David A Glickenstein
 Professor
 Associate Head, Mathematics Graduate Program
 Member of the Graduate Faculty
Contact
 (520) 6212463
 Mathematics, Rm. 204
 Tucson, AZ 85721
 dglicken@arizona.edu
Degrees
 Ph.D. Mathematics
 University of California at San Diego, La Jolla, California, United States
 Precompactness of solutions to the Ricci flow and a maximum principle for combinatorial Yamabe flow
Awards
 Undergraduate Advising Award
 University of Arizona Department of Mathematics, Spring 2021
Interests
No activities entered.
Courses
202425 Courses

Research Tutorial Group
MATH 596G (Fall 2024)
202324 Courses

Dissertation
MATH 920 (Spring 2024) 
Global Differential Geom
MATH 537B (Spring 2024) 
Independent Study
MATH 599 (Spring 2024) 
Research Tutorial Group
MATH 596G (Spring 2024) 
Dissertation
MATH 920 (Fall 2023) 
Global Differential Geom
MATH 537A (Fall 2023) 
Independent Study
MATH 599 (Fall 2023) 
Research Tutorial Group
MATH 596G (Fall 2023)
202223 Courses

Calculus II
MATH 129 (Spring 2023) 
Dissertation
MATH 920 (Spring 2023) 
Independent Study
MATH 599 (Spring 2023) 
Research Tutorial Group
MATH 596G (Spring 2023) 
Dissertation
MATH 920 (Fall 2022) 
Linear Algebra
MATH 513 (Fall 2022) 
Research Tutorial Group
MATH 596G (Fall 2022)
202122 Courses

Dissertation
MATH 920 (Spring 2022) 
Independent Study
MATH 599 (Spring 2022) 
Research Tutorial Group
MATH 596G (Spring 2022) 
TopologyGeometry
MATH 534B (Spring 2022) 
Dissertation
MATH 920 (Fall 2021) 
Research Tutorial Group
MATH 596G (Fall 2021) 
TopologyGeometry
MATH 534A (Fall 2021)
202021 Courses

Dissertation
MATH 920 (Spring 2021) 
Independent Study
MATH 599 (Spring 2021) 
Dissertation
MATH 920 (Fall 2020) 
Independent Study
MATH 599 (Fall 2020) 
Research Tutorial Group
MATH 596G (Fall 2020) 
Theory Graphs+Networks
CSC 543 (Fall 2020) 
Theory Graphs+Networks
MATH 443 (Fall 2020) 
Theory Graphs+Networks
MATH 543 (Fall 2020)
201920 Courses

Dissertation
MATH 920 (Spring 2020) 
Independent Study
MATH 599 (Spring 2020) 
Research
MATH 900 (Spring 2020) 
Research Tutorial Group
MATH 596G (Spring 2020) 
Topics Geometry+Topology
MATH 538 (Spring 2020) 
Calculus II
MATH 129 (Fall 2019) 
Dissertation
MATH 920 (Fall 2019) 
Independent Study
MATH 599 (Fall 2019) 
Research
MATH 900 (Fall 2019) 
Research Tutorial Group
MATH 596G (Fall 2019)
201819 Courses

Calculus II
MATH 129 (Spring 2019) 
Independent Study
MATH 599 (Spring 2019) 
Research
MATH 900 (Spring 2019) 
Research Tutorial Group
MATH 596G (Spring 2019) 
Dissertation
MATH 920 (Fall 2018) 
Independent Study
MATH 599 (Fall 2018) 
Research Tutorial Group
MATH 596G (Fall 2018)
201718 Courses

Dissertation
MATH 920 (Spring 2018) 
Independent Study
MATH 599 (Spring 2018) 
Research Tutorial Group
MATH 596G (Spring 2018) 
TopologyGeometry
MATH 534B (Spring 2018) 
Dissertation
MATH 920 (Fall 2017) 
Independent Study
MATH 599 (Fall 2017) 
Research Tutorial Group
MATH 596G (Fall 2017) 
TopologyGeometry
MATH 534A (Fall 2017)
201617 Courses

