based Models to Continuum Mechanics through Kinetic Theory in Mathematical Biology | 20 | Friday 15 May 2026 15:00-18:00; Monday 18 May 2026 10:00-13:00; Tuesday 19 May 2026 11:00-13:00 15:00-17:00; Wednesday 20 May 2026 11:00-13:00 15:00-17:00; Thursday 21 May 2026 11:00-13:00 15:00-17:00; Friday 22 May 2026 11:00-13:00 in Sala Rionero | Taught by Prof. Preziosi and Prof. Nadia Loy |
| Basic Quantum Mechanics | 20 | September – December 2026 | Taught by Prof. Raffaele Carlone |
| Representations of Groups | 20 | September – December 2026 | Taught by Prof. Marco Trombetti |
| Differential Fields in Model Theory | 20 | May – July 2026 | Taught by Prof. Giuseppina Terzo |
| An Introduction To Directional Maximal And Singular Averages | 16 | 1–31 March 2026 – COMPLETED | Taught by Prof. Ioannis Parissis |
| Introduction to the Ricci flow | 20 | November–December 2025 – COMPLETED | Taught by Prof. Carlo Mantegazza |
| Partial differential equations | 24 | February 2026 – COMPLETED | Taught by Prof. Giacomo Ascione |
| Topics in Group Theory | 20 | March – May 2026 | Taught by Prof. Maria De Falco and Prof. Carmen Musella |
| THE ALEXANDROV-BAKELMAN-PUCCI METHOD AND ITS APPLICATION | 20 | October–December 2026 | Taught by Prof. Daniele Castorina |
| Convection-diffusion equations: from hydrodynamics limits to W^(1,2)-solutions | 20 | October–November 2026 | Taught by Prof. Stefano Buccheri |
| Kinetic Equations for Complex Systems | 20 | October–November 2026 | Taught by Dr Marco Menale |
| Rank-Metric Codes: Algebraic and Combinatorial Interlacings | 20 | July 2026 | Taught by Dr Paolo Santonastaso and Dr Giovanni Longobardi |
| Combinatorial pregeometries | 20 | January–February 2027 | Taught by Dr Flavio Salizzoni |
| Advanced Topics in Algebraic Geometry | 20 | May–June 2027 | Taught by Prof. Francesco Polizzi |
| The Alexandrov-Bakelman-Pucci method and its applications | 20 | September–December 2026 | Taught by Prof. Daniele Castorina |
Further courses will be borrowed from the Master's degree programmes. PhD students attend seminar series held at the DMA. A research stay abroad is an essential part of the training programme.
Courses marked "to be activated" are courses for which lecturers have declared their availability; they will be activated upon request by interested students.
Every year, summer courses organised by the Scuola Matematica Interuniversitaria (SMI) take place in Perugia. Since the University is a member of the CIAFM consortium, courses offered by the SMI are automatically recognised by the Doctoral Board of the PhD Programme in Mathematics and may be included in the PhD students' study plans: https://www.smi-math.unipr.it/.
A variational theory of non-local problems, Prof. Andrea Braides
Monday 23 March: 10:30-12:30 and 14:30-16:30; Tuesday 24 March: 8:30-10:30.
This school is intended for early-career researchers and PhD students interested in an environment that, along with
the necessary technical tools, allows them to address both static and dynamic problems related to multi-scales variational models, particularly those involving non-local interactions at small scales.
PROGRAM OF THE SCHOOL
24 h course :
• Andrea Braides (Università di Roma Tor Vergata)
“Analysis of non-local variational problems”
4 talks held by :
• Roberto Alicandro (Università degli studi di Napoli
Federico II)
• Stefano Almi (Università degli studi di
Napoli Federico II)
• Giuliana Fusco (Scuola Superiore
Meridionale)
• Giovanni Scilla (Università degli studi
di Napoli Federico II)