Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac ...
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is ...
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include: Hopf algebras underlying renormalization schemes in quantum field theory; noncommutative geometry with applications to index theory on one hand and the study of ...
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, Sieberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some ...
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; and another part on the popularization of mathematics and the situation of women in mathematics.
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