Mathematics

UniFE

• Alessia Ascanelli
• Cinzia Bisi
• Chiara Boiti
• Walter Boscheri
• Lorenzo Brasco
• Andrea Corli
• Vincenzo Coscia
• Giacomo Dimarco
• Federica Ferretti
• Carlo Giannelli
• Maria Giulia Lugaresi
• Marco Marozzi
• Alex Massarenti
• Massimiliano Mella
• Claudia Menini
• Michele Miranda
• Lorenzo Pareschi
• Maria Cristina Patria
• Guido Sciavicco
• Giulio Tralli

UNIMORE

Cristina Acciarri

Silvia Bonettini

Simona Bonvicini

Gioia Carinci

Maria Rita Casali

Paola Cristofori

Michela Eleuteri

Rouven Frassek

Stefania Gatti

Cristian Giardina'

Claudio Giberti

Serena Guarino Lo Bianco

Claudia Landi

Luisa Malaguti

Giuseppe Mazzuoccolo

Carlo Mercuri

Sergio Polidoro

Federica Porta

Marco Prato

Simone Rebegoldi

Gloria Rinaldi

Elena Rossi

Federica Sani

Elisa Sovrano

Valentina Taddei

Cecilia Vernia

Luca Zanni

Giovanni Zini

UniPR

Alessandra Aimi

Andrea Appel

Paolo Baroni

Anna Benini

Federico Bergenti

Leonardo Biliotti

Marzia Bisi

Filippo Cagnetti

Andrea Cattaneo

Cristiana De Filippis

Maria Groppi

Chiara Guardasoni

Luca Francesco Giuseppe Lorenzi

Costantino Medori

Francesco Morandin

Massimiliano Morini

Lorenzo Nicolodi

Giampiero Palatucci

Alberto Saracco

Adriano Tomassini

Alessandro Zaccagnini

Michela Zedda  

Other University

Andrea Bandini

Rita Fioresi

Anita Pasotti

Massimiliano Rosini

The PhD program in Mathematics is based on close collaboration among the three universities of Ferrara, Modena-Reggio Emilia, and Parma. This synergistic action has been a well-established reality at both regional and national levels since 2013, providing the opportunity for PhD students to benefit from the scientific resources and educational offerings of the three institutions across various fields of Mathematics. Students also benefit from the broad spectrum of expertise available within the Academic Board. The joint PhD program provides graduates with greater visibility and significantly more prestige compared to a PhD program offered by a single institution.

The PhD program represents a highly advanced educational path aimed at training highly qualified professionals in Mathematics and the mathematical foundations of Computer Science. Graduates acquire advanced skills in theoretical tools, models, and mathematical methods, which are also applicable in interdisciplinary contexts.

For example, but not limited to, these include fields such as artificial intelligence, renewable energy, infectious diseases, and environmental risks associated with climate change. These aspects naturally connect to scientific computing, data science, differential modeling, and biomathematics—critical areas that play a central role both in the faculty composition and in the educational offerings provided to doctoral students. The program also trains highly professional figures in the fields of History and Didactics of Mathematics, which are particularly relevant in a region committed to teacher education.

The declared objectives are achieved through a range of activities, from theoretical training to participation in national and international schools, workshops, and research periods in third-party institutions. These allow doctoral students to establish collaborative and professional contacts and to deepen their understanding of academic and non-academic contexts. The potential for growth in the educational and research project of the PhD program aligns with the strategic goals of the three participating universities, and in particular, with the three departments dedicated to Mathematics.

The foundation for strengthening the educational offering is the consultation with stakeholders:

• Internally, the presidents of the Master’s Degree courses in Mathematics from the three universities (Ferrara, Modena-Reggio Emilia, and Parma) provided suggestions to consolidate the PhD educational offering based on the Master’s curricula. They also suggested the organization of research orientation activities conducted by the Doctoral Board to benefit final-year students, aiming to encourage participation in PhD entrance exams and help potential candidates determine their aptitude for research. To this end, starting from the 2024/2025 academic year, an orientation day called “Ph.D. Open Day” has been introduced to increase awareness among prospective students about the opportunities offered by the PhD program.
• External stakeholders, representing industries and professions in the field, emphasized the need for the Mathematics PhD program to differentiate itself from other STEM PhDs by its ability to provide solid mathematical training. While current industry roles often require operational skills, there is a strong demand for professionals with a solid theoretical foundation in Mathematics and Statistics. Moreover, the specialization of skills must be accompanied by an ability to interpret the world and address the new challenges arising from its evolution.

Special attention is given to the candidate selection process, with targeted announcements on dedicated web pages both nationally (e.g., the PhD program website and mailing lists of the Italian Society for Applied Mathematics, the Italian Mathematical Union, and the National Institute for Advanced Mathematics) and internationally (e.g., MathJobs.uk and personal contacts between faculty members and foreign institutions).

The PhD in Mathematics opens numerous career paths, thanks to the high-level qualification in mathematical research and its applications. Career and professional opportunities include research roles in academia, public and private institutions, and industry; positions as training managers in scientific disciplines within schools and private institutions; and roles in technologically advanced sectors of services and production. Common career paths include:

• Academic Researcher:The PhD in Mathematics is the most common path to becoming a university professor or academic researcher in various fields of mathematics and its applications both in Italy and abroad.
• Industrial Researcher:Mathematical skills are highly sought after in many companies, especially in technology, finance, and data management sectors.
• Data Analyst:Data analysis has become a highly demanded field in recent years, particularly in artificial intelligence. A PhD in Mathematics provides the necessary skills to work as a data analyst.
• Financial Analyst:Banks and financial institutions often hire experts in financial mathematics to analyze financial risks and develop investment strategies.
• Programming Manager:Programming requires a good understanding of mathematics and computational logic. A PhD in Mathematics can prepare students for leadership roles in software development for complex projects.
• Teachers or School Administrators:Qualified positions in secondary schools and private institutions, leveraging advanced expertise in mathematical and scientific disciplines.
• Experts in EU Research Programs:Professionals capable of conceiving and executing applied research and innovation projects for public and private research centers.

Advanced skills in theoretical tools, models, and mathematical methods are also in high demand in other fields, such as insurance companies, biomedical and pharmacological centers, management in public and private institutions, public administration, and consultancy services. In these fields, Mathematics graduates can engage in high-level analysis, develop new models and mathematical methods, and contribute to solving complex problems. As highlighted in meetings with representatives from organizations in production and professional sectors, mathematical education offers an added value compared to other STEM disciplines. Professionals capable of "understanding" modern scientific literature and translating it into simple, comprehensible terms for their team members are increasingly necessary and critical in companies focused on technological development. These profiles represent a long-term investment for companies and are part of the top tier of employees, ensuring growth and innovation.

To encourage this vital aspect, the PhD program will organize consultation sessions with stakeholders concerning the desired professional profiles, through public events such as meetings and workshops involving all PhD students. Our goal is to develop doctoral candidates' teamwork capabilities, ensuring that educational activities are aligned with fostering an understanding of how production systems are evolving today. The growing demand for mathematical stylizations makes mathematics a crucial contributor in this field.

PhD students have access to an adeguate number of courses, seminars, and scientific events of high quality and quantity. These initiatives involve high-profile Italian and international scholars and experts from academia, research institutions, and companies. The educational program incorporates elements of interdisciplinarity, multidisciplinarity, and transdisciplinarity, while always respecting the specific nature of the PhD program.

PhD students in Mathematics can design a personalized program within the general framework of the training pathway, tailored to their inclinations and interests. The PhD program is structured to provide students with a strong theoretical foundation through a series of lectures and seminars organized by the three universities involved in the project. These lectures cover all areas of research in Mathematics, from theoretical aspects in Analysis, Probability, Geometry, Algebra, Didactics, and History of Mathematics, to more applied topics such as Mathematical Physics, Numerical Analysis, and Computer Science. The curriculum includes elements of interdisciplinarity, multidisciplinarity, and transdisciplinarity.

