Yaar Solomon's Home page - Research

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Research:

My Ph.D. dissertation can be found here.
Multiscale substitution movies can be downloaded here 1, 2.
An example of a multiscale tiling, in the OEIS (On-line Encyclopedia of Integer Sequences) can be found here.

Multiscale Example:

Multiscale example

Flow example

Publications and preprints

The net created from the Penrose tiling is biLipschitz to the integer lattice. arXiv. pdf. arXiv:0711.3707.

Substitution tilings and separated nets with similarities to the integer lattice. Israel Journal of Mathematics, 181, 445-460, (2011). pdf. Journal link. arXiv:0810.5225.

Functions of substitution tilings as a Jacobian. Proceedings of the American Mathematical Society, 141, 3853-3863, (2013). pdf. Journal link. arXiv:1005.1375.

A simple condition for bounded displacement. Journal of Mathematical Analysis and Applications, 414 (1), 134-148, (2014). pdf. Journal link. arXiv:1111.1690.

With David Simmons, A Danzer set for axis parallel boxes. Proceedings of the American Mathematical Society, 144 (6), 2725-2729, (2016). pdf. Journal link. arXiv:1409.0926.

With Barak Weiss, Dense forests and Danzer sets. Annales scientifiques de l'Ècole normale supèrieure, 49 (5), 1053-1074, (2016). pdf. Journal link. arXiv:1406.3807.

With Omri Solan and Barak Weiss, On problems of Danzer and Gowers and dynamics on the space of closed subsets of R^d. International Mathematics Research Notices (IMRN), 2017 (21), 6584–6598, (2017). pdf. Journal link. arXiv:1510.07179.

Continuously many bounded displacement non-equivalences in substitution tiling spaces. Journal of Mathematical Analysis and Applications, 492 (1), (2020). pdf. Journal link. arXiv:2004.07387.

With Michael Boshernitzan, On visibility problems with an infinite, discrete, set of obstacles. Discrete and Computational Geometry, 66 (2), 590-612, (2021). pdf. Journal link. arXiv:1805.11679.

With Dirk Frettlöh and Yotam Smilansky, Bounded displacement non-equivalence in substitution tilings. Journal of Combinatorial Theory Series A, 177, (2021), 105326. pdf. Journal link. arXiv:1907.01597.

With Yotam Smilansky, Multiscale substitution tilings. Proceedings of the London Mathematical Society, 123 (6), 517-564, (2021). pdf. Journal link. arXiv:2003.11735.

With Faustin Adiceam and Barak Weiss, Cut-and-project quasicrystals, lattices, and dense forests. Journal of the London Mathematical Society, 105 (2), 1167-1199, (2022). pdf. Journal link. arXiv:1907.03501.

With Yotam Smilansky, A dichotomy for bounded displacement equivalence of Delone sets. Ergodic Theory Dynamical Systems, 42 (8), 2693-2710, (2022). pdf. Journal link. arXiv:2011.00106.

With Yotam Smilansky, Discrepancy and rectifiability of almost linearly repetitive Delone sets. Nonlinearity, 35, 6204–6217, (2022). pdf. Journal link. arXiv:2109.14564.

With Shrey Sanadhya and Tom Meyerovitch, A note on reduction of tiling problems. Israel Journal of Mathematics, 267, 421-435, (2025). pdf. Journal link. arxiv:2211.07140.

With Shrey Sanadhya and Tom Meyerovitch, Periodicity of joint co-tiles in Z^d. Discrete Analysis, (Nov. 2024). pdf. Journal link. arxiv:2301.11255.

With Daniel Kalmanovich, On the stability, complexity, and distribution of similarity classes of the longest edge bisection process for triangles. pdf. arxiv:2601.13663.

List of Coauthors:

Faustin Adiceam, Michael Boshernitzan, Dirk Frettlöh, Daniel Kalmanovich, Tom Meyerovitch, Shrey Sanadhya, David Simmons, Yotam Smilansky, Omri Solan, Barak Weiss.

Contact information:

E-mail: yaars at bgu.ac.il.
Office:
     Building 58, Room 317
Phone numbers:
   +972 (0) 8 6477883 (Office),
   +972+972 (0) 8 6477650 (Fax),

Yaar Solomon,
Department of Mathematics,
Ben Gurion University of the Negev
Be'er Sheva, 84105, ISRAEL.