Alan Lew **
**

I am a Postdoctoral Associate at the Department of Mathematical Sciences at Carnegie Mellon University. Previously, I was a postdoc at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem. I finished my PhD studies at the Mathematics Department at the Technion, Israel Institute of Technology, under the supervision of Prof. Roy Meshulam.

My research is in the area of Combinatorics. I like to work on problems related to geometry and topology (such as the study of collapsibility and Leray numbers of simplicial complexes and their relation to Helly-type theorems, or questions about the rigidity of graphs). I am also interested in the study of Laplacian (and Laplacian-like) operators on graphs and simplicial complexes.

Preprints

M. Krivelevich, A. Lew, P. Michaeli, "Rigid partitions: from high connectivity to random graphs", arXiv:2311.14451.

A. Lew, "Asymptotic behaviour of Laplacian eigenvalues of subspace inclusion graphs", arXiv:2308:08397.

A. Lew, "Laplacian eigenvalues of independence complexes via additive compound matrices", arXiv:2307.14496.

A. Lew, "Garland's method for token graphs", arXiv:2305.02406.

A. Lew, E. Nevo, Y. Peled, O. E. Raz, "Rigidity expander graphs", arXiv:2304.01306.

Published papers

M. Kim, A. Lew, “Extensions of the Colorful Helly Theorem for d-collapsible and d-Leray complexes”, Forum of Mathematics, Sigma, Volume 12 (2024).

A. Lew, E. Nevo, Y. Peled, O. E. Raz, "On the d-dimensional algebraic connectivity of graphs", Israel Journal of Mathematics, Volume 256 (2023).

M. Kim, A. Lew, “Leray numbers of tolerance complexes”, Combinatorica, Volume 43 (2023).

A. Lew, E. Nevo, Y. Peled, O. E. Raz, "Sharp threshold for rigidity of random graphs", Bulletin of the London Mathematical Society, Volume 55 Issue 1, (2022).

M. Kim, A. Lew, “Complexes of graphs with bounded independence number”, Israel Journal of Mathematics, Volume 249 (2022).

A. Lew, “Representability and boxicity of simplicial complexes”, Discrete & Computational Geometry, Volume 68 (2021)

A. Lew, “Collapsibility of simplicial complexes of hypergraphs”, The Electronic Journal of Combinatorics , Volume 26 Issue 4 (2019).

A. Lew, “Spectral gaps, missing faces and minimal degrees”, Journal of Combinatorial Theory, Series A , Volume 169 (2019).

A. Lew, “The Spectral Gaps of Generalized Flag Complexes and a Geometric Hall-type Theorem”, International Mathematics Research Notices , Volume 2020 Issue 11 (2018).

Extended Abstract

M. Kim, A. Lew, “Complexes of graphs with bounded independence number (extended abstract)”, Proceedings of the 32nd International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire, Issue 84B (2020).

Theses

A. Lew, “Studies in topological combinatorics ”, Ph. D. Thesis, Technion - Advisor: Roy Meshulam (2021).

- A. Lew, “Spectral gaps of generalized flag complexes”, M. Sc. Thesis, Technion - Advisor: Roy Meshulam (2017).

Presentations and Posters

Asymptotic behavior of Laplacian eigenvalues of subspace inclusion graphs

Eigenvalues of high dimensional Laplacian operators

My Scratch user page, including some interactive math demonstrations, games and puzzles.