##### Papers

- Worlitzer, V.M., Ariel, G., and Lazar, E.A., "The Voronoi pair correlation function", arXiv, 2022.
- Lu, J., Lazar, E.A., and Rycroft, C.H., "An extension to VORO++ for multithreaded computation of Voronoi cells", arXiv, 2022.
- Lazar, E.A., Lu, J., and Rycroft, C.H., "Voronoi cell analysis: The shapes of particle systems", arXiv,
*Am. J. Phys.*90:469, 2022.

- Lazar, E.A. and Shoan, A. "Voronoi chains, blocks, and clusters in perturbed square lattices", arXiv,
*J. Stat. Mech.*103204, 2020.

- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J., "Distribution of Topological Types in Grain-Growth Microstructures",
arXiv,
*Phys. Rev. Lett.*125:015501, 2020.

- Yoon, T.J., Lazar, E.A., Ha, M.Y., Lee, W.B., and Lee, Y-W., "Topological extension of the isomorph theory based on the Shannon entropy", arXiv,
*Phys. Rev. E.*100:012118, 2019. - Yoon, T.J., Lazar, E.A., Ha, M.Y., Lee, W.B., and Lee, Y-W., "Topological generalization of the rigid-nonrigid transition in soft-sphere and
hard-sphere fluids", arXiv,
*Phys. Rev. E.*99:052603, 2019. - Yoon, T.J., Ha, M.Y., Lazar, E.A., Lee, W.B., and Lee, Y-W., "Topological Characterization of Rigid-Nonrigid Transition across the Frenkel Line", arXiv,
*J. Phys. Chem. Lett.*9:6524, 2018. - Lazar, E.A. "VoroTop: Voronoi Cell Topology Visualization and Analysis Toolkit", arXiv,
*Model. Simul. Mater. Sci. Eng.*26:1, 2017. - Lazar, E.A. and Srolovitz, D.J. "Topological Analysis of Local Structure in Atomic Systems",
*preprint*, chapter in*Statistical Methods for Materials Science: The Data Science of Microstructure Characterization*, CRC Press 2019. - Lutz, F.H., Mason, J.K., Lazar, E.A., and MacPherson, R.D. "Roundness of Grains in Cellular Microstructures", arXiv,
*Phys. Rev. E.*96:023001, 2017. - Lazar, E.A. "Classifying Structure in Two-Dimensional Point Sets via Voronoi Topology", unpublished notes.
- Lazar, E.A. and Pemantle, R. "Coarsening in one dimension: invariant and asymptotic states", arXiv,
*Israel J. Math.*221:1, 2017. - Leipold, H., Lazar, E.A., Brakke, K.A., and Srolovitz, D.J. "Statistical Topology of Perturbed Two-Dimensional Lattices", arXiv,
*J. Stat. Mech.*P043103, 2016.

- Landweber, P.S., Lazar, E.A., Patel, N. "On fiber diameters of continuous maps", arXiv,
*Amer. Math. Monthly*123:4, 2016 (see also "A Surprise For Big-Data Analytics"). - Lazar, E.A., Han, J. and Srolovitz, D.J. "A Topological Framework for Local Structure Analysis in Condensed Matter", arXiv,
*Proc. Natl. Acad. Sci.*112:E5769, 2015. - Mason, J.K., Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "Geometric and
topological properties of the canonical grain growth microstructure", arXiv,
*Phys. Rev. E.*92:063308, 2015. - Wang, R., Lazar, E.A., Park, H., Millis, A.J., Marianetti, C.A. "Selectively Localized Wannier
Functions", arXiv,
*Phys. Rev. B.*90:165125, 2014. - Hilhorst, H.J., Lazar, E.A. "Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations", arXiv,
*J. Stat. Mech.*10:P10021, 2014. - Keller, T., Cutler, B., Lazar, E.A., Yauney, G., Lewis, D.J. "Comparative Grain Topology",
*Acta Materialia*, 66:414, 2014. - Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "Statistical topology of three-dimensional Poisson-Voronoi cells
and cell boundary networks", arXiv,
*Phys. Rev. E.*88:063309, 2013. - Mason, J.K., Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "Statistical topology of cellular networks in two and three dimensions",
*Phys. Rev. E.*86:051128, 2012. - Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "Complete topology of cells, grains, and bubbles in three-dimensional microstructures", arXiv,
*Phys. Rev. Lett.*109:095505, 2012. - Mason, J.K., Ehrenborg, R. and Lazar, E.A. "A geometric
formulation of the Law of Aboav-Weaire in two and three dimensions",
*J. Phys. A*45:065001, 2012. - Lazar, E.A., "The Evolution of Cellular Structures via Curvature Flow", Thesis, Princeton University, 2011.
- Lazar, E.A., Mason, J.K., MacPherson, R.D. and Srolovitz, D.J. "A more accurate
three-dimensional grain growth algorithm",
*preprint*,*Acta Materialia*, 59:6837, 2011.

- Lazar, E.A., MacPherson, R.D. and Srolovitz, D.J. "A more
accurate two-dimensional grain growth algorithm",
*preprint*,*Acta Materialia*, 58:364, 2010. - Lazar, E.A. "Molecular Dynamic Studies in the Fracturing of Metals." Honors Thesis, Yeshiva University, 2005.
- Lazar, E.A. "A Visual Demonstration of the Fundamental Theorem of Calculus",
*unpublished*, 2003.

##### Software

*VoroTop*is a modern set of open-source tools for analyzing structure of spatial point sets in three dimensions. The power of this approach results from its coarse-graining of structural data in a natural configuration space, instead of in the image of this space under a continuous mapping, which has notable theoretical restrictions.

##### Coauthors and collaborators

Aaron Koolyk, Hebrew University

Amanda Redlich, UMass Lowell

Amir Shoan, Bar-Ilan University

Andrew Millis, Columbia University

Benjamin Matschke, Boston University

Chris Marianetti, Columbia University

Chris Rycroft , University of Wisconsin—Madison

Dan Lewis, Rensselaer Polytechnic Institute

David Srolovitz, The University of Hong Kong

Frank Lutz, Technische Universität Berlin

Gil Ariel, Bar Ilan University

Hannes Leipold, University of Southern California

Henk Hilhorst, Laboratoire de Physique Théorique

Jeremy Mason, University of California, Davis

Jian Han, City University of Hong Kong

Amanda Redlich, UMass Lowell

Amir Shoan, Bar-Ilan University

Andrew Millis, Columbia University

Benjamin Matschke, Boston University

Chris Marianetti, Columbia University

Chris Rycroft , University of Wisconsin—Madison

Dan Lewis, Rensselaer Polytechnic Institute

David Srolovitz, The University of Hong Kong

Frank Lutz, Technische Universität Berlin

Gil Ariel, Bar Ilan University

Hannes Leipold, University of Southern California

Henk Hilhorst, Laboratoire de Physique Théorique

Jeremy Mason, University of California, Davis

Jian Han, City University of Hong Kong

Jiayin Lu, Harvard University

Ken Brakke, Susquehanna University

Min Young Ha, Seoul National University

Neel Patel, Instituto de Ciencias Matemáticas

Peter Landweber, Rutgers University

Richard Ehrenborg, University of Kentucky

Robert MacPherson, Institute for Advanced Study

Robin Pemantle, University of Pennsylvania

Runzhi Wang, Columbia University

Shlomo Ta'asan, Carnegie Mellon University

Tae Jun Yoon, Los Alamos National Laboratory

Trevor Keller, National Institute of Standards and Technology

Vasco Worlitzer, Bar Ilan University

Won Bo Lee, Seoul National University

Youn-Woo Lee, Seoul National University

Ken Brakke, Susquehanna University

Min Young Ha, Seoul National University

Neel Patel, Instituto de Ciencias Matemáticas

Peter Landweber, Rutgers University

Richard Ehrenborg, University of Kentucky

Robert MacPherson, Institute for Advanced Study

Robin Pemantle, University of Pennsylvania

Runzhi Wang, Columbia University

Shlomo Ta'asan, Carnegie Mellon University

Tae Jun Yoon, Los Alamos National Laboratory

Trevor Keller, National Institute of Standards and Technology

Vasco Worlitzer, Bar Ilan University

Won Bo Lee, Seoul National University

Youn-Woo Lee, Seoul National University