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Daniel Klain


generic faculty blue silhouette of a male head and shoulders
Daniel A. KlainProfessor
  • College
    College of Sciences
  • Department
    Mathematical Science
  • Phone
    (978) 934-4474
  • Email

Research 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)