Topological methods for complex-analytic Brauer groups

Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under suitable assumptions on the fundamental group and the Pontrjagin dual of the second homotopy group. I apply this to Lie groups, Hopf manifolds, and complex-analytic surfaces.Comment: 20 pages, minor corrections, to appear in Topolog

Topological methods for searching barriers and reaction paths

We present a family of algorithms for the fast determination of reaction paths and barriers in phase space and the computation of the corresponding rates. The method requires the reaction times be large compared to the microscopic time, irrespective of the origin - energetic, entropic, cooperative - of the timescale separation. It lends itself to temperature cycling as in simulated annealing and to activation-relaxation routines. The dynamics is ultimately based on supersymmetry methods used years ago to derive Morse theory. Thus, the formalism automatically incorporates all relevant topological information.Comment: 4 pages, 4 figures, RevTex

Special functions, conformal blocks, Bethe ansatz, and SL(3,Z)

This is the talk of the second author at the meeting "Topological Methods in Physical Sciences", London, November 2000. We review our work on KZB equations.Comment: 10 pages, AMSLaTe

Solving equations by topological methods

In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations