Moduli of super Riemann surfaces

The basic properties of super Riemann surfaces are presented, and their supermoduli spaces are constructed, in a manner suitable for the application of algebro-geometric techniques to string theory.Supported in part by NSF Grant No. DMS-8704401Supported in part by NSF Grants No. DMS-8501783 and No. DMS-86107301(1)     

Optimal spacing and weights in diffusion monte carlo

We describe how to select optimal values of the time step τ and how to allocate computer time in order to minimize the error bar of the unbiased energy estimate (τ = 0 limit) in diffusion Monte Carlo simulations (DMC ). Several polynomial models are considered, appropriate for both linearly biased and quadratically biased algorithms. An efficient nonoptimal design is also reported, which has the advantage of checking the model's adequacy. Further, we compare the efficiency of linearly biased and quadratically biased DMC, and we estimate the efficiency of DMC versus Green's function Monte Carlo.     

Connections on the total Picard sheaf and the KP hierarchy

A family of connections is introduced on a direct limit of Poincaré sheaves of a curve. These connections descend to connections on the corresponding direct limit of Picard sheaves, defined globally on the Jacobian of the curve. All such connections are classified; in particular they are all flat. Krichever's algebro-geometric solutions of the KP equations are recovered upon trivializing the resulting \tdD-modules over the complement of the divisor.Supported in part by NSF grant no. 58-1353149.     

Versik processes: First steps

A. M. Versik defined a property of finite-state stationary stochastic processes that formally is slightly weaker than D. S. Ornstein’s very weak Bernoulli (VWB) property. Versik conjectured his property was equivalent withVWB. The conjecture is false. We construct a zero entropy Versik process that is not loosely Bernoulli (LB) and, by taking a skew product of this process with the two-shift, we produce aK process that is Versik but notVWB. Our technique for constructing a non-LB process differs from the few known methods.     

Zur Theorie der analytischen Mannigfaltigkeiten im Raume vonn komplexen Veränderlichen

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