Interdisciplinarity allows doctoral students to collaborate across various disciplines, fostering the development of shared competencies and cognitive goals. Transdisciplinary training helps students develop teamwork skills by creating collaborations that lead to conceptual exchanges and integration, aimed at understanding complex problems. According to UNESCO, transdisciplinarity is the intellectual space where connections between isolated topics can be explored and revealed.

Many language and IT courses, as well as activities in scientific communication, research management, and understanding of European and international research systems, are guaranteed through the IUSS of the University of Ferrara and similar initiatives at the other institutions.

Educational activities address topics related to the doctoral student's training project as well as subjects relevant to societal debates on science and its impact. These include areas such as artificial intelligence, renewable energy, infectious diseases, and environmental risks associated with climate change. These topics are naturally connected to scientific computing, data science, differential modeling, and biomathematics—critical elements that play a central role in both the composition of the teaching staff and the training provided to doctoral students. Furthermore, the extensive network of national and international contacts allows students access to a wide range of experiences and knowledge, enabling them to develop their research in innovative and creative ways. This also translates into the possibility of obtaining double, multiple, or joint degrees in collaboration with other universities.

The PhD in Mathematics aims to train highly qualified professionals capable of conducting independent research and producing original and significant results. This goal is achieved through a highly specialized training program, structured over three years, focused on developing research capabilities in Mathematics and its possible applications. Specifically, the program seeks to train mathematicians who can fully exploit the potential of theoretical tools, models, and mathematical and statistical methods to address the inherent complexity of problems in applied sciences and industry.

Mathematics today plays a fundamental role in developing models and methods for machine learning and data analysis, which are the foundation of intelligent systems. Machine learning, in particular, uses techniques from linear algebra, optimization, functional analysis, and probability theory to develop models and methods capable of learning from data and making autonomous decisions. Graph theory and computational geometry are crucial for artificial intelligence in representing and visualizing data, as well as for developing optimization and search algorithms.

The program also aims to improve Mathematics education and, more generally, scientific disciplines in secondary schools, universities, and private accredited institutions. It promotes the dissemination of mathematical culture and the training of highly qualified teachers.

The first-year program includes a series of advanced theoretical lectures given by members of the Academic Board and visiting professors, along with participation in national and international schools and workshops led by international scholars. The disciplinary courses, monitored and updated annually to reflect the cultural and scientific evolution of the field, offer students the opportunity to acquire advanced skills in various areas of Mathematics and establish direct connections with the international scientific community. Additionally, students follow personalized paths under the guidance of a tutor to introduce them to the specific themes of their research. This training lays the foundation for the doctoral student's autonomy in conceiving, designing, implementing, and disseminating research and innovation projects, with appropriate guidance and support from tutors, co-tutors, and possibly external supervisors of international stature.

From the second year onward, the training program is structured to allow students to focus primarily on their chosen research project after completing mandatory courses and exams. In this way, students can deepen their knowledge and acquire advanced skills in their area of interest, conducting high-quality research that can lead to original and significant results. To this end, doctoral students are provided with adequate financial and structural resources to carry out their research activities, supported by university funds specifically allocated to the PhD program. Additionally, the PhD program encourages and facilitates doctoral students’ participation in teaching and tutoring activities, ensuring these are consistent with and complementary to their research activities.

The growth of doctoral students as members of the scientific community is also supported through internal interactions among students, presentations of research findings in seminars organized by the three universities, and participation as speakers in national and international conferences, workshops, and training schools. Attendance at summer courses organized by the Interuniversity Mathematics School (https://www.smi-math.unipr.it/) in Perugia, as well as other national schools specifically designed for mathematical research training, is strongly encouraged.

Great attention is given to the preparation of the doctoral thesis, including annual evaluations of students’ research progress. The thesis preparation represents the culmination of the training process, demonstrating students' ability to conduct independent research and produce original and significant results.

