Alan Lew

          Link to arXiv papers

          Google scholar profile

Preprints

• An approximate version of Brouwer's Laplacian conjecture. arXiv:2601.17575.
• An eigenvalue interlacing approach to Garland's method. arXiv:2508.17279.
• Sums of Laplacian eigenvalues and sums of degrees. arXiv:2508.04209.
• Stiffness matrices of graph blow-ups and the d-dimensional algebraic connectivity of complete bipartite graphs, with Yunseong Jung. arXiv:2504.01181.
• Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs. arXiv:2410.04563.

Published Papers

• On the k-volume rigidity of a simplicial complex in R^d, with Eran Nevo, Yuval Peled and Orit Raz. Forum of Mathematics, Sigma, Volume 13, e195, 2025.
• Minimum degree conditions for graph rigidity, with Michael Krivelevich and Peleg Michaeli. Bulletin of the London Mathematical Society, Volume 58, Issue 1, 2025.
• Rigid partitions: from high connectivity to random graphs, with Michael Krivelevich and Peleg Michaeli. Journal of Combinatorial Theory, Series B, Volume 175, 2025.
• Rigidity expander graphs, with Eran Nevo, Yuval Peled and Orit Raz. Combinatorica, Volume 45, 2025.
• Laplacian eigenvalues of independence complexes via additive compound matrices. Discrete Analysis, 2024:15, 2024.
• Asymptotic behavior of Laplacian eigenvalues of subspace inclusion graphs. Journal of the London Mathematical Society, Volume 110, Issue 3, 2024.
• Garland's method for token graphs. Linear Algebra and its Applications, Volume 700, 2024.
• Extensions of the Colorful Helly Theorem for d-collapsible and d-Leray complexes, with Minki Kim. Forum of Mathematics, Sigma, Volume 12, 2024.
• On the d-dimensional algebraic connectivity of graphs, with Eran Nevo, Yuval Peled and Orit Raz. Israel Journal of Mathematics, Volume 256, 2023.
• Leray numbers of tolerance complexes, with Minki Kim. Combinatorica, Volume 43, 2023.
• Sharp threshold for rigidity of random graphs, with Eran Nevo, Yuval Peled and Orit Raz. Bulletin of the London Mathematical Society, Volume 55, Issue 1, 2022.
• Complexes of graphs with bounded independence number, with Minki Kim.  Israel Journal of Mathematics, Volume 249, 2022.
• Representability and boxicity of simplicial complexes. Discrete & Computational Geometry, Volume 68, 2021.
• Collapsibility of simplicial complexes of hypergraphs. The Electronic Journal of Combinatorics, Volume 26, Issue 4, 2019.
• Spectral gaps, missing faces and minimal degrees. Journal of Combinatorial Theory, Series A, Volume 169, 2019.
• The Spectral Gaps of Generalized Flag Complexes and a Geometric Hall-type Theorem. International Mathematics Research Notices, Volume 2020, Issue 11, 2018.

Extended Abstracts

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

Theses

• Studies in topological combinatorics. Ph. D. Thesis, Technion - Advisor: Roy Meshulam, 2021.
• Spectral gaps of generalized flag complexes. M. Sc. Thesis, Technion - Advisor: Roy Meshulam, 2017.

• New approaches to Garland’s method
• Sums of Laplacian eigenvalues and sums of degrees
• Asymptotic behavior of Laplacian eigenvalues of subspace inclusion graphs
• Eigenvalues of high dimensional Laplacian operators
• Rigidity expander graphs
• 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

• Art Galleries
• Eden Paint App (a paint application with automatic coloring based on the Eden growth model)
• My Scratch user page, including some interactive math demonstrations, games and puzzles