David A Glickenstein

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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.
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  We define barycentric coordinates on a Riemannian manifold using Karcher'scenter of mass technique applied to point masses for n+1 sufficiently closepoints, determining an n-dimensional 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 18-month study. Obesity.
• , T. D., & , D. G. (2021). Determinant of the finite volume Laplacian.
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  The 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 two-dimensional finiteelements on a non-Delaunay triangulation. Nonetheless, in many cases two- andthree-dimensional 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.
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  Thurston's circle packing approximation of the Riemann Mapping (proven togive the Riemann Mapping in the limit by Rodin-Sullivan) 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 discreteLipschitz-Killing 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), 208-216.
• 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 non-linear projections. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, 25(1), 481-490.
• Glickenstein, D. A. (2018). A Bug's Eye View: The Riemannian Exponential Map on Polyhedral Surfaces. MATHEMATICAL INTELLIGENCER, 40(2), 1-9.
• Glickenstein, D. A. (2018). Make PVC Polyhedra. Math Horizons, 25(3), 25-27. doi:10.1080/10724117.2018.1424463
• Glickenstein, D. A. (2018). Multi-Level Steiner Trees. 17th International Symposium on Experimental Algorithms (SEA 2018).
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  In the classical Steiner tree problem, given an undirected, connected graph$G=(V,E)$ with non-negative edge costs and a set of \emph{terminals}$T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$that spans the terminals. The problem is APX-hard; the best known approximationalgorithm has a ratio of $\rho = \ln(4)+\varepsilon < 1.39$. In this paper, westudy a natural generalization, the \emph{multi-level 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 Multi-level Network Design, Quality-of-Service Multicast tree,Grade-of-Service Steiner tree, and Multi-Tier 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 multi-level infrastructure.[Journal_ref: ]
• Glickenstein, D., & Liang, J. (2018). Asymptotic Behavior of beta-Polygon Flows. JOURNAL OF GEOMETRIC ANALYSIS, 28(3), 2902-2925.
• Glickenstein, D., & Thomas, J. (2017). Duality structures and discrete conformal variations of piecewise constant curvature surfaces. ADVANCES IN MATHEMATICS, 320, 250-278.
• Glickenstein, D., & Wu, L. (2017). Soliton metrics for two-loop renormalization group flow on 3D unimodular Lie groups. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 19(3), 1977-1982.
• Haynes, P. L., Silva, G. E., Howe, G. W., Thomson, C. A., Butler, E. A., Quan, S. F., Sherrill, D., Scanlon, M., Rojo-Wissar, 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., Rojo-Wissar, 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, S315-S315.
• Champion, D., Glickenstein, D., & Young, A. (2011). Regge's Einstein-Hilbert functional on the double tetrahedron. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 29(1), 108-124.
• Glickenstein, D. A. (2011). DISCRETE CONFORMAL VARIATIONS AND SCALAR CURVATURE ON PIECEWISE FLAT TWO- AND THREE-DIMENSIONAL MANIFOLDS. JOURNAL OF DIFFERENTIAL GEOMETRY, 87(2), 201-237.
• Glickenstein, D., & Payne, T. L. (2010). Ricci flow on three-dimensional, unimodular metric Lie algebras. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 18(5), 927-961.
• Glickenstein, D. A. (2008). Riemannian Groupoids and Solitons for Three-Dimensional Homogeneous Ricci and Cross-Curvature Flows. INTERNATIONAL MATHEMATICS RESEARCH NOTICES.
• Chow, B. t., & Glickenstein, D. (2007). Semidiscrete geometric flows of polygons. AMERICAN MATHEMATICAL MONTHLY, 114(4), 316-328.
• Glickenstein, D. A. (2007). A monotonicity property for weighted Delaunay triangulations. DISCRETE & COMPUTATIONAL GEOMETRY, 38(4), 651-664.
• Chow, B., Glickenstein, D., & Lu, P. (2006). Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature. MATHEMATISCHE ZEITSCHRIFT, 254(1), 1-28.
• Glickenstein, D. A. (2005). A combinatorial Yamabe flow in three dimensions. TOPOLOGY, 44(4), 791-808.
• Glickenstein, D. A. (2005). A maximum principle for combinatorial Yamabe flow. TOPOLOGY, 44(4), 809-825.
• Chow, B., Glickenstein, D., & Lu, P. (2003). Metric transformations under collapsing of Riemannian manifolds. MATHEMATICAL RESEARCH LETTERS, 10(5-6), 737-746.
• Glickenstein, D. A. (2003). Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates. GEOMETRY & TOPOLOGY, 7, 487-510.
• Glickenstein, D., & Strichartz, R. S. (1996). Nonlinear self-similar measures and their Fourier transforms. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 45(1), 205-220.

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., Rojo-Wissar, D., Mayer, C., Glickenstein, D. A., & Billings, J. M. (2022). 0139 Work duration affects how prior-night sleep predicts next-day 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, A397-398.
• 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, A398-399.
• Skulas-Ray, A. C., Glickenstein, D. A., Silva Torres, G. E., Mayer, C., Thomson, C. A., Rojo-Wissar, 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 Data-Driven 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 RG-2 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., Rojo-Wissar, 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.
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  This is a book review, but it is really more of a review paper with a bit of a book review at the end.