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.

The relaxed area of $S^1$-valued singular maps in the strict $BV$-convergence

Bellettini G, Carano S, Scala R. The relaxed area of $S^1$-valued singular maps in the strict $BV$-convergence. ESAIM: Control, Optimization and Calculus of Variations [Internet]. 2022 ;28:38. Available from: http://cvgmt.sns.it/paper/5440/

Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature

Manini D. Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature.; 2022.

Rigidities of Isoperimetric inequality under nonnegative Ricci curvature

Cavalletti F, Manini D. Rigidities of Isoperimetric inequality under nonnegative Ricci curvature.; 2022.

Isoperimetric inequality in noncompact MCP spaces

Cavalletti F, Manini D. Isoperimetric inequality in noncompact MCP spaces. Proc. Am. Math. Soc. 2022 ;150:3537-3548.

An example of a weakly mixing BV vector field which is not strongly mixing

Zizza M. An example of a weakly mixing BV vector field which is not strongly mixing.; 2022.

Properties of Mixing BV Vector Fields

Bianchini S, Zizza M. Properties of Mixing BV Vector Fields. Communications in Mathematical Physics [Internet]. 2023 ;402:1953–2009. Available from: https://doi.org/10.1007%2Fs00220-023-04780-z

From symplectic capacities to periodic Hamiltonian flows

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Morse theory in infinite dimension old and new

Read more about Morse theory in infinite dimension old and new

Minimal surfaces and the Bernstein problem

We will start from some classical results on minimal surfaces, including the theory of Douglas Rado with the final goal to discuss the recent results on the Bernstein problem for stable minimal surfaces.

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A Class of non-Gaussian Measures and Related Analysis

Read more about A Class of non-Gaussian Measures and Related Analysis

Mathematics