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The book collects relevant contributions presented at a conference, organized in honour of Carlo Cercignani, that took place at Politecnico di Milano on May 24–28, 2021. Different research areas characterizing the scientific work of Carlo Cercignani have been considered with a particular focus on: mathematical and numerical methods for kinetic equations; kinetic modelling of gas mixtures and polyatomic gases; applications of the Boltzmann equation to electron transport, social phenomena and epidemic spread; turbulence modelling; the Einstein Classical Program; Dynamical Systems Theory.

Differential equations --- Mathematical physics --- differentiaalvergelijkingen --- wiskunde --- fysica --- Física matemàtica

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This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

Operator theory. --- Operator Theory. --- Functional analysis --- Mathematical physics --- Operator theory --- Teoria d'operadors --- Física matemàtica

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This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Mecànica celeste --- Relativitat general (Física) --- Astrometria --- Física matemàtica --- Celestial mechanics

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Mathematical physics. --- Mathematical physics --- Physique mathématique --- Periodicals. --- Périodiques --- Physical mathematics --- Physics --- Mathematics --- theoretical physics --- experimental physics --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Física. --- Física --- Física matemàtica

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This book continues the applications of mathematics, more specifically of theta, eta, and zeta functions, and modular forms, to various areas of theoretical physics. It is a follow-up and extension in some sense of the author’s earlier book entitled A window into zeta and modular physics. Some of the main topics are 1. A new approach to logarithmic corrections to black hole entropy 2. My recent work that provides for an explicit cold plasma-black hole connection 3. Generalization of work of physicists on certain asymptotic problems relating to string theory, for example, by way of the general theory of modular forms of non-positive weight 4. A construction of the E8 root lattice, its theta function, and its relevance for heterotic string theory 5. Applications of elliptic functions to KdV, nonlinear Schrödinger, and Duffing equations, for example, including a discussion of Lax pairs and the Miura transformation 6. Finite temperature zeta functions and partition functions for quantum fields in thermal equilibrium on various curved background spacetimes 7. Exact solutions of the Einstein gravitational field equations for Lemaitre and inhomogeneous cosmological models, with a special focus on the Szekeres–Szafron exact solutions by way of the Weierstrass elliptic function 8. Elementary particles and my zeta function formula for higher spin fermionic particles; this covers, in particular, the gravitino particle (of spin 3/2) and bosons with integral spin s = 2, 3, 4, 5. These are some sample topics. Others include the continuous Heisenberg model, reaction diffusion systems, Dirichlet and Hecke L-functions, the modular j-invariant, the computation of the one-loop effective potential for non-compact symmetric spaces, the BTZ black hole, Jacobi inversion formulas, etc. Thus, there is a very large range of material with the first 9 chapters of preliminary, expositional background for mathematicians and physicists.

Mathematical physics. --- Number theory. --- General relativity (Physics). --- Mathematical Physics. --- Number Theory. --- General Relativity. --- Relativitat general (Física) --- Teoria de nombres --- Física matemàtica