mathematics

Shahar Mozes

Shahar Mozes is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Shahar Mozes rather than just read about it. In short: Shahar Mozes (Hebrew: שחר מוזס) is an Israeli mathematician. Mozes received in 1991, his doctorate from the Hebrew University of Jerusalem with thesis Actions of Cartan subgroups under the supervision of Hillel Fürstenberg.

Key takeaways

Shahar Mozes belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Shahar Mozes to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Shahar Mozes from memory before moving on to harder problems.

Reference excerpt

Shahar Mozes (Hebrew: שחר מוזס) is an Israeli mathematician. Mozes received in 1991, his doctorate from the Hebrew University of Jerusalem with thesis Actions of Cartan subgroups under the supervision of Hillel Fürstenberg. At the Hebrew University of Jerusalem, Mozes became in 1993 a senior lecturer, in 1996 associate professor, and in 2002 a full professor. Moses does research on Lie groups and discrete subgroups of Lie groups, geometric group theory, ergodic theory, and aperiodic tilings. His collaborators include Jean Bourgain, Alex Eskin, Elon Lindenstrauss, Gregory Margulis, and Hee Oh. In 2000 Mozes received the Erdős Prize. In 1998 he was an invited speaker with talk Products of trees, lattices and simple groups at the International Congress of Mathematicians (ICM) in Berlin. He was a plenary speaker at the ICM Satellite Conference on "Geometry Topology and Dynamics in Negative Curvature" held at the Raman Research Institute of the International Centre for Theoretical Sciences (ICTS) from August 2 to August 7, 2010.

Selected publications Mozes, Shahar (1989). "Tilings, substitution systems and dynamical systems generated by them". Journal d'Analyse Mathématique. 53 (1): 139–186. doi:10.1007/BF02793412. ISSN 0021-7670. Mozes, Shahar (1990). "Reflection processes on graphs and Weyl groups". Journal of Combinatorial Theory, Series A. 53 (1): 128–142. doi:10.1016/0097-3165(90)90024-Q. ISSN 0097-3165. Mozes, Shahar (1992). "Mixing of all orders of Lie groups actions". Inventiones Mathematicae. 107 (1): 235–241. Bibcode:1992InMat.107..235M. doi:10.1007/BF01231889. ISSN 0020-9910. Lubotzky, Alexander; Mozes, S.; Raghunathan, M. S. (1993). "Cyclic subgroups of exponential growth and metrics on discrete groups" (PDF). C. R. Acad. Sci. Paris. Séries I. 317: 735. Archived from the original (PDF) on 2022-12-23. Retrieved 2019-12-01. Mozes, Shahar (1995). "Epimorphic subgroups and invariant measures". Ergodic Theory and Dynamical Systems. 15 (6): 1207–1210. doi:10.1017/S0143385700009871. ISSN 0143-3857. Burger, M.; Mozes, S. (1996). "CAT(-1)-Spaces, Divergence Groups and their Commensurators". Journal of the American Mathematical Society. 9 (1): 57–93. doi:10.1090/S0894-0347-96-00196-8. JSTOR 2152840. Eskin, Alex; Mozes, Shahar; Shah, Nimish (1996). "Unipotent Flows and Counting Lattice Points on Homogeneous Varieties". The Annals of Mathematics. 143 (2): 253. doi:10.2307/2118644. JSTOR 2118644. S2CID 18628583. Eskin, A.; Mozes, S.; Shah, N. (1997). "Non-divergence of translates of certain algebraic measures". Geometric and Functional Analysis. 7: 48–80. doi:10.1007/PL00001616. Burger, Marc; Mozes, Shahar (1997). "Finitely presented products of trees" (PDF). C. R. Acad. Sci. Paris. Séries I. 324: 747–752. doi:10.1016/S0764-4442(97)86938-8. Mozes, S. (1997). "Aperiodic tilings". Inventiones Mathematicae. 128 (3): 603–611. Bibcode:1997InMat.128..603M. doi:10.1007/s002220050153. Eskin, A.; Margulis, G.; Mozes, S. (1998). "Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture". Annals of Mathematics. 147 (1): 93–141. doi:10.2307/120984. JSTOR 120984. Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S. (2000). "The word and Riemannian metrics on lattices of semisimple groups". Publications Mathématiques de l'IHÉS. 91: 5–53. doi:10.1007/BF02698740. Burger, Marc; Mozes, Shahar (2000). "Groups acting on trees: from local to global structure" (PDF). Publications Mathématiques de l'IHÉS. 92: 113–150. doi:10.1007/BF02698915. Burger, Marc; Mozes, Shahar (2000). "Lattices in product of trees" (PDF). Publications Mathématiques de l'IHÉS. 92: 151–194. doi:10.1007/BF02698916. Eskin, Alex; Mozes, Shahar; Oh, Hee (2002). "Uniform exponential growth for linear groups". International Mathematics Research Notices. 2002 (31): 1675–1683. arXiv:math/0108157. doi:10.1155/S1073792802108099. ISSN 1073-7928. Glasner, Yair; Mozes, Shahar (2005). "Automata and Square Complexes". Geometriae Dedicata. 111: 43–64. arXiv:math/0306259. doi:10.1007/s10711-004-1815-2. Druţu, Cornelia; Mozes, Shahar; Sapir, Mark (2009). "Divergence in lattices in semisimple Lie groups and graphs of groups". Transactions of the American Mathematical Society. 362 (5): 2451–2505. arXiv:0801.4141. doi:10.1090/S0002-9947-09-04882-X. Bourgain, Jean; Furman, Alex; Lindenstrauss, Elon; Mozes, Shahar (2011). "Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus". Journal of the American Mathematical Society. 24: 231–280. doi:10.1090/S0894-0347-2010-00674-1.

References

External links "Plenary lecture 9 by Shahar Mozes". YouTube. International Centre for Theoretical Sciences. 2 November 2016. (ICTS Conference, August 2010 — Mozes describes joint work with Bourgain, Furman, and Lindenstrauss.)

Worked examples

Example 1 — a first encounter with Shahar Mozes

Start with the simplest possible case. Write down what Shahar Mozes claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Shahar Mozes before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Shahar Mozes ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Shahar Mozes

In research: Shahar Mozes appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Shahar Mozes in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Shahar Mozes is common in secondary-school and first-year university syllabi. It links to neighbouring topics Academic staff of the Hebrew University of Jerusalem, Asian mathematician stubs, Erdős Prize recipients, so understanding it makes those chapters shorter.
In everyday life: Look for Shahar Mozes outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Shahar Mozes in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Shahar Mozes means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Shahar Mozes out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Shahar Mozes in simple terms?

Why does Shahar Mozes matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Shahar Mozes?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Shahar Mozes.