Trends in Contemporary Mathematics

Description

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 Front Matter....Pages i-x Interpolation and Comparison Methods in the Mean Field Spin Glass Model....Pages 1-12 Integrability of Dirac Reduced Bi-Hamiltonian Equations....Pages 13-32 Some Open Problems About Aspherical Closed Manifolds....Pages 33-46 Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions....Pages 47-57 Exploring Noncommutative Algebras via Deformation Theory....Pages 59-72 Mathematical Models and Solutions for the Analysis of Human Genotypes....Pages 73-84 Kodaira-Spencer Formality of Products of Complex Manifolds....Pages 85-95 Monomial Transformations of the Projective Space....Pages 97-103 Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods....Pages 105-124 Challenges in Geometric Numerical Integration....Pages 125-135 Integral Hodge Classes, Decompositions of the Diagonal, and Rationality Questions....Pages 137-149 Unlikely Intersections and Pell’s Equations in Polynomials....Pages 151-169 Birational Geometry of Projective Varieties and Directed Graphs....Pages 171-180 Dynkin and Extended Dynkin Diagrams....Pages 181-193 Tracking Control of 1D Scalar Conservation Laws in the Presence of Shocks....Pages 195-219 Finite Simple Groups of Small Essential Dimension....Pages 221-228 Geometric Constructions of Extremal Metrics on Complex Manifolds....Pages 229-247 Deriving Ohm’s Law from the Vlasov-Maxwell-Boltzmann System....Pages 249-262 Kinetic Theory and Gas Dynamics, Some Historical Perspectives....Pages 263-276 Recent Advances in Nonlinear Potential Theory....Pages 277-292 Partial Regularity Results in Optimal Transportation....Pages 293-307