##### Papers

**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 **Lazar, E.A.**"Classifying Structure in Two-Dimensional Point Sets via Voronoi Topology", unpublished notes.**Lazar, E.A.**and Pemantle, R. "Coarsening in one dimension: invariant and asymptotic states", arXiv,*Israel J. Math.*221:1, 2017.- Leipold, H.,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, Max Planck Institute for Mathematics

Chris Marianetti, Columbia University

Dan Lewis, Rensselaer Polytechnic Institute

David Srolovitz, University of Pennsylvania

Frank Lutz, Technische Universität Berlin

Hannes Leipold, University of Southern California

Henk Hilhorst, Laboratoire de Physique Théorique

Jeremy Mason, University of California, Davis

Jian Han, University of Pennsylvania

Ken Brakke, Susquehanna University

Min Young Ha, Seoul National University

Neel Patel, University of Michigan

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, Seoul National University

Trevor Keller, National Institute of Standards and Technology

Won Bo Lee, Seoul National University

Youn-Woo Lee, Seoul National University