# Jean Taylor

Jean Ellen Taylor (born September 17, 1944) is an American mathematician and professor emeritus at Rutgers University. She was elected a Fellow of the American Mathematical Society in 2013.

## Quotes

* Surface tension is commonly thought of as a fluid phenomenon; the mere mention of the term brings to mind bugs skimming over water, liquids rising or falling in capillary tubes—and soap films and soap bubbles. But there is in fact a notion of surface tension (which is surface energy per unit surface area) for the interface between any two substances, or even between one substance and a vacuum. This surface energy arises from the fact that atoms (or molecules, or ions) of a given substance have a different environment at the interface between that substance and another than those in the bulk of the substance. (Sometimes even the composition of the surface is different from the bulk; this occurs for instance in soapy water having an interface with air.)
** Taylor, J. E. (1978). "Crystalline variational problems". Bulletin of the American Mathematical Society 84 (4): 568-588. ISSN 0002-9904. DOI:10.1090/S0002-9904-1978-14499-1. (quote from p. 568)
* Grain boundaries and surfaces of crystalline materials have a surface free energy which in general depends on the normal direction of the interface relative to the crystal lattice(s). Determining the surface energy minimizing configurations of such interfaces, for a given surface free energy function, is an interesting mathematical problem; it reduces in the case of isotropic (i.e. constant) surface energy to the minimal surface problem. A first step is to classify minimizing cones, since they can arise as tangent cones to minimizing or asymptotically minimizing surfaces. In the isotropic case for two-dimensional surfaces in $R^{3}$, the only minimizing cones are planes. For anisotropic surface energy functions, we give here a catalog of 12 types of embedded minimizing cones, and prove that it is a complete catalog among embedded minimizing crystalline cones ...
** Allard, William K.; Almgren, Jr., Frederick J., eds. (1986). "Complete catalog of minimizing embedded crystalline cones by Jean E. Taylor". Geometric Measure Theory and the Calculus of Variations; Proceedings of the Summer Institute on Geometric Measure Theory and the Calculus of Variations, held at Humboldt State University, Arcata, California, July 16–August 3, 1984. Proc. Symposia Math, vol. 44. American Mathematical Soc.. pp. 379–403. ISBN 978-0-8218-1470-3.
* Item: Retirement party for Joanne Elliott. One of my (male) colleagues reminisced about seeing Joanne as an attractive young woman in the common room at Princeton surrounded by young men eager to be near her. The comment made me very uncomfortable, since it placed emphasis on her attractiveness in a setting where conversations are often mathematical. If only the men had been clustered around her because they were eager to hear her theorems and conjectures! But at least as the story was related, that was not the case.
** (September 1991)"In Her Own Words: Six Mathematicians Reflect on Their Lives and Careers". Notices of the American Mathematical Society;Special Issue on Women in Mathematics 36 (7): 702–706. (quote from p. 706)
* The subject of motion by crystalline curvature is of interest for three quite distinct reasons. One is that some physical surface energies and physical models of crystal growth simply do give rise to such motion. Another is its use as a way to approximate motion of curves by curvature, both for computation and possibly for proving theorems. The third is that this motion simply is interesting and beautiful in its own right, having results that sometimes parallel those for ordinary curvature and sometimes are strikingly different.
** "Motion of curves by crystalline curvature, including triple junctions and boundary points by Jean E. Taylor". Differential Geometry: Partial Differential Equations on Manifolds. Proc. Symp. Pure Math, vol. 54, Part 1. American Mathematical Soc.. 1993. pp. 417–438. ISBN 978-0-8218-1494-9. (quote from p. 417)
* A surface free energy function is defined to be crystalline if its Wulff shape (the equilibrium crystal shape) is a polyhedron. All the questions that one considers for the area functional, where the surface free energy per unit area is 1 for all normal directions, can be considered for crystalline surface free energies. Such questions are interesting for both mathematical and physical reasons. Methods from the geometric calculus of variations are useful for studying a number of such questions; a survey of some of the results is given.
** (2002). "Nonlinear partial differential equations and applications: Crystalline variational methods". Proceedings of the National Academy of Sciences 99 (24): 15277–15280. ISSN 0027-8424. DOI:10.1073/pnas.222494799.