Joe Lauer
Assistant Teaching Professor 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
Number Theory
MATH223
Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.
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Multivariable Calculus
MATH205
Most real-world systems that one may want to model, whether in the natural or in the social sciences, have many interdependent parameters. To apply calculus to these systems, we need to extend the ideas and techniques of single-variable Calculus to functions of more than one variable. Topics include vectors, matrices, determinants, polar, cylindrical, and spherical coordinates, curves, partial derivatives, gradients and directional derivatives, Lagrange multipliers, multiple integrals, vector calculus: line integrals, surface integrals, divergence, curl, Green's Theorem, Divergence Theorem, and Stokes’ Theorem.