David Bachman

Professor of Mathematics

With Pitzer Since: 2004
Field Group: Mathematics
Campus Address: Avery 220
Phone: 909.607.7961
Campus email: david_bachman@pitzer.edu
Office Hours: Mondays, Wednesdays & Fridays 10:00-11:00 a.m.

Educational Background

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

Research Interests

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.

Recent Courses

Mathematics for 3D Printing (MATH10B)

Calculus I (MATH30)

Calculus II (MATH31)

Calculus III (MATH32)

Introduction to Methods of Proof (MATH100)

Differential Geometry (MATH142)

Math, Art and Environment (MATH009)

Differential Geometry (MATH142)

Low-Dimensional Topology (MATH145B)

Recent Publications

“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).

Recent Conferences and Invited Talks

“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.

Selected Grants, Awards, and Honors

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

Mathematical Association of America Tensor-SUMMA grant, for the Claremont College’s Gateway to the Mathematical Sciences program, 2010-2011.

Additional Information

Curriculum Vitae

Personal Academic Website

Page last updated on November 3, 2016