معرفی
David Bachman is a Professor of Mathematics at Pitzer College, part of the Claremont Colleges consortium. Since joining in 2004, he has contributed extensively to low-dimensional topology, particularly in knot theory, 3-manifold topology, and Heegaard splittings. His work bridges geometric and topological concepts, including studies of hyperbolic geometry, minimal surfaces, and contact structures.
Educational Background:
- PhD in Mathematics from the University of Texas at Austin
- BS in Mathematics from the State University of New York at Binghamton
His research interests focus on the interplay between topological and geometric properties of 3-manifolds, with a strong emphasis on Heegaard splittings, thin position, Dehn surgery, and their applications. He has developed theories linking topological index to minimal surfaces and explored algorithmic aspects of Heegaard genus computation.
Dr. Bachman’s recent publications highlight the complexity of Heegaard splittings in 3-manifolds, including destabilization phenomena, almost normal surfaces, and connections to computational hardness (NP-Hardness of Heegaard genus). His work often involves collaborations with researchers like Ryan Derby-Talbot and Eric Sedgwick.
Scientific Awards and Grants:
- NSF Research Grant (PI, DMS–1207804), 'Applications of Topologically Minimal Surfaces', 2012-15
- MAA Tensor-SUMMA grant for the Claremont Colleges' Gateway to the Mathematical Sciences program, 2010-11
He has also contributed to pedagogy through books like Advanced Calculus Demystified (2007) and A Geometric Approach to Differential Forms (2nd edition, 2012), which are widely used in undergraduate and graduate mathematics education.