The PhD program also pursues internationalization objectives, including awarding double, multiple, or joint degrees in collaboration with other universities. Mobility, both incoming and outgoing, is actively encouraged towards universities, research institutions, companies, and cultural or social institutions, with particular attention to international experiences.

Each participating institution typically supervises three doctoral students per doctoral cycle. At the beginning of the program, each student is assigned a faculty supervisor and one or more co-supervisors (at least one of whom must be a member of the Academic Board). These supervisors guide the student’s training, assist in integrating them into the research environment in Mathematics, and support the proposal and planning of their individual study plan, considering possible research topics of interest. The supervisor and co-supervisors take on the scientific responsibility for guiding and supporting the student through their training and research journey until the thesis is completed.

See the activities

The PhD program pursues mobility and internationalization objectives, including the awarding of double, multiple, or joint degrees in collaboration with other universities. Mobility is encouraged both inbound and outbound, toward universities, research institutions, companies, and cultural or social organizations, with particular attention to international experiences. Numerous co-supervision agreements for theses, either as the primary institution or as the host, have been established, resulting in the awarding of double, multiple, or joint degrees, or are currently in progress.

Additionally, starting with the 39th cycle, the European project DATAHYKING (HORIZON-MSCA-European Joint Doctorates-2021-DN-01-01) has been implemented. This project involves the training of four doctoral students in co-supervision with RWTH Aachen University, Katholieke Universiteit Leuven, Université de Lille, and Technical University of Munich.

Regarding faculty exchange, in recent years, various funding opportunities have been secured from INdAM (National Institute of Higher Mathematics) for visiting professors. The consistent goal of the PhD program is to consolidate and, if possible, increase the number of co-supervision agreements for doctoral students under the guidance of external faculty members. This strengthens national and international scientific relationships, ensuring doctoral students experience mobility periods aligned with their research project, ideally lasting at least six months, at reputable academic and/or industrial institutions or public or private research entities, whether in Italy or abroad. A well-established practice is the request for the Doctor Europaeus title, which can be obtained after spending at least three months at a European research institution. Beyond promoting the mobility of doctoral students within European universities or research institutions, mobility periods toward qualified extra-European research institutions are also being encouraged and implemented.

Equipment and/or Laboratories

In all three departments (UNIMORE, UNIFE, UNIPR), the following are available:

• Laboratories for Scientific Computing,
• Classrooms equipped with videoconferencing capabilities,
• Computer workstations, network connections, and Wi-Fi,
• Offices dedicated to doctoral students.

Library Resources

The three libraries collectively house over 50,000 volumes covering all course topics. The Ferrara site alone has more than 20,000 volumes related to course subjects, complemented by collections at the other consortium sites. Among them, several hundred volumes form the Mathematics Library Collection, part of the Historical Collections of the University of Ferrara.

The three libraries have maintained subscriptions for over 20 years, fully covering course topics. The Mathematics and Computer Science Library in Ferrara is a branch of the Scientific-Technical Library. It subscribes to 289 current journals covering all course topics, supplemented by those of the other consortium sites. The library also manages the publication of the Annals of the University of Ferrara, Mathematics Section, published by Springer.

E-resources

More than 1,600 electronic journals in mathematics, over 1,200 in computer science, and more than 1,840 multidisciplinary e-books are accessible online. The Document Delivery and interlibrary loan service allows access to resources not available at the three universities.

Software tools include MATLAB, MAPLE, numerical solvers, CoCoa, Singular, and programming languages such as Fortran, C/C++, Python, and Julia. Dedicated offices and personal computers are available. The three sites also have several computing clusters accessible to students. Additionally, within specific research projects (ISCRA grants), students can access HPC resources provided by CINECA.

Additional Resources

The departments are affiliated with INdAM and serve as its research units; doctoral students can join the National Groups and, in this case, can benefit from INdAM Schools and participate in the funding calls for these Groups.

The Departments have an agreement with INdAM and are research units of the same; doctoral students can join the National Groups and, in this case, can benefit from INdAM Schools and participate in the funding calls for these Groups.