Mathematical Analysis, Modelling, and Applications | Mathematics Area - SISSA

Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry 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, 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.

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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:

Geometry and Mathematical Physics
Mathematical Analysis, Modelling, and Applications
MSc in Mathematics (Laurea Magistrale in Matematica) in collaboration with the University of Trieste
Master Degree in Data Science and Scientific Computing in collaboration with the Universities of Trieste and Udine, and with ICTP
Joint SISSA-ICTP professional Master in High Performance Computing (MHPC)

Laboratories:

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

Area Coordinator

Antonio Lerario

Faculty

Massimiliano Berti, Professor
Stefano Bianchini, Professor
Andrea Braides, Professor
Ugo Bruzzo, Professor
Ludwik Dabrowski, Professor
Gianni Dal Maso, Professor
Antonio De Simone, Professor
Gregorio Falqui, Professor
Barbara Fantechi, Professor
Nicola Gigli, Professor
Antonio Lerario, Professor
Marcello Porta, Professor
Gianluigi Rozza, Professor
Jacopo Stoppa, Professor
Alessandro Tanzini, Professor
Andrea Cangiani, Associate Professor
Tamara Grava, Associate Professor
Davide Guzzetti, Associate Professor
Igor Krasovsky, Associate Professor
Alberto Maspero, Associate Professor
Giovanni Noselli, Associate Professor
Andrea Ricolfi, Associate Professor
Luca Rizzi, Associate Professor
Nicolò Sibilla, Associate Professor
Rafael Torres, Associate Professor
Ricardo Grande Izquierdo, Assistant Professor
Pasquale Claudio Africa, Assistant Professor
Pavlo Gavrylenko, Assistant Professor
Michele Girfoglio, Assistant Professor
Beatrice Langella, Assistant Professor
Federico Pichi, Assistant Professor
Niccolò Tonicello, Assistant Professor

Former Faculty Members

Former Professors

Visiting Professors

Rodica Toader, Università di Udine
Andrea Mola, IMT Lucca
Gianfausto Dell'Antonio, Visiting Professor
Giovanni Stabile, Visiting Professor

Area Secretariat

Read more about Home

TBA

Read more about TBA

Relative heat content asymptotics for sub-Riemannian manifolds

Agrachev A, Rizzi L, Rossi T. Relative heat content asymptotics for sub-Riemannian manifolds. Analysis & PDE [Internet]. 2024 ;17:2997–3037. Available from: http://dx.doi.org/10.2140/apde.2024.17.2997

Comments on the regularity of harmonic maps between singular spaces

Gennaioli L, Gigli N, Zhang H-C, Zhu X-P. Comments on the regularity of harmonic maps between singular spaces.; 2024.

A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces

Gennaioli L, Gigli N. A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces. Canadian Mathematical Bulletin. 2024 ;67:49–59.

Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds

Caselli M, Gennaioli L. Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds.; 2023.

On the Hausdorff Measure of $\mathbbR^n$ with the Euclidean Topology

Bagnara M, Gennaioli L, Leccese GMaria, Luongo E. On the Hausdorff Measure of $\mathbbR^n$ with the Euclidean Topology. Real Analysis Exchange [Internet]. 2023 ;48. Available from: http://dx.doi.org/10.14321/realanalexch.48.1.1649735306

Fourier transform of BV functions, isoperimetry, and discrepancy theory

Beretti T, Gennaioli L. Fourier transform of BV functions, isoperimetry, and discrepancy theory.; 2024.

Existence and blow-up for non-autonomous scalar conservation laws with viscosity

Bianchini S, Leccese GMaria. Existence and blow-up for non-autonomous scalar conservation laws with viscosity. Journal of Mathematical Analysis and Applications [Internet]. 2025 ;542:128761. Available from: https://www.sciencedirect.com/science/article/pii/S0022247X24006838

Dissipative solutions to Hamiltonian systems

Bianchini S, Leccese GMaria. Dissipative solutions to Hamiltonian systems. Kinetic and Related Models. 2024 ;17.

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