Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other,...

This volume introduces some mathematical and physical tools and methods required to follow the recent developments, and provides insight in various active areas of mathematical physics, including duality, gauge field theory, conformal field theory, topological field theory, noncommutative geometry, and geometry of low-dimensional manifolds.

This volume can be divided into two parts: a purely mathematical part with contributions on finance mathematics, interactions between geometry and physics and different areas of mathematics; another part on the popularization of mathematics and the situation of women in mathematics.