The transparency and power of geometric constructions has been a
source of inspiration to generations of mathematicians. The beauty
and persuasion of pictures, communicated in words or drawings,
continues to provide the intuition and arguments for working with
complicated concepts and structures of modern mathematics. This
volume contains a selection of articles exploring geometric
approaches to problems in algebra, algebraic geometry and number
theory.
Key topics include:
* Curves and their Jacobians
* Algebraic surfaces
* Moduli spaces, Shimura varieties
* Motives and motivic integration
* Number-theoretic applications, rational points
* Combinatorial aspects of algebraic geometry
* Quantum cohomology
* Arithmetic dynamical systems
The collection gives a representative sample of problems and
most recent results in algebraic and arithmetic geometry; the text
can serve as an intense introduction for graduate students and
those wishing to pursue research in these areas.
Contributors: I. Bauer, F. Bogomolov, N. Budur, F. Catanese,
C.-L. Chai, R. Cluckers, C. De Concini, J.S. Ellenberg, F.
Grunewald, B. Hassett, T. Hausel, F. Loeser, J. Pineiro, R. Pink,
C. Procesi, M. Spitzweck, P. Swinnerton-Dyer, L. Szpiro, H.
Tamvakis, Y. Tschinkel, T.J. Tucker, A. Venkatesh, and Y.G.
Zarhin.
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