" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

This paper uses sample data to study the problem of comparing populations on finite-
dimensional parallelizable Riemannian manifolds and more general trivial vector bundles …

A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume
of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in …

Consider equilateral pentagons $ V_1,\ldots, V_5 $ in the Euclidean plane. When we
identify pentagons that differ by translation, rotation, and magnification, the moduli space of …

We prove that Dyck's Surface, which is the connected sum of three projective planes, is a
fine moduli stack of possibly-degenerate similarity classes of triangles, where degeneracy is …

We study the problem of determining the least symmetric triangle, which arises both from
pure geometry and from the study of molecular chirality in chemistry. Using the …

We show that when parameterized by triples of angles, the set of similarity classes of
labeled, oriented, possibly degenerate triangles has the natural structure of the Clifford torus …

This dissertation covers 2 novel applications of Optimal Transport to the statistical analysis of
shape distributions and images. 1) Analysis of non-Euclidean data requires statistical tools …

Random walks in R 3 are classical objects in geometric probability which have, over the last
70 years, been rather successfully used as models of polymers in solution. Modifying the …

Let us consider a family $ F (\alpha,\beta,\gamma,\delta) $ of convex quadrangles in the
plane with given angles $\{\alpha,\beta,\gamma,\delta\} $ and with the perimeter $2\pi …