Conference Service Mandl

abstract: Analytic number theory and Diophantine approximation are important and closely connected areas of number theory. The two topics have roots that are as old as mathematics, the first one being motivated initially by the study of prime numbers, while the second concerns the nature of numbers. In the last ten years there have been several striking developments in both fields (for example, Green and Tao's proof of arbitrarily long arithmetic progressions of primes and the work of Rivoal and others on zeta values at odd integers). This summer school will be an occasion for graduate students and young researchers to learn some of the latest developments in these rapidly developing fields and eventually contribute to them.

abstract: Physical duality symmetries relate special limits of the various consistent string theories (Types I, II, Heterotic string and their cousins, including F-theory) one to another. By comparing the mathematical descriptions of these theories, one reveals often quite deep and unexpected mathematical conjectures. The best known string duality to mathematicians, Type IIA/IIB duality also called {it mirror symmetry}, has inspired many new developments in algebraic and arithmetic geometry, number theory, toric geometry, Riemann surface theory, and infinite dimensional Lie algebras. Other string dualities such as Heterotic/Type II duality and F-Theory/Heterotic string duality have also, more recently, led to series of mathematical conjectures, many involving elliptic curves, K3 surfaces, and modular forms.

abstract: The purpose of the workshop is to highlight the research of female number theorists.