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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 analysismechanics of materialsmicromagneticsmodelling 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.

mathLab seminars

Recurrent Zoom link of the seminars: https://sissa-it.zoom.us/j/7306190508

Date Speaker Room Seminar
November 9, 2022, time 15.00 Stefano Zampini (KAUST) A-133 Device Accelerated Solvers with PETSc. Current Status, Future Perspectives and Applications
November 16, 2022, time 15.00 Robert Nurnberg (Università di Trento) A-131 A generalized DeTurck trick for anisotropic curve shortening flow
November 23, 2022, time 14.00 Lorenzo Mascotto (Università di Milano Bicocca) A-139 Enriching Galerkin methods
December 7, 2022, time 14.00 Andreas Dedner (University of Warwick) A-137 A General Approach for Implementing Virtual Element Schemes
January 24, 2023, time 14.00 Zhaonan Dong (INRIA) A-133 and online A posteriori error analysis for discontinuous Galerkin methods on polygonal and polyhedral meshes
January 25, 2023, time 16.00 Arran Fernandez (Eastern Mediterranean University) online Fractional differential equations: initialisation, singularity, and dimensions
October 24, 2023, time 11.00 Davide Riccobelli, MOX — Politecnico di Milano A-133 Brain mechanics and neurological diseases: exploring insights from mathematical modeling.
November 17, 2023, time 12.00 Francesco Bonaldi (LAMPS — Université de Perpignan) A-134 Darcy flows and contact mechanics in fractured porous media
December 6, 2023, time 16.00 Paolo Piersanti (Indiana University) A-133 Variational Inequalities and their applications in elasticity and glaciology
December 4, 2023, time 15.00 Pablo Alexei Gazca Orozco (Albert-Ludwigs-Universitat Freiburg) A-128-129 Numerical computations and thermodynamically complete models for inelastic behaviour in solids

Markov diffusion semigroups and functional inequalities

After a brief introduction to general Dirichlet forms and their connections with contraction semigroups and self-adjoint operators, we will focus on the diffusive case,
aiming to investigate some analytic and geometric aspects of Markov diffusion semigroups and their infinitesimal generators.
A particular attention will be given to functional inequalities that can be studied in this framework, including but not limited to Poincaré, Sobolev and log Sobolev inequalities, and to relations with Ricci curvature bounds.

Topics in mathematical epidemiology

In this course, we revisit the classical compartmental models of mathematical epidemiology and present some of their recent advances. The topics can be organized into three main modules. In the first module, we trace the history of epidemiological models starting from the pioneering work of Bernoulli (1766) up to the well-known Susceptible-Infected-Removed (SIR) model by Kermack and McKendrick (1927) and its subsequent variants. We study in detail the SIR-like models by using tools from stability theory and bifurcation theory of dynamical systems.

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