Dissertation
MATH 920 (Spring 2017) 
Independent Study
MATH 599 (Spring 2017) 
Research
MATH 900 (Spring 2017) 
Research Tutorial Group
MATH 596G (Spring 2017) 
Topics Geometry+Topology
MATH 538 (Spring 2017) 
Dissertation
MATH 920 (Fall 2016) 
Independent Study
MATH 599 (Fall 2016) 
Research
MATH 900 (Fall 2016) 
Research Tutorial Group
MATH 596G (Fall 2016)
201516 Courses

Directed Research
MATH 492 (Spring 2016) 
Dissertation
MATH 920 (Spring 2016) 
Mathematical Modeling
MATH 485 (Spring 2016) 
Research Tutorial Group
MATH 596G (Spring 2016)
Scholarly Contributions
Books
 Chow, B., Chu, S., Glickenstein, D. A., Guenther, C., Isenberg, J., Ivey, T., Knopf, D., Lu, P., Luo, F., & Ni, L. (2015). The Ricci Flow: Techniques and Applications Part IV. American Mathematical Society.
Journals/Publications
 Glickenstein, D. A. (2016). Distortion estimates for barycentric coordinates on Riemannian simplices. submitted.More infoWe define barycentric coordinates on a Riemannian manifold using Karcher'scenter of mass technique applied to point masses for n+1 sufficiently closepoints, determining an ndimensional Riemannian simplex defined as a "Karchersimplex." Specifically, a set of weights is mapped to the Riemannian center ofmass for the corresponding point measures on the manifold with the givenweights. If the points lie sufficiently close and in general position, this mapis smooth and injective, giving a coordinate chart. We are then able to computefirst and second derivative estimates of the coordinate chart. These estimatesallow us to compare the Riemannian metric with the Euclidean metric induced ona simplex with edge lengths determined by the distances between the points. Weshow that these metrics differ by an error that shrinks quadratically with themaximum edge length. With such estimates, one can deduce convergence resultsfor finite element approximations of problems on Riemannian manifolds.[Journal_ref: ]
 Glickenstein, D. A. (2022). Determinant of the Finite Volume Laplacian. Discrete and Computational Geometry.
 Glickenstein, D. A. (2022). The impact of social rhythm and sleep disruptions on waist circumference after job loss: A prospective 18month study. Obesity.
 , T. D., & , D. G. (2021). Determinant of the finite volume Laplacian.More infoThe finite volume Laplacian can be defined in all dimensions and is a naturalway to approximate the operator on a simplicial mesh. In the most generalsetting, its definition with orthogonal duals may require that not all volumesare positive; an example is the case corresponding to twodimensional finiteelements on a nonDelaunay triangulation. Nonetheless, in many cases two andthreedimensional Laplacians can be shown to be negative semidefinite with akernel consisting of constants. This work generalizes work in two dimensionsthat gives a geometric description of the Laplacian determinant; in particular,it relates the Laplacian determinant on a simplex in any dimension to certainvolume quantities derived from the simplex geometry.[Journal_ref: ]
 Bell, B., Glickenstein, D., Hamm, K., & Scheidegger, C. (2021). Persistent Classification: A New Approach to Stability of Data and Adversarial Examples. preprint.
