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Homogeneous flows, moduli spaces, and arithmetic : proceedings of the Clay Mathematics Institute Summer School, Centro di Recerca Matematica Ennio de Giorgi, Pisa, Italy, June 11 - July 6, 2007 by Manfred Leopold Einsiedler, Manfred Leopold Einsiedler, David Alexandre Ellwood, Alex Eskin, Dmitry Kleinbock, Elon Lindenstrauss (eds.) is a nonfiction available to read on EtoBox.
What is Homogeneous flows, moduli spaces, and arithmetic : proceedings of the Clay Mathematics Institute Summer School, Centro di Recerca Matematica Ennio de Giorgi, Pisa, Italy, June 11 - July 6, 2007 about?
This book contains a wealth of material concerning two very active and interconnected directions of current research at the interface of dynamics, number theory and geometry. Examples of the dynamics considered are the action of subgroups of $\textrm{SL}(n,\mathbb{R})$ on the space of unit volume lattices in $\mathbb{R}^n$ and the action of $\textrm{SL}(2,\mathbb{R})$ or its subgroups on moduli spaces of flat structures with prescribed singularities on a surface of genus $\ge 2$. Topics covered include the following: (a) Unipotent flows: non-divergence, the classification of invariant measures, equidistribution, orbit closures. (b) Actions of higher rank diagonalizable groups and their invariant measures, including entropy theory for such actions. (c) Interval exchange maps and their connections to translation surfaces, ergodicity and mixing of the Teichmüller geodesic flow, dynamics of rational billiards. (d) Application of homogeneous flows to arithmetic, including applications to the distribution of values of indefinite quadratic forms at integral points, metric Diophantine approximation, simultaneous Diophantine approximations, counting of integral and rational points on homoge
Who reads Homogeneous flows, moduli spaces, and arithmetic : proceedings of the Clay Mathematics Institute Summer School, Centro di Recerca Matematica Ennio de Giorgi, Pisa, Italy, June 11 - July 6, 2007?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Manfred Leopold Einsiedler, Manfred Leopold Einsiedler, David Alexandre Ellwood, Alex Eskin, Dmitry Kleinbock, Elon Lindenstrauss (eds.)
- Publisher
- American Mathematical Society for the Clay Mathematics Institute, Cambridge, MA; American Mathematical Society
- Published
- 2010
- Language
- EN
- ISBN
- 9780821847428
- Category
- nonfiction
- Subjects
- Mathematics, Stem