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.

Independence of synthetic curvature dimension conditions on transport distance exponent

Akdemir A, Colinet A, McCann R, Cavalletti F, Santarcangelo F. Independence of synthetic curvature dimension conditions on transport distance exponent. Trans. Amer. Math. Soc. [Internet]. 2021 ;374:5877–5923. Available from: https://doi.org/10.1090/tran/8413

Isoperimetric inequality under Measure-Contraction property

Cavalletti F, Santarcangelo F. Isoperimetric inequality under Measure-Contraction property. [Internet]. 2019 ;277(9):2893 - 2917. Available from: https://www.sciencedirect.com/science/article/pii/S0022123619302289

Introduction to Convex Integration

Convex integration is a technique for the construction of “strange" solutions to certain nonlinear systems of partial differential equations. The technique originates in the work of John Nash (1954) on C1 isometric embeddings and has been developed into a powerful general method for certain problems in differential geometry and in the calculus of variations.

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A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems

Nonino M, Ballarin F, Rozza G. A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems. Fluids [Internet]. 2021 ;6:229. Available from: https://www.mdpi.com/2311-5521/6/6/229

A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems

Karatzas EN, Nonino M, Ballarin F, Rozza G. A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems. Computer & Mathematics With Applications [Internet]. 2021 . Available from: https://www.sciencedirect.com/science/article/pii/S0898122121002790

A local approach to parameter space reduction for regression and classification tasks

Romor F, Tezzele M, Rozza G. A local approach to parameter space reduction for regression and classification tasks. arXiv preprint arXiv:2107.10867. 2021 .

Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces

Romor F, Tezzele M, Rozza G. Multi-fidelity data fusion for the approximation of scalar functions with low intrinsic dimensionality through active subspaces. In: Proceedings in Applied Mathematics & Mechanics. Vol. 20. Proceedings in Applied Mathematics & Mechanics. Wiley Online Library; 2021.

ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis

Romor F, Tezzele M, Rozza G. ATHENA: Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis. Software Impacts. 2021 ;10:100133.

A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers

Gidoni P, Riva F. A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers. [Internet]. 2021 ;60(5):191. Available from: https://doi.org/10.1007/s00526-021-02067-6

On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity

Riva F. On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity. [Internet]. 2020 ;30(3):903 - 951. Available from: https://doi.org/10.1007/s00332-019-09595-8

Mathematics