 Glickenstein, D. A. (2017). Euclidean formulation of discrete uniformization of the disk. Geometry, Imaging, and Computing.More infoThurston's circle packing approximation of the Riemann Mapping (proven togive the Riemann Mapping in the limit by RodinSullivan) is largely based onthe theorem that any topological disk with a circle packing metric can bedeformed into a circle packing metric in the disk with boundary circlesinternally tangent to the circle. The main proofs of the uniformization usehyperbolic volumes (Andreev) or hyperbolic circle packings (by Beardon andStephenson). We reformulate these problems into a Euclidean context, whichallows more general discrete conformal structures and boundary conditions. Themain idea is to replace the disk with a double covered disk with one sideforced to be a circle and the other forced to have interior curvature zero. Theentire problem is reduced to finding a zero curvature structure. We also showthat these curvatures arise naturally as curvature measures on generalizedmanifolds (manifolds with multiplicity) that extend the usual discreteLipschitzKilling curvatures on surfaces.[Journal_ref: ]
 Glickenstein, D., Hamm, K., Huo, X., Mei, Y., & Stoll, M. (2021). Editorial: Mathematical Fundamentals of Machine Learning. Frontiers in Applied Mathematics and Statistics, 7.
 Haynes, P. L., Apolinar, G. R., Mayer, C., Kobayashi, U., Silva, G. E., Glickenstein, D. A., Thomson, C. A., & Quan, S. F. (2021). Inconsistent social rhythms are associated with abdominal adiposity after involuntary job loss: An observational study. Obes Sci Pract, 7(2), 208216.
 Butler, E. A., Glickenstein, D. A., Silva Torres, G. E., Quan, S. F., Thomson, C. A., & Haynes, P. L. (2019). Inconsistent Social Rhythms are Associated with Higher Waist Circumference Following Job Loss. Society of Behavioral Medicine annual meeting.
 Faust, R., Glickenstein, D., & Scheidegger, C. (2019). DimReader: Axis lines that explain nonlinear projections. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, 25(1), 481490.
 Glickenstein, D. A. (2018). A Bug's Eye View: The Riemannian Exponential Map on Polyhedral Surfaces. MATHEMATICAL INTELLIGENCER, 40(2), 19.
 Glickenstein, D. A. (2018). Make PVC Polyhedra. Math Horizons, 25(3), 2527. doi:10.1080/10724117.2018.1424463
 Glickenstein, D. A. (2018). MultiLevel Steiner Trees. 17th International Symposium on Experimental Algorithms (SEA 2018).More infoIn the classical Steiner tree problem, given an undirected, connected graph$G=(V,E)$ with nonnegative edge costs and a set of \emph{terminals}$T\subseteq V$, the objective is to find a minimumcost tree $E' \subseteq E$that spans the terminals. The problem is APXhard; the best known approximationalgorithm has a ratio of $\rho = \ln(4)+\varepsilon < 1.39$. In this paper, westudy a natural generalization, the \emph{multilevel Steiner tree} (MLST)problem: given a nested sequence of terminals $T_{\ell} \subset \dots \subsetT_1 \subseteq V$, compute nested trees $E_{\ell}\subseteq \dots \subseteqE_1\subseteq E$ that span the corresponding terminal sets with minimum totalcost. The MLST problem and variants thereof have been studied under variousnames including Multilevel Network Design, QualityofService Multicast tree,GradeofService Steiner tree, and MultiTier tree. Several approximationresults are known. We first present two simple $O(\ell)$approximationheuristics. Based on these, we introduce a rudimentary composite algorithm thatgeneralizes the above heuristics, and determine its approximation ratio bysolving a linear program. We then present a method that guarantees the sameapproximation ratio using at most $2\ell$ Steiner tree computations. We comparethese heuristics experimentally on various instances of up to 500 verticesusing three different network generation models. We also present variousinteger linear programming (ILP) formulations for the MLST problem, and comparetheir running times on these instances. To our knowledge, the compositealgorithm achieves the best approximation ratio for up to $\ell=100$ levels,which is sufficient for most applications such as network visualization ordesigning multilevel infrastructure.[Journal_ref: ]
