Vincenzo Recupero

Associate Professor (L. 240)
Department of Mathematical Sciences (DISMA)

Profile

Research interests

Discontinuous ordinary differential equations
Functional analysis
Hypercomplex and quaternionic analysis
Mathematical analysis of hysteresis models
Nonlinear analysis
Partial differential equations

Scientific branch

MATH-03/A - Mathematical Analysis
(Area 0001 - Mathematical and computer sciences)

Research topics

  • Partial differential equations for models of phase transitions. We analyze partial differential equations of quasi-parabolic and hyperbolic type, arising in model of phase transition. In particular we study the Penrose-Fife and Stefan models, also coupled with laws of phase relaxation and with the Cattaneo heat flux law.
  • Quaternionic functional Analysis and Hypercomplex Analysis. We study the development of functional analysis in a quaternionic (or more generally noncommutative) framework, originally motivated by the remark of G. Birkhoff and J. von Neumann that quantum mechanics may be formulated not only on complex Hilbert spaces, but also on Hilbert spaces having the quaternions as the set of scalars.We study the theory of functions of one or several variables and its applications to noncommutative functional analysis, in particular to quaternionic spectral analysis and quaternionic operators semigroups.
  • Rate independent and Moreau’s processes. We address the analysis of rate independent operators which arise as solution operators of rate independent evolutionary variational inequalities originally motivated by models of elastoplasticity and hysteresis: e.g. the “play operator” of elastoplasticity (the solution operator of a variational inequality characterized by a closed convex set of constraints), and the Moreau's “sweeping processes”, a more general class of variational inequalities which has also found applications in economic theory, crowd motion modelling, and electric circuits. In particular we study the continuity of such solution operators with respect to different topologies, which ensures robustness of the model on the one hand, and applicability of a variety of mathematical tools for its analysis and treatment, on the other hand.

Skills

ERC sectors

PE1_8 - Analysis
PE1_21 - Application of mathematics in sciences
PE1_12 - Mathematical physics
PE1_10 - ODE and dynamical systems
PE1_9 - Operator algebras and functional analysis

SDG

Goal 4: Quality education
Goal 10: Reduced inequalities

Conferences

  • Two-day Workshop on Nonlinear Analysis, Program committee
  • Summer School on Multi- Rate Processes, Slow-Fast Systems and Hysteresis 2019, Chairman of the organizing committee
  • Control of of State Constrained Dynamical Systems 2017, Program committee
  • Summer School on Multi-Rate Processes, Slow-Fast Systems and Hysteresis 2017, Chairman of the organizing committee

Other research or teaching roles outside Politecnico

  • Ricercatore, presso Tongji University (16/9/2013-8/11/2013)

Teaching

Collegi of the degree programmes

Teachings

PhD

Bachelor of Science

MostraNascondi A.A. passati

Research

Research fields

Research groups

Publications

PoliTO co-authors

Selected publications View all publications in Porto@Iris

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