Trends in Contemporary Mathematics

The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell’s equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the “INdAM Day”, an initiative born in 2004 to present the most recent developments in contemporary mathematics.

Table of Contents

Chapter 1 Interpolation and Comparison Methods in the Mean Field Spin Glass Model
Chapter 2 Integrability of Dirac Reduced Bi-Hamiltonian Equations
Chapter 3 Some Open Problems About Aspherical Closed Manifolds
Chapter 4 Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions
Chapter 5 Exploring Noncommutative Algebras via Deformation Theory
Chapter 6 Mathematical Models and Solutions for the Analysis of Human Genotypes
Chapter 7 Kodaira-Spencer Formality of Products of Complex Manifolds
Chapter 8 Monomial Transformations of the Projective Space
Chapter 9 Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods
Chapter 10 Challenges in Geometric Numerical Integration
Chapter 11 Integral Hodge Classes, Decompositions of the Diagonal, and Rationality Questions
Chapter 12 Unlikely Intersections and Pell’s Equations in Polynomials
Chapter 13 Birational Geometry of Projective Varieties and Directed Graphs
Chapter 14 Dynkin and Extended Dynkin Diagrams
Chapter 15 Tracking Control of 1D Scalar Conservation Laws in the Presence of Shocks
Chapter 16 Finite Simple Groups of Small Essential Dimension
Chapter 17 Geometric Constructions of Extremal Metrics on Complex Manifolds
Chapter 18 Deriving Ohm’s Law from the Vlasov-Maxwell-BoltzmannSystem
Chapter 19 Kinetic Theory and Gas Dynamics, Some Historical Perspectives
Chapter 20 Recent Advances in Nonlinear Potential Theory
Chapter 21 Partial Regularity Results in Optimal Transportation