 Glickenstein, D., & Liang, J. (2018). Asymptotic Behavior of betaPolygon Flows. JOURNAL OF GEOMETRIC ANALYSIS, 28(3), 29022925.
 Glickenstein, D., & Thomas, J. (2017). Duality structures and discrete conformal variations of piecewise constant curvature surfaces. ADVANCES IN MATHEMATICS, 320, 250278.
 Glickenstein, D., & Wu, L. (2017). Soliton metrics for twoloop renormalization group flow on 3D unimodular Lie groups. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 19(3), 19771982.
 Haynes, P. L., Silva, G. E., Howe, G. W., Thomson, C. A., Butler, E. A., Quan, S. F., Sherrill, D., Scanlon, M., RojoWissar, D. M., Gengler, D. N., & Glickenstein, D. A. (2017). Longitudinal assessment of daily activity patterns on weight change after involuntary job loss: the ADAPT study protocol. BMC PUBLIC HEALTH, 17.
 Haynes, P., Silva, G. E., Gengler, D., RojoWissar, D., Nair, U., Oliver, R., Glickenstein, D., Sherrill, D., & Quan, S. (2017). HIGH PREVALENCE OF OVER THE COUNTER SLEEP AID USE AMONG INDIVIDUALS WHO HAVE EXPERIENCED INVOLUNTARY JOB LOSS. ANNALS OF BEHAVIORAL MEDICINE, 51, S315S315.
 Champion, D., Glickenstein, D., & Young, A. (2011). Regge's EinsteinHilbert functional on the double tetrahedron. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 29(1), 108124.
 Glickenstein, D. A. (2011). DISCRETE CONFORMAL VARIATIONS AND SCALAR CURVATURE ON PIECEWISE FLAT TWO AND THREEDIMENSIONAL MANIFOLDS. JOURNAL OF DIFFERENTIAL GEOMETRY, 87(2), 201237.
 Glickenstein, D., & Payne, T. L. (2010). Ricci flow on threedimensional, unimodular metric Lie algebras. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 18(5), 927961.
 Glickenstein, D. A. (2008). Riemannian Groupoids and Solitons for ThreeDimensional Homogeneous Ricci and CrossCurvature Flows. INTERNATIONAL MATHEMATICS RESEARCH NOTICES.
 Chow, B. t., & Glickenstein, D. (2007). Semidiscrete geometric flows of polygons. AMERICAN MATHEMATICAL MONTHLY, 114(4), 316328.
 Glickenstein, D. A. (2007). A monotonicity property for weighted Delaunay triangulations. DISCRETE & COMPUTATIONAL GEOMETRY, 38(4), 651664.
 Chow, B., Glickenstein, D., & Lu, P. (2006). Collapsing sequences of solutions to the Ricci flow on 3manifolds with almost nonnegative curvature. MATHEMATISCHE ZEITSCHRIFT, 254(1), 128.
 Glickenstein, D. A. (2005). A combinatorial Yamabe flow in three dimensions. TOPOLOGY, 44(4), 791808.
 Glickenstein, D. A. (2005). A maximum principle for combinatorial Yamabe flow. TOPOLOGY, 44(4), 809825.
 Chow, B., Glickenstein, D., & Lu, P. (2003). Metric transformations under collapsing of Riemannian manifolds. MATHEMATICAL RESEARCH LETTERS, 10(56), 737746.
 Glickenstein, D. A. (2003). Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates. GEOMETRY & TOPOLOGY, 7, 487510.
 Glickenstein, D., & Strichartz, R. S. (1996). Nonlinear selfsimilar measures and their Fourier transforms. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 45(1), 205220.
Proceedings Publications
 Glickenstein, D. A., Karamchandani, A. J., Korbut, C., Bang, M., Aucoin, A., Callovini, L., Lin, K. K., & Haynes, P. L. (2023, June). 0023 Circadian fragmentation and stability distinguish employment status. In Sleep, 46, A10.
 Haynes, P. L., Fung, C., RojoWissar, D., Mayer, C., Glickenstein, D. A., & Billings, J. M. (2022). 0139 Work duration affects how priornight sleep predicts nextday energy expenditure in Emergency Response System telecommunicators. . In Sleep, 45, A62.
 Haynes, P. L., Apolinar, G., Thomson, C. A., Quan, S. F., Silva, G. E., Kobayashi, U., & Glickenstein, D. A. (2019, Fall). Social rhythm instability is associated with abdominal adiposity after involuntary job loss.. In Sleep.
