Joe Lauer
Lecturer in Mathematics
My research interests lie in geometric evolution equations and geometric analysis. This is an active area where problems allow one to use a wide variety of techniques from analysis, PDE theory, differential geometry and topology. Often it is the combination of several of these tools which proves the most fruitful. More specifically, I focus on smoothness questions in mean curvature flow, curve shortening flow and Ricci Flow, three geometric PDEs that have found applications in many fields.
Outside of my work in the Math Department I am also an Assistant Coach with Wellesley Cross Country and Track and Field.
Education
- B.A. or B.S., University of Waterloo
- M.S., McGill University
- Ph.D., Yale University
Current and upcoming courses
Differential Equations with Applied Linear Algebra
MATH215
This course is designed to examine the degree to which a function can be determined by an algebraic relationship it has with its derivative(s) --- a so-called ordinary differential equation (ODE). For instance, can one completely catalog all functions which equal their own derivative? In service of developing techniques for solving certain classes of differential equations, some fundamental notions from linear algebra and complex numbers are presented. Differential equation topics include modeling with and solving first- and second-order ODEs, separable ODEs, and a discussion of higher order and non-linear ODEs; linear algebra topics include solving systems via elementary row operations, bases, dimension, determinants, column space, and eigenvalues/vectors.
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Graph Theory
MATH325
Graph Theory has origins both in recreational mathematics problems (i.e., puzzles and games) and as a tool to solve practical problems in many areas of society. Topics covered will include trees and distance, connectivity and paths, network flow, graph coloring, directed graphs, and tournaments. In addition, students will gain a sense of what it means to do research in graph theory.