mathematics

Tsachik Gelander

Tsachik Gelander 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 Tsachik Gelander rather than just read about it. In short: Tsachik Gelander (Hebrew: צחיק גלנדר) is an Israeli mathematician working in the fields of Lie groups, topological groups, symmetric spaces, rigidity, lattices and discrete subgroups (of Lie groups as well as general locally compact groups). He was a professor of mathematics at the Hebrew University of Jerusalem from 2006 until 2013, and has been at the Weizmann Institute of Science from 2013, and at Northwestern Un…

Key takeaways

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

Reference excerpt

Tsachik Gelander (Hebrew: צחיק גלנדר) is an Israeli mathematician working in the fields of Lie groups, topological groups, symmetric spaces, rigidity, lattices and discrete subgroups (of Lie groups as well as general locally compact groups). He was a professor of mathematics at the Hebrew University of Jerusalem from 2006 until 2013, and has been at the Weizmann Institute of Science from 2013, and at Northwestern University from 2022. Gelander earned his PhD from the Hebrew University of Jerusalem in 2003, under the supervision of Shahar Mozes. His doctoral dissertation, Counting Manifolds and Tits Alternative, won the Haim Nessyahu Prize in Mathematics, awarded by the Israel Mathematical Union for the best annual doctoral dissertation in mathematics. After holding a Gibbs Assistant Professorship at Yale University, and faculty positions at the Hebrew University of Jerusalem and the Weizmann Institute of Science, Gelander joined Northwestern where he is currently a professor of mathematics. He contributed to the theory of lattices, Fuchsian groups and local rigidity, and the work on Chern's conjecture and the Derivation Problem. Among his well-known results is the solution to the Goldman conjecture, i.e. that the action of O u t ( F n ) {\displaystyle Out(F_{n})} on the deformation variety of a compact Lie group is ergodic when n {\displaystyle n} is at least 3 {\displaystyle 3} . He gave the distinguished Nachdiplom Lectures at ETH Zurich in 2011, and was an invited speaker at the 2018 International Congress of Mathematicians, giving a talk under the title of Asymptotic Invariants of Locally Symmetric Spaces. He was one of the recipients of the first call of the European Research Council (ERC) Starting Grant (2007), and in 2021 he won the ERC Advanced Grant.

Selected publications Gelander, Tsachik (15 September 2004). "Homotopy type and volