**Daniel A. Klain**Professor

**College**College of Sciences**Department**Mathematical Science**Phone**(978) 934-4474**Email**Daniel_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

## 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 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

## 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**- Colloquium, 2009*- Lowell, MA*- 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**- Colloquium, 2002*- Lowell, MA*- 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*- Germany*- Analysis Seminar, 1997**- 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)*