PhD in Mathematics

• Commutative algebra and classical algebraic geometry
• Algebra and combinatorics - Complex analysis
• Geometric and harmonic analysis for data analysis and machine learning
• Phase space geometric analysis of pdes
• Geometric analysis on Carnot groups
• Stochastic analysis and applications
• Applications of microlocal analysis to mathematical physics
• Stochastic optimal control
• Data science and artificial intelligence
• Didactics of mathematics
• Nonlocal equations and fractional minimal surfaces
• Quantitative finance
• Geometry of varieties
• Continuum mechanics
• Statistical mechanics and applications
• Functional analysis methods for pdes
• Optimization methods for ill-posed inverse problems in imaging
• Numerical optimization methods without derivatives
• Numerical linear algebra and applications
• Numerical methods for the treatment of differential problems and in data science
• Geometric modeling and processing
• Mathematical models in medicine and physiology
• Non-linear wave propagation and non-equilibrium thermodynamics
• Properties of linear and non-linear elliptic operators
• Properties of subelliptic operators
• Random fields and percolation
• Dynamical systems and applications
• Quantum information theory
• Perturbation theory and spectral analysis in quantum mechanics
• Geometric measure theory
• Spectral theory
• Geometric and computational topology

Appointed by RD n. 709/2023 Prot n. 149534 on Jun 02, 2023

PhD researchers will have a qualified and specific training in all the research fields of mathematics, and willl be able to perform an autonomous research activity in pure or applied math. Indeed they will receive a deep training in a large spectrum of emergent scientific problems, and a personalized training in a specific mathematical field. Hence, they will be able to develop mathematical theories in new directions or to develop models which require a deep mathematical knowledge. The PhD will be able to study and solve new problems posed by different fields with a rigorous mathematical approach. For this reason they will have carrier opportunities either in academic endehavior where pure research can be developed, or of industrial, financial or biomedical context where applied math is developed, or they could cover responsibility positions in private or public research centers. Finally they will be able to work in any context where projectual and management skillls are required.

The fellows:

• in the first and second years will take courses to strengthen their math background and in their research field,
• from the first year they will focus on training through research,
• will participate in seminars and in specialized conferences,
• will perform activity of scientific computing,
• will take courses to acquire specific skills, as for example ability of communication skills, grant writing skills.

Activities to facilitate entering academic institutions:

• thematic seminars on the topics of pure and applied mathematics
• participation to national and international conferences and workshop, giving short contributions/communications.

Activities for carrier development in private sector, industrial or financial:

• secondments in industrial or financial research centres,
• participation to talks delivered by industrial managers.

The PhD course is characterized by the following elements The course includes fellowships within the ERC project of Prof Lupini HEU_2021_DAT_LUPINI_M_01, and it is partner in the projects:

• MSCA Staff Exchanges 2021 (HORIZON-MSCA-2021-SE-01), Project ID: 101086123, project acronym CALIGOLA
• COST: CA21109, project acronym CaLISTA

Both projects encourage mobility of PhD students among the partner institutions, and lecturers giving seminars and courses.

The PhD course is also involved in the project lead by Prof. Mongardi within the so called "bando strutture of Unibo" which will fund summer schools and will allow phd students to visit some of the most prestigious departments of mathematics worldwide.
Our PhD course signs several co-tutorship agreements (for both incoming and outgoing students) with renowned foreign universities.
Admission colloquium can be attended in English.
PhD classes can be held in English, in presence of foreign professors or students.

The main expected results are original mathematical scientific results to be included in the final phd theses, and possibly in manuscripts to be submitted to scientific journals with anonymous peer review. Moreover, phd students may produce software packages and submit talks and posters to national and international conferences or other scientific events.