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Daniel Klain

Daniel Klain is a professor and Chair of MATHEMATICAL SCIENCES at UMass Lowell.
Daniel A. KlainChair, Professor
  • CollegeCollege of Sciences
  • DepartmentMathematical Science
  • Phone(978) 934-4474
  • EmailDaniel_Klain@uml.edu

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

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), Teaching - MIT
  • National Science Foundation Graduate Fellowship (1990), Scholarship/Research - National Science Foundation
  • National Merit Scholar (Raytheon Corporate Merit Scholarship) (1986) - Raytheon Corporate

Publications

  • Chen, C., Khovanova, T., Klain, D.A. (2014) "Volume bounds for shadow covering," Transactions of the American Mathematical Society 366:3 pp. 1161–1177
  • Klain, D.A. (2012) "Steiner symmetrization using a finite set of directions," Advances in Applied Mathematics 48:2 pp. 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 pp. 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 pp. 4585-4601
  • Klain, D.A. (2011) "On the equality conditions of the brunn-minkowski theorem," Proceedings of the American Mathematical Society 139:10 pp. 3719-3726
  • Klain, D.A. (2010) "Containment and inscribed simplices," Indiana University Mathematics Journal 59:4 pp. 1232-1244
  • Klain, D.A. (2010) "Covering shadows with a smaller volume," Advances in Mathematics 224:2 pp. 601-619
  • Feldman, D.V., Klain, D.A. (2009) "Angles as probabilities," American Mathematical Monthly 116:8 pp. 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 pp. 143-154
  • Klain, D.A. (2006) "Isometry-invariant valuations on hyperbolic space," Discrete and Computational Geometry 36:3 pp. 457-477
  • Klain, D.A. (2005) "An error estimate for the isoperimetric deficit," Illinois Journal of Mathematics 49:3 pp. 981-992
  • Klain, D.A. (2004) "An intuitive derivation of Heron's formula," American Mathematical Monthly 111:8 pp. 709-712
  • Klain, D.A. (2004) "The Minkowski problem for polytopes," Advances in Mathematics 185:2 pp. 270-288
  • Klain, D.A. (2000) "Even valuations on convex bodies," Transactions of the American Mathematical Society 352:1 pp. 71-93
  • Klain, D.A. (2000) "Free polygon enumeration and the area of an integral polygon," Discrete Mathematics 218:1-3 pp. 109-119
  • Klain, D.A. (1999) "An Euler Relation for Valuations on Polytopes," Advances in Mathematics 147:1 pp. 1-34
  • Klain, D.A. (1998) "Kinematic formulas for finite vector spaces," Discrete Mathematics 179:1-3 pp. 121-132
  • Klain, D.A., Rota, G.C. (1997) "A continuous analogue of Sperner's theorem," Communications on Pure and Applied Mathematics 50:3 pp. 205-223
  • Klain, D.A. (1997) "Invariant valuations on star-shaped sets," Advances in Mathematics 125:1 pp. 95-113
  • Klain, D.A. (1996) "Star valuations and dual mixed volumes," Advances in Mathematics 121:1 pp. 80-101

Presentations

  • - Combinatorics Seminar, 2012
  • , 2011 - Lowell, MA
  • - Fifth International Workshop on Convex Geometry - Analytic Aspects, 2011 - Cortona, Italy
  • - Mathematics Semicar, 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

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)