Trends in Contemporary Mathematics

1. Front Matter

   Pages i-x

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2. Interpolation and Comparison Methods in the Mean Field Spin Glass Model

   • Francesco Guerra

   Pages 1-12

3. Integrability of Dirac Reduced Bi-Hamiltonian Equations

   • Alberto De Sole, Victor G. Kac, Daniele Valeri

   Pages 13-32

4. Some Open Problems About Aspherical Closed Manifolds

   • Wolfgang Lück

   Pages 33-46

5. Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

   • Gunther Cornelissen, Matilde Marcolli

   Pages 47-57

6. Exploring Noncommutative Algebras via Deformation Theory

   • Pavel Etingof

   Pages 59-72

7. Mathematical Models and Solutions for the Analysis of Human Genotypes

   • Giuseppe Lancia

   Pages 73-84

8. Kodaira-Spencer Formality of Products of Complex Manifolds

   • Marco Manetti

   Pages 85-95

9. Monomial Transformations of the Projective Space

   • Olivier Debarre, Bodo Lass

   Pages 97-103

10. Progress in the Theory of Nonlinear Diffusion: Asymptotics via Entropy Methods

    • Juan Luis Vázquez

    Pages 105-124

11. Challenges in Geometric Numerical Integration

    • Ernst Hairer

    Pages 125-135

12. Integral Hodge Classes, Decompositions of the Diagonal, and Rationality Questions

    • Claire Voisin

    Pages 137-149

13. Unlikely Intersections and Pell’s Equations in Polynomials

    • Umberto Zannier

    Pages 151-169

14. Birational Geometry of Projective Varieties and Directed Graphs

    • Paolo Cascini

    Pages 171-180

15. Dynkin and Extended Dynkin Diagrams

    • Idun Reiten

    Pages 181-193

16. Tracking Control of 1D Scalar Conservation Laws in the Presence of Shocks

    • Rodrigo Lecaros, Enrique Zuazua

    Pages 195-219

17. Finite Simple Groups of Small Essential Dimension

    • Arnaud Beauville

    Pages 221-228

18. Geometric Constructions of Extremal Metrics on Complex Manifolds

    • Claudio Arezzo

    Pages 229-247

19. Deriving Ohm’s Law from the Vlasov-Maxwell-Boltzmann System

    • Laure Saint-Raymond

    Pages 249-262

20. Kinetic Theory and Gas Dynamics, Some Historical Perspectives

    • Tai-Ping Liu

    Pages 263-276

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.

• Computational mathematics
• Interdisciplinary mathematics
• PDE
• partial differential equations

• Istituto Nazionale di Alta Matematica "Francesco Severi", Roma, Italy

  Vincenzo Ancona

• Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Roma, Italy

  Elisabetta Strickland

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