Research
////////////////////////////////////////////


Papers

Dotterrer, Dominic, Guth, Larry. "2-complexes with large 2-girth." To appear in Discrete & Computational Geometry. arxiv:1509.03871.

Matthew Kahle. "Random simplicial complexes." Book chapter, to appear in Handbook of Discrete & Computational Geometry (3rd edition). arXiv:1607.07069.

Bobrowski, Omer, Skraba, Primoz. "Maximally Persistent Cycles in Random Geometric Complexes." To appear in Annals of Applied Probability. arXiv:1509.04347.

Omer Bobrowski, Matthew Kahle. "Topology of random geometric complexes: a survey." (to appear in AMS Proceedings of Symposia in Applied Mathematics). arXiv:1409.4734.

Christopher Hoffman, Matthew Kahle, Elliot Paquette. "The threshold for integer homology in random d-complexes." Discrete & Computational Geometry. May 2017. arXiv:1308.6232.

Matthew Kahle, Elizabeth Meckes. "Erratum: Limit theorems for Betti numbers of random simplicial complexes." Homology, Homotopy and Applications. Jan 2016. arXiv:1501.03759.

Matthew Kahle, Boris Pittel. "Inside the critical window for cohomology of random k-complexes." Random Structures & Algorithms . Jan 2016. arXiv:1301.1324.

Matthew Kahle, Birra Taha. "New lower bounds on $\chi(R^d)$ for $d=8 \dots 12$." Geombinatorics . Jul 2015. arXiv 1409:1278.

Michael Davis, Matthew Kahle. "Random graph products of finite groups are rational duality groups." J. Topol. . Feb 2014.

Matthew Kahle. "Topology of random simplicial complexes: a survey." To appear in AMS Contemporary Volumes in Mathematics. Nov 2014. arXiv:1301.7165.

Matthew Kahle. "Sharp vanishing thresholds for cohomology of random flag complexes." Ann. of Math.. Aug 2014. arXiv:1207.0149.

Yuliy Baryshnikov, Peter Bubenik, Matthew Kahle. "Min-type Morse theory for configuration spaces of hard spheres." International Mathematics Research Notices. Feb 2013. arxiv:1108.3061.

Matthew Kahle, Elizabeth Meckes. "Limit theorems for Betti numbers of random simplicial complexes." Homology, Homotopy and Applications. May 2013. arXiv:1009.4130.

Dominic Dotterrer, Matthew Kahle. "Coboundary expanders." Journal of Topology and Analysis. Nov 2012. arXiv:1012.5316.

Matthew Kahle. "Sparse locally-jammed disk packings." Annals of Combinatorics. Oct 2012.

Gunnar Carlsson, Jackson Gorham, Matthew Kahle, Jeremy Mason. "Computational topology for configuration spaces of hard disks." Physical Review E. Jan 2012. arxiv:1301.7165.

Matthew Kahle. "Random geometric complexes." Discrete & Computational Geometry. Jan 2011. arXiv:0910.1649.

Eric Babson, Christopher Hoffman, Matthew Kahle. "The fundamental group of random 2-complexes." J. Amer. Math. Soc.. Jan 2011. arXiv:0711.2704.

Matthew Kahle. "Topology of random clique complexes." Discrete Math. Aug 2009. arXiv:0605536.

Matthew Kahle. "Points in a triangle forcing small triangles." Geombinatorics. Oct 2009. arXiv:0811.2449.

Matthew Kahle. "The neighborhood complex of a random graph." Journal of Combinatorial Theory, Series A. Sep 2007. The neighborhood complex of a random graph.

Matthew Kahle. "Scatters, unavoidable shapes, and crystallization." Geombinatorics. Oct 2005.

Preprints

Christopher Hoffman, Matthew Kahle, Elliot Paquette. "Spectral gaps of random graphs and applications to random topology." arXiv:1201.0425.

Sukhada Fadnavis, Matthew Kahle. "Warmth and mobility of random graphs." arXiv:1009.0792.

In Preparation

Matthew Kahle. "Configuration spaces of hard spheres in an infinite strip (w/ R. MacPherson)."

Talks

Matthew Kahle. "Survey talk on Random Simplicial Complexes." Sep 2017.