Jesse Ratzkin

Department of Mathematics
University of Connecticut

Research

Roughly speaking, I am interested in studying geometric structures which can be determined by differential equations on manifolds. For instance, you could look for constant mean curvature embeddings of a surface in three-space, or for complete constant scalar curvature metrics on a subdomain of a sphere. In both of these problems the geometry and analysis play off each other in beautiful ways. Also, to analyze the problems one must do analysis on noncompact manifolds.

CV, research statement, teaching statement, and AMS cover sheet, all in pdf format

Publications and Preprints

• An End-to-End Gluing Construction for Constant Mean Curvature Surfaces PhD Thesis, 2001
• And End to End Gluing Construction for Metrics of Constant Positive Scalar Curvature Indiana Univ. Math. J. Vol. 52 (2003), pg. 703--726.
• On the Nondegeneracy of Constant Mean Curvature Surfaces, joint with Nick Korevaar and Rob Kusner, to appear in Geom. Funct. Anal. This paper gives a general bound for the space of L^2 Jacobi fields on a coplanar, genus zero CMC surface. In particular, we show almost all triunduloids are nondegenerate (i.e. have no L^2 Jacobi fields).
• A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains, joint with Andrejs Treibergs, to appear. Consider n Brownian cops chasing one Brownian thief with all motion restricted to a line. We find how many cops you need so that the expected capture time of the thief is finite.

Lecture Notes

Math Circle notes: notes for a series of three lectures on fractals, geared towards motivated high school students. Lecture 1. Lectures 2 and 3. Nick Korevaar wrote the supporting MAPLE code.

Constant mean curvature surfaces. These are lecture notes for a series of 4 lectures Nick, Nat, Andrejs and I gave on constant mean curvature during a minicourse in the summer of 2002.

UConn Geometry Seminar

Teaching

Previous courses:

• at the University of Connecticut:
  • Math 210 Fall 2006
  • Math 115 Fall 2006
  • Math 252 Spring 2006
  • Math 211 Spring 2006
  • Math 210 Fall 2005
  • Math 210 (multivariable calc), Spring 2005
  • Math 223 (geometry) Spring 2005
  • Math 115 (Calculus I), Fall 2004
  • Math 223 (Geometry), Fall 2004
• at the University of Utah:
  -
  • Differential equations, Spring 2004
  • PDE for engineers, Fall 2003
  • Topics in Geometry: the Yamabe Problem, Spring 2003
  • Trigonometry, Fall 2002
  • Linear Algebra, Spring 2002

Some Mathematical Links:

• The Geometry, Analysis, Numerics and Graphics Program: They have a lot of neat pictures of minimal and constant mean curvature surfaces. Also, they have several faculty who work on problems closely related to those I think about.
• The minimal surfaces group at Granada does great work and has a fantastic list of links and preprints on their site.
• Math Preprints This is a great resource for math articles. Anything that gets posted here stays forever, so you can download preprint versions of papers going back to 1994 (or so). And all the Annals articles get posted here.
• Mathscinet has references and reviews to articles going back to the early 1900's
• Dan Pollack was my advisor. Ok, he still gives me advice; but it's a less formal arrangement now.

The requisite list of links which have nothing to do with math.

• I am a co-founder and member of the board of directors of the Salt Lake City Bicycle Collective. We do all sorts of bike-related stuff, like teaching kids how to repair bikes, and providing valet parking for bikes. We're just all around bicycle freaks.
• Critical Mass! Or try Michael Bluejay's Critical Mass Hub. The revolution will not be motorized!
• More bike links here.
• the Ultimate Players Association.
• Record labels: Aum Fidelity, Tzadik, Okka Disk, Eremite and Kranky. Most of these are tiny labels.
• Comic strips: Apples and Orbifolds, Bob the Angry Flower, Cat and Girl and Ted Rall
• McSweeney's