 Glickenstein, D. A., Kobayashi, U., Silva, G. E., Quan, S. F., Thomson, C. A., Apolinar, G., & Haynes, P. L. (2020, June). Social rhythm instability is associated with abdominal adiposity after involuntary job loss.. In Sleep, 43, A397398.
 Haynes, P. L., Glickenstein, D. A., Thomson, C. A., Liu, Y., & Mayer, C. M. (2020, June). Sleep fragmentation an sleep restriction are associated with increased energy intake among individuals who have involuntarily lost their jobs. In Sleep, 43, A398399.
 SkulasRay, A. C., Glickenstein, D. A., Silva Torres, G. E., Mayer, C., Thomson, C. A., RojoWissar, D. M., & Haynes, P. L. (2019, June). Longer Sleep Duration Precedes Greater Water Intake at Breakfast. In Sleep, 42, A72.
Presentations
 Miller, L., Glickenstein, D. A., & Lin, K. (2022). Applied Mathematics and Statistics for DataDriven Discovery. SIAM Conference on Applied Mathematics Education.
 Glickenstein, D. A. (2021, April). Discrete conformal geometry and adversarial examples of neural networks. University of Wyoming colloquium. Laramie, WY (online).
 Glickenstein, D. A. (2021, April). The zoo of discrete conformal structures. Workshop on the Geometry of Circle Packings. Toronto, Canada (online): Fields Institute.
 Glickenstein, D. A. (2021, May). Determinant of finite volume Laplacian.. Fields Institute Seminar. Toronto, Canada (online): Fields Institute.
 Glickenstein, D. A. (2021, November). Discrete conformal geometry and adversarial examples of neural networks. Math of Data and Decisions at Davis seminar. Davis, CA (online): UC Davis.
 Butler, E. A., Glickenstein, D. A., Silva Torres, G. E., Quan, S. F., Thomson, C. A., & Haynes, P. L. (2019, Spring). Inconsistent Social Rhythms are Associated with Higher Waist Circumference Following Job Loss. Society of Behavioral Medicine annual meeting. Washington D.C.: Society of Behavioral Medicine.
 Glickenstein, D. A. (2019, February). Discrete Conformal and Harmonic Maps for Surface Analysis.. Analysis, Dynamics, and Applications Seminar. Tucson, AZ.
 Glickenstein, D. A. (2016, 12). 3 invited talks. 9th Minimeeting in Differential Geometry. Guanajuato, Mexico: CIMAT.
 Glickenstein, D. A. (2015, 01). The RG2 bracket flow on Lie groups and related flows. Special Session on Ricci Curvature for Homogeneous Spaces and Related Topics, Joint Mathematics Meetings. San Antonio, TX: AMS/MAA.
 Glickenstein, D. A. (2015, 12). Curvature Flows on Homogeneous Spaces: Applications of the Bracket Flow. SIAM Conference on Analysis of PDE: Session on PDE and Geometric Analysis. Scottsdale, AZ: SIAM.
 Glickenstein, D. A. (2014, 04). Numerical Riemannian Geometry. Arizona State Differential Geometry Seminar. Tempe, AZ.
Poster Presentations
 Haynes, P. L., Apolinar, G., Thomson, C. A., Quan, S. F., Silva, G. E., Kobayashi, U., & Glickenstein, D. A. (2020, Spring). Social rhythm instability is associated with abdominal adiposity after involuntary job loss.. Sleep.
 Haynes, P. L., Glickenstein, D. A., Thomson, C. A., Liu, Y., & Mayer, C. M. (2020, Spring). Sleep fragmentation an sleep restriction are associated with increased energy intake among individuals who have involuntarily lost their jobs. Sleep.
 Quan, S. F., Sherrill, D. L., Glickenstein, D. A., Oliver, R., Nair, U. S., RojoWissar, D., Gengler, D., Silva Torres, G. E., & Haynes, P. L. (2017, March). High prevalence of over the counter sleep aid use among individuals who have experienced involuntary job loss. Society of Behavioral Medicine. San Diego, CA.
Reviews
 Chow, B., Glickenstein, D. A., & Luo, F. (2016. Ricci flow for shape analysis and surface registration: theories, algorithms and applications, by Wei Zeng and Xianfeng David Gu.More infoThis is a book review, but it is really more of a review paper with a bit of a book review at the end.