Mathematics

Purpose of the PhD Course

The aim of the PhD Course in Mathematical Analysis, Modelling, and Applications is to educate graduate students in the fields of mathematical analysis and mathematical modelling, and in the applications of mathematical and numerical analysis to science and technology. The goal is to enable PhDs to work as high level researchers in these fields in universities, research institutes, and private companies.

This PhD Course continues in a unified way the PhD Courses in Mathematical Analysis and in Applied Mathematics, active until the academic year 2012-2013.

Research Topics

The activity in mathematical analysis is mainly focused on Dynamical Systems and PDEs, on the Calculus of Variations, on Hyperbolic Conservation Laws and Transport Problems, on Geometric Analysis and on Geometry and Control theory. Connections of these topics with differential geometry and reduced order modelling are also developed.

The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, computational fluid and solid dynamics, numerical analysis and scientific computing, and problems related to control theory.

The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is developed in collaboration with MathLab  for the study of problems coming from the real world, industrial and medical applications, and complex systems.

Admission to PhD Program

• Number of PhD Positions available: 8.

The entrance examination procedure will be based on:

• Evaluation of academic and scientific qualifications
• Written exam: in presence*
• Oral exam: in presence*

Important Dates and Info: Entrance Sessions

• Deadline for application: 9 February 2025.
• Exams: 10-11 March 2025.

• Deadline for application: 30 August 2025.
• Exams: 10-11 September 2025.

Important Dates and Info: Progress Exams

• Date: 15 September 2025
• Exam commission: prof. N. Gigli (president), prof. A. Cangiani (secretary), prof. L. Rizzi, dr. B. Langella, dr. P.C. Africa, dr. N. Tonicello.

• Date: 9 September 2025
• Exam commission: prof. G. Rozza (president), prof. S. Bianchini, prof. G. Noselli (secretary), prof. A. Maspero, dr. R. Grande Izquierdo, dr. P.C. Africa.

• Date: 25 September 2025

Other PhD Positions

• Joint SISSA-TU/Eindhoven PhD position

Faculty

Former Faculty Members

Visiting Professors

External Collaborators

Temporary Scientific Staff

Support Staff

PhD Students

Fourth Year Students

Third Year Students

Second Year Students

First Year Students

Previous PhD Theses

Click here to see the previous PhD Theses.

Regulation

Click here to see the regulation of this PhD course (in Italian).

Research topics

• Nonlinear solid mechanics: finite elasticity and elasto-plasticity
• Soft matter elasticity: polymers, liquid crystals, granular materials
• Electro-magneto-mechanically coupled systems
• Variational methods fracture mechanics
• Dynamic fracture mechanics
• Scientific computing
• Cell motility and Mechano-biology
• Stokes Equations

Grants

• ERC Advanced Grant “MicroMotility” grant agreement no. 340685 MicroMotility, Principal Investigator: Antonio De Simone.

Research topics

• Homogenization of variational problems
• Gamma-Convergence and relaxation
• Variational methods in continuum mechanics
• Variational methods in rate independent evolution problems
• Variational methods in phase transitions
• Variational methods in micromagnetics
• Applications of geometric measure theory
• Existence problems in the calculus of variations
• Hamilton-Jacobi equations

Grants

• National Research Project (PRIN 2015) “Calculus of Variations”, funded by the Italian Ministry of Education, University, and Research, February 5, 2017 – February 5, 2020, National Coordinator: Luigi Ambrosio.

Research topics

• Stochastic Geometry
• Real algebraic Geometry
• Sub-Riemannian geometry
• Optimal Control and Optimal Synthesis
• Feedback Equivalence and Feedback Invariants
• Switching Systems
• Ensemble Control
• Control of Fluid Mechanics Systems
• Optimal Transportation
• Applications to Hamiltonian Dynamics

Useful links

• Blog of the Geometry and Control group
• https://webusers.imj-prg.fr/~davide.barilari/seminar.php
• Interesting events

Research topics

• Periodic solutions with oscillatory and superlinear nonlinearities
• Sturmian theory for multipoints and for matrix equations
• Functional boundary value problems a la Conti-Lasota
• A general spectral theory for nonsymmetric BVP

 Main External Collaborators

• G. Vidossich
• S. Ahmad
• G. A. Degla
• M. Gaudenzi
• F. Zanolin
• A. Fonda

Research topics

• Hyperbolic Systems of Conservation Laws in One Space Dimension
• Fundamental theory: existence, uniqueness and continuous dependence of weak entropy admissible solutions, characterization of semigroup trajectories
• Problems with large BV data, blow-up of BV norm, local existence and uniqueness
• Structure of solutions, local behavior, structural stability, generalized shift-differentiability w.r.t. parameters
• Initial-boundary problems, inhomogeneous balance laws, asymptotic blow-up patterns, global existence
• Convergence rates for approximation schemes: wave-front tracking, Glimm, finite element
• Vanishing viscosity approximations, a-priori estimates, convergence
• Flow of weakly differentiable vector fields
• Linear transport problems

Research topics

• KAM for PDEs
• Water waves, KdV, Schrödinger and Klein-Gordon equations
• Hamiltonian systems
• Birkhoff normal form for PDEs and long time existence
  • Long time existence results for quasi-linear Hamiltonian PDEs
  • Paradifferential normal forms
• Chaotic Dynamics and Arnold Diffusion
• Variational Methods
• Perturbative Methods in Critical Point Theory
• Benjamin-Feir and modulational instability

Research Group

Main External Collaborators

A research group in mathematical analysis has been active at SISSA since 1978, the year SISSA was founded. Starting from 2000, the activity of this group has been extended to mathematical modelling and applications. 

Research Topics

The activity in mathematical analysis is mainly focused on Dynamical Systems and PDEs, on the Calculus of Variations, on Hyperbolic Conservation Laws and Transport Problems, on Geometric Analysis and on Geometry and Control theory. Connections of these topics with differential geometry and reduced order modeling are also developed.

The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials,  cell motility and mechano-biology,  micromagnetics, modelling of biological systems, computational fluid and solid dynamics and problems related to control theory.

The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Faculty

Former Faculty Members

Visiting Professors

External Collaborators

Temporary Scientific Staff

Seminars

Click here to see the seminars of this research group.

Events and Workshops

Click here to see events and workshops  organized by this research group.

Publications

Click here to see the publications of this research group.