Expertise
Convex geometry, geometric tomography, integral geometry, combinatoricsResearch Interests
Convex Geometry, Geometric Tomography, Integral Geometry, Combinatorics
Education
- Ph D: Mathematics, (1994), Massachusetts Institute of Technology - Cambridge, MA
Dissertation/Thesis Title: Star Measures and Dual Mixed Volumes - BS: Mathematics, (1990), Massachusetts Institute of Technology - Cambridge, MA
Selected Awards and Honors
- Mathematical Sciences Teaching Excellence Award (2010), Teaching - UMass, Lowell
- Mathematical Sciences Teaching Excellence Award (2003), Teaching - UMass, Lowell
- Sigma Xi Young Faculty Award (2000), Service, University - Georgia Tech
- Jon A. Bucsela Prize in Mathematics (1990), Scholarship/Research - MIT
- National Science Foundation Graduate Fellowship (1990), Scholarship/Research - National Science Foundation
- National Merit Scholar (Raytheon Corporate Merit Scholarship) (1986) - Raytheon Corporate
Selected Publications
- Chen, C., Khovanova, T., Klain, D.A. (2014). Volume bounds for shadow covering. Transactions of the American Mathematical Society, 366(3) 1161–1177.
- Klain, D.A. (2012). Steiner symmetrization using a finite set of directions. Advances in Applied Mathematics, 48(2) 340-353.
- Bianchi, G., Klain, D.A., Lutwak, E., Yang, D., Zhang, G. (2011). A countable set of directions is sufficient for Steiner symmetrization. Advances in Applied Mathematics, 47(4) 869-873.
- Klain, D.A. (2011). If you can hide behind it, can you hide inside it? Transactions of the American Mathematical Society, 363(9) 4585-4601.
- Klain, D.A. (2011). On the equality conditions of the brunn-minkowski theorem. Proceedings of the American Mathematical Society, 139(10) 3719-3726.
- Klain, D.A. (2010). Containment and inscribed simplices. Indiana University Mathematics Journal, 59(4) 1232-1244.
- Klain, D.A. (2010). Covering shadows with a smaller volume. Advances in Mathematics, 224(2) 601-619.
- Feldman, D.V., Klain, D.A. (2009). Angles as probabilities. American Mathematical Monthly, 116(8) 732-735.
- Rybnikov, K., Daniels, K., Klain, D.A., Jones, B., Durante, V. (2008). Statistical Estimation of Euler Characteristic from Volumetric Data.
- Klain, D.A. (2007). Bonnesen-type inequalities for surfaces of constant curvature. Advances in Applied Mathematics, 39(2) 143-154.
- Klain, D.A. (2006). Isometry-invariant valuations on hyperbolic space. Discrete and Computational Geometry, 36(3) 457-477.
- Klain, D.A. (2005). An error estimate for the isoperimetric deficit. Illinois Journal of Mathematics, 49(3) 981-992.
- Klain, D.A. (2004). An intuitive derivation of Heron's formula. American Mathematical Monthly, 111(8) 709-712.
- Klain, D.A. (2004). The Minkowski problem for polytopes. Advances in Mathematics, 185(2) 270-288.
- Klain, D.A. (2000). Even valuations on convex bodies. Transactions of the American Mathematical Society, 352(1) 71-93.
- Klain, D.A. (2000). Free polygon enumeration and the area of an integral polygon. Discrete Mathematics, 218(1-3) 109-119.
- Klain, D.A. (1999). An Euler Relation for Valuations on Polytopes. Advances in Mathematics, 147(1) 1-34.
- Klain, D.A. (1998). Kinematic formulas for finite vector spaces. Discrete Mathematics, 179(1-3) 121-132.
- Klain, D.A., Rota, G.C. (1997). A continuous analogue of Sperner's theorem. Communications on Pure and Applied Mathematics, 50(3) 205-223.
- Klain, D.A. (1997). Invariant valuations on star-shaped sets. Advances in Mathematics, 125(1) 95-113.
- Klain, D.A. (1996). Star valuations and dual mixed volumes. Advances in Mathematics, 121(1) 80-101.
Selected Presentations
- - Combinatorics Seminar, 2012
- - Colloquium, 2011 - Lowell, MA
- - Fifth International Workshop on Convex Geometry - Analytic Aspects, 2011 - Cortona, Italy
- - Mathematics Seminar, 2011 - Boston, MA
- - PROMYS, 2011
- - Thematic Program on Asymptotic Geometric Analysis, 2010 - Toronto, Canada
- - 19th Annual Fall Workshop on Computational Geometry, 2009
- - AMS Special Session (Discrete Geometry and Combinatorics), 2009 - Worcester, MA
- - Colloquium, 2009 - Lowell, MA
- - Colloquium, 2009
- - AMS Special Session (Convex and Integral Geometry), 2008 - Middletown, CT
- - Colloquium, 2008
- - Colloquium, 2008
- - Colloquium, 2008
- - Colloquium and Analysis Seminar, 2008
- - AARMS Analysis Days (Conference in honour of A. C. Thompson), 2007
- - AMS Special Session (Discrete and Convex Geometry), 2006 - Durham, NH
- - Undergraduate Lunch Seminar, 2006
- - AARMS Summer Graduate School Lectures, 2005
- - Colloquium, 2005
- - Gian-Carlo Rota Memorial Lecture, 2004 - Italy
- - AMS Special Session (Topological Combinatorics), 2003 - Binghamton, NY
- - Colloquium, 2003
- - Colloquium, 2003
- - GASC Seminar, 2003 - Boston, MA
- - AMS Special Session (Convex Geometry), 2002 - Boston, MA
- - Colloquium, 2002 - Lowell, MA
- - Colloquium, 2002
- - HRUMC 2002-Special Session, 2002
- - Colloquium, 2001 - Lowell, MA
- - AMS Special Session (Gian-Carlo Rota Memorial), 2000 - Washington, DC
- - AMS Special Session (Invariance in Convex Geometry), 2000 - Lowell, MA
- - Colloquium, 1999
- - Colloquium, 1999
- - Colloquium, 1999
- - Combinatorics Seminar, 1999
- - Combinatorics Seminar, 1999
- - Combinatorics Seminar, 1999
- - Geometry Seminar, 1999
- - Geometry/Topology Seminar, 1999
- - SAAC Lecture, 1999
- - SAAC Lecture and Combinatorics Seminar, 1999
- - Second International Workshop on Convex Geometry - Analytic Aspects, 1999 - Cortona, Italy
- - SUM/SAAC Lecture and Colloquium, 1999
- - 9th Annual Southeastern Geometry Conference, 1998
- - Algebra and Discrete Mathematics Seminar, 1998
- - CMS Summer Meeting (Session in Convex Geometry), 1998 - St. John, New Brunswick
- - Colloquium, 1998
- - Colloquium, 1998
- - Combinatorics Seminar, 1998
- - AMS Special Session (Harmonic Analysis and Convexity), 1997 - 1997 Memphis, TN
- - Analysis Seminar, 1997
- - Analysis Seminar, 1997 - Germany
- - Combinatorial Convexity and Algebraic Geometry, 1997 - Oberwolfach, Germany
- - Combinatorics Seminar, 1997
- - Convex Geometry, 1997 - Oberwolfach, Germany
- - Geometry Seminar, 1997
- - Combinatorics Seminar, 1996
- - Conference on the Affine Geometry of Convex Sets, 1996
- - PROMYS Guest Lecture, 1996
- - Rotafest, 1996
- - Workshop in Random Methods in Convex Geometry, 1996
- - Convex Geometry Seminar, March 1996
- - Convex Geometry Seminar, February 1996
- - AMS/SMM Special Session (Convexity and Combinatorial Geometry), 1995 - Guanajuato, Mexico
- - Analysis Seminar, 1995
- - Combinatorics Seminar, 1995
- - Combinatorics Seminar, 1995
- - Probability Seminar, 1995
- - AMS Special Session (Geometric Convexity), 1994 - Brooklyn, NY
- - Analysis Seminar, 1994 - Atlanta, GA
- - Combinatorics Seminar, 1994 - Boston, MA
Selected Contracts, Fellowships, Grants and Sponsored Research
- Co-PI (2003), Grant - NSF (Division of Mathematical Sciences)
- Convex Geometry and Geometric Invariant Theory (1998), Grant - NSF (Geometric Analysis)
- Mixed Volumes (1996), Grant - NSF (Geometric Analysis)