**Office:** Simons 508**Email:**benjamin.mcmillan@stonybrook.edu

I am Ben McMillan, a postdoc with a joint appointment at Stony Brook math and the Simons Center for Geometry and Physics. My current research interests are differential geometry, particularly the geometry of PDE.

I have two papers extending this work:

Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations I: Geometry

Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Laws

Although my current interests are in differential geometry, in the past I was very interested in graph theory. Work with Cheng Yeaw Ku resulted in the paper

C. Y. Ku and B. McMillan, *Independent sets of maximal size in tensor powers of vertex transitive graphs*, Journal of Graph Theory, 60 (4) (2009), 295-301.
[PDF]

*Conservation laws and parabolic Monge-Ampere equations*, Geometry/Topology Seminar, Stony Brook, 9/25/2018. [PDF]*Obstructions to flatness via the equivalence method*, Equivalence and EDS Seminar, Stony Brook, 2/15/2017. [PDF]*Exterior Differential Systems, definitions and examples*, Equivalence and EDS Seminar, Stony Brook, 2/8/2017.*The Geometry and Conservation Laws of Parabolic Equations*, Topology Seminar, OSU, 10/25/2016. [PDF]*The Geometry and Conservation Laws of Parabolic Equations*, Geometry/Topology seminar, Stony Brook, 10/4/2016. [PDF]*The Geometry and Conservation Laws of Parabolic Equations*, Geometric Analysis seminar, Rutgers, 9/27/2016. [PDF]*The Geometry and Conservation Laws of Parabolic Equations*, Student Differential Geometry Seminar, Berkeley, 9/24/2015.*The Geometry of Conservation Laws*, Student Differential Geometry Seminar, Berkeley, 12/5/2014.*Moving Frames and Geometric Invariants*, Graduate Student Topology & Geometry Conference, UT Austin, 4/5/2014. [PDF]*The Newlander-Nirenberg Theorem*, The Cartan Seminar, Stanford, 2/27/2014. [PDF]*Spencer Cohomology and Geometric Invariants*, Student Differential Geometry Seminar, Berkeley, 2/10/2014. [PDF]*Euler-Lagrange systems of EDS*, Student Differential Geometry Seminar, Berkeley, 11/14/2013 and 11/21/2013. [PDF]*The Newlander-Nirenberg Theorem*, Student Differential Geometry Seminar, Berkeley, 4/10/2013. [PDF]*Calibrated Geometries*, Student Differential Geomrety Seminar, Berkeley, 2/6/2013.*Holonomy on Riemannian Manifolds*, Student Differential Geometry Seminar, Berkeley, 11/13/2012. [PDF]*EDS - Riemannian Surfaces Isometrically Embed in Space*, Student Differential Geometry Seminar, Berkeley, 9/25/2012. [PDF]*Exterior Differential Systems*, Harmonic Analysis and PDE Seminar, Berkeley, 4/3/2012.*Curvature and Local/Global Results in Geometry*, Many Cheerful Facts seminar, Berkeley, 4/8/2011.*Stochastic Loewner Evolutions and the Ginibre-Girko Ensemble*, Summer Undergraduate Research Fellowship presentation, Caltech, 10/2009.