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.

Publications

Link to arXiv papers

Google scholar profile

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

• Rigidity expander graphs (updated version)

• Leray numbers of tolerance complexes

• Representability and boxicity of simplicial complexes

• Collapsibility of simplicial complexes of graphs and hypergraphs

• Complexes of graphs with bounded independence number (interactive poster)

• Spectral gaps of generalized flag complexes (slides) + poster

Extra

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