26 citations · 77 across the 15 of their papers we have counts for
15 papers
Cohomology of complex supertori
Hargun Bhatia, Soumya Ganguly, Zhiyuan Jiang +2
We consider supertori which are quotients of affine superspace by translations by algebraically independent odd parameters. Specifically, we describe the ring structure of its spac…
Students' Experience of Cultural Differences Between Mathematics and Physics
Jeffrey M. Rabin, Andrew Meyertholen, Brian Shotwell
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific phy…
The combinatorics of supertorus sheaf cohomology
Jesse Kim, Jeffrey M. Rabin, Brendon Rhoades
Affine superspace has a single bosonic coordinate and fermionic coordinates . Let be the supertorus obtained by quotienting $\m…
Radial expansion preserves hyperbolic convexity and radial contraction preserves spherical convexity
Dhruv Kohli, Jeffrey M. Rabin
On a flat plane, convexity of a set is preserved by both radial expansion and contraction of the set about any point inside it. Using the Poincaré disk model of hyperbolic geometry…
Asymmetric expansion preserves hyperbolic convexity
Dhruv Kohli, Jeffrey M. Rabin
In an earlier paper we showed that the radial expansion of a hyperbolic convex set in the Poincaré disk about any point inside it results in a hyperbolic convex set. In this work,…
Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint
Mitchell J. Rothstein, Jeffrey M. Rabin
The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. Th…
Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing
Amir B. Aazami, Arlie O. Petters, Jeffrey M. Rabin
We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particula…
D-modules on 1|1 Supercurves
Mitchell J. Rothstein, Jeffrey M. Rabin
It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal Δin their product. We establish that the categories of D-m…
Periodicity and Growth in a Lattice Gas with Dynamical Geometry
Karin Baur, Jeffrey M. Rabin, David A. Meyer
We study a one-dimensional lattice gas "dynamical geometry model" in which local reversible interactions of counter-rotating groups of particles on a ring can create or destroy lat…
On Decomposing N=2 Line Bundles as Tensor Products of N=1 Line Bundles
Fausto Ongay, Jeffrey M. Rabin
We obtain the existence of a cohomological obstruction to expressing N=2 line bundles as tensor products of N=1 bundles. The motivation behind this paper is an attempt at understan…
Magnification relations in gravitational lensing via multidimensional residue integrals
Neal Dalal, Jeffrey M. Rabin
We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence…
Geodesics and BPS States in N=2 Supersymmetric QCD
Jeffrey M. Rabin
Conformal mapping techniques are used to determine analytically the geodesics on the Seiberg-Witten Riemann surface which correspond to the BPS dyon states in N=2 SUSY QCD with gau…
Super Curves, their Jacobians, and super KP equations
M. J. Bergvelt, J. M. Rabin
We study the geometry and cohomology of algebraic super curves, using a new contour integral for holomorphic differentials. For a class of super curves (``generic SKP curves'') we…
Old and New Fields on Super Riemann Surfaces
Jeffrey M. Rabin
The ``new fields" or ``superconformal functions" on super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus…
Super Elliptic Curves
Jeffrey M. Rabin
A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard group…