David Bachman

PhD, Mathematics, The University of Texas at Austin
BS, Mathematics, State University of New York at Binghamton

Knot theory and 3-Manifold Topology: normal and almost normal surfaces, Heegaard splittings, thin position, Dehn surgery, contact structures

Geometry: hyperbolic geometry, minimal surfaces, surface modelling

Mathematics for 3D Printing (MATH10B)

Calculus I (MATH30)

Calculus II (MATH31)

Calculus III (MATH32)

Introduction to Methods of Proof (MATH100)

Math, Art and Environment (MATH009)

Differential Geometry (MATH142)

Low-Dimensional Topology (MATH145B)

“Stabilizing and Destabilizing Heegaard Splittings of Sufficiently Complicated 3-Manifolds,” Mathematische Annalen, 355 (2013), no. 2, 697–728.

“Almost normal surfaces with boundary,” (with R. Derby-Talbot and E. Sedgwick), Contemporary Mathematics, 597 (2013), 177–194.

“On the Existence of High Index Topologically Minimal Surfaces,” Mathematical Research Letters, vol. 17, no. 3 (2010). With Jesse Johnson.

“Topological Index Theory for Surfaces in 3-Manifolds,” Geom. Topol., vol.14, no.1 (2010).

“Connected Sums of Unstabilized Heegaard Splittings are Unstabilized,” Geom. Topol., vol.12, no.4 (2008).

Advanced Calculus eMYSTiFieD. New York: McGraw-Hill, 2007.

A Geometric Approach to Differential Forms. Boston: Birkhauser (1st edition, 2006; 2nd edition, 2012).

“Normalizing Topologically Minimal Surfaces,” presented at Mathematical Congress of the Americas, Guanajuato, Mexico, August 5-9, 2013.

“Normalizing Topologically Minimal Surfaces,” presented at Low-dimensional Topology and Geometry, Toulouse, France, June 24-28, 2013.

“Normalizing Topologically Minimal Surfaces,” presented at AMS Section Meeting, Ames, IA, April 27, 2013.

“Parallels between Geometrically Minimal and Topologically Minimal Surfaces,” Workshop on Minimal Surfaces, 3-Manifold Topology and Related Topics, Boston, MA, April 28, 2013.

“Topological, PL, and Geometric Minimal Surfaces,” 46th Spring Topology and Dynamics Conferences (semi-plenary speaker), Mexico City, Mexico, March 22-24, 2012.

“Topological, PL, and Geometric Minimal Surfaces,” The 8th East Asian School of Knots and Related Topics (plenary speaker), Daejeon, Korea, January 9-12, 2012.

“Normalizing Topologically Minimal Surfaces,” paper presented at the American Mathematical Society Section Meeting, Iowa City, IA, March 20, 2011.

NSF Research Grant (PI, DMS–1207804), “Applications of Topologically Minimal Surfaces,” 2012-15.

Mathematical Association of America Tensor-SUMMA grant, for The Claremont Colleges’ Gateway to the Mathematical Sciences program, 2010-11.

Curriculum Vitae (pdf)