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A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

A quadratic surface given by the equation x^2+2rz=0.

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

The polynomial giving the number of colorings with m colors of a structure defined by a permutation group.

An iterated fibration of Eilenberg-Mac lane spaces. Every topological space has this homotopy type.

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

A generalized conformal mapping.