David Bachman, PhD
Professor of Mathematics
Ph.D., Mathematics, The University of Texas at Austin
B.S., 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.
Game Theory: poker models, combinatorial game theory
The Mathematics of Patterns (MATH10B2)
Calculus II (MATH31)
Calculus III (MATH 32)
Linera Algebra (MATH60)
Differential Geometry (MATH142)
“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: Birkh¨auser, 2006
Recent Conferences and Invited Talks:
“Normalizing Topologically Minimal Surfaces,” paper presented at the American Mathematical Society Section Meeting, Iowa City, IA, March 20, 2011
"Topological, PL and geometric minimal surfaces," paper presented in the MIT Topology Seminar, Boston, MA, March 2010.
"Topological, PL and geometric minimal surfaces," paper presented in the Boston College Topology Seminar, Boston, MA, March 2010.
Conference organizer, Southern California Topology Colloquium, Pomona College, Claremont, CA, February 2010. With Jim Hoste and Erica Flapan.
"Persistence of Essential Surfaces after Dehn Filling," paper presented in the Princeton Topology Seminar, Princeton, NJ, September, 2009.
"Convergence of Discrete Poker Models," paper presented at the MAA Mathfest, Portland, OR, August, 2009.
"Topological Index Theory for Surfaces in 3-manifolds," paper presented at the Yale Topology Seminar and the Columbia Topology Seminar, October 2008; the Cascade Topology Conference, Portland, OR, November 2008; and at the Joint Meetings of the American Mathematical Society and the Mathematical Association of America, Washington, DC, January 2009.
Selected Grants, Awards, and Honors:
NSF Research Grant (PI, DMS–0906151), “Topologically Minimal Surfaces in 3-Manifolds,” 2009-12.
Mathematical Association of America Tensor-SUMMA grant, for the Claremont College's Gateway to the Mathematical Sciences program, 2010-2011.