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Research fields

  • geometry, in particular algebraic, differential, and noncommutative geometry, also with applications to quantum field and string theory
  • mathematical analysis, in particular calculus of variations, control theory, partial and ordinary differential equations
  • mathematical modelling, in particular mechanics of solids and fluids, modelling of complex and biological systems, multiscale analysis
  • mathematical physics, in particular integrable systems and their applications, nonlinear partial differential equations, mathematical aspects of quantum physics
  • numerical analysis and scientific computing, applied to partial differential equations and to control problems

PhD and MSC courses:

Laboratories:

  • SISSA MathLab: a laboratory for mathematical modeling and scientific computing
  • SAMBA a laboratory in collaboration with the Cognitive Neuroscience Group

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Numerical Solution of Partial Differential Equations with deal.II

The course "Numerical Solution of PDEs with deal.II" offers a focused exploration of solving Partial Differential Equations (PDEs) using the Finite Element Method (FEM), employing the deal.II software library. Key components of the course include an introduction to PDEs, basics of numerical methods and FEM analysis, practical training using deal.II, and hands-on projects. The course will also cover High-Performance Computing (HPC) techniques for parallelizing, optimizing, and load balancing FEM simulations for real-world applications.

Advanced Topics in Scientific Computing

This course provides a high level introduction to the numerical analysis of PDES and related high-performance computing techniques, focusing on problems in mechanics such as fluid dynamics. Students will acquire advanced understanding on Computational modelling techniques, both theoretical and practical. The course will utilise a combination of frontal lectures and live programming demonstrations using the C++ deal.ii (dealii.org) Finite Element Library.

High Performance Computing for Data Science

The course will utilize a combination of frontal lectures and live programming demonstrations. The course will maintain a balance of approximately 50% frontal lectures and 50% hands-on sessions. The course is designed to be highly interactive, with ample opportunities for students to ask questions and engage in discussions during both the frontal lectures and hands-on sessions. Course materials and further details here.  

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