Publications

(the preprints have only arxiv links, the published papers have both the journal link and arxiv link and the content of those may differ)

Preprints

Bounding the High Order Edge Expansion via High Order Radius, joint with Tali Kaufman, Arxiv link.

Simplicial complexes arising from elementary matrix groups and high dimensional expanders, joint with Tali Kaufman, Arxiv link.

High dimensional analogue of metric distortion for simplicial complexes, on hold due to major revisions in order to make the results accessible. Arxiv link.

Journal Publications

Local Spectral Expansion Approach to High Dimensional Expanders Part II: Mixing and Geometrical overlapping, Discrete and Computational Geometry, in press, Journal linkArxiv link.

Non p-norm approximated Groups, joint with Alex Lubotzky, Journal d’Analyse Mathematique, in press, Arxiv link.

High order random walks: Beyond spectral gaps, joint with Tali Kaufman, Combinatorica, in press, Arxiv link.

Local spectral expansion approach to high dimensional expanders part I: Descent of spectral gaps, Discrete and Computational Geometry, Volume 59, issue 2, 2018, 293-330. Journal linkArxiv link.

Angle criteria for uniform convergence of averaged projections and cyclic or random products of projections, Israel Journal of Mathematics, Volume 223, issue 1, 2018, 343-362 . Journal link, Arxiv link

Vanishing of cohomology with coefficients in representations on Banach spaces of groups acting on Buildings, Commentarii Mathematici Helvetici, 92 (2017), no. 2, 389–428.  Journal link, Arxiv link.

Averaged projections, angles between groups and strengthening of Banach property (T), Mathematische Annalen, 367 (2017), no. 1-2, 623–666. Journal link, Arxiv link.

Property (T) for groups acting on simplicial complexes through taking an “average” of Laplacian eigenvalues, Groups, Geometry and Dynamics,Volume 9, Issue 4, 2015, pp. 1131–1152, Journal link, Arxiv link.

Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes,  Groups, Geometry and Dynamics, Volume 9, Issue 1, 2015, pp. 67–101, Journal link, Arxiv link.

Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces, Mathematische Zeitschrift. (2014) 278: 649-661, Journal link, Arxiv link.

An intermediate quasi-isometric invariant between subexponential asymptotic dimension growth and Yu’s Property A, Internat. J. Algebra and Comput., (2014) 24 (6) : 909-922, Journal link, Arxiv link.

Property A and the existence of a Markov process with a trivial Poisson boundary, Bull. London Math. Soc. (2014) 46 (4): 836-846, Journal link, Arxiv link.

 

Conference Publications

High order random walks: Beyond spectral gaps, joint with Tali Kaufman, Published in RANDOM (conference proceedings), RANDOM2018.

Contruction of new examples of high dimensional expanders, joint with Tali Kaufman, Published in STOC 2018 (conference proceedings), STOC2018.

 

 

Lecture Notes

Lecture notes of a course I gave on “Expander graphs and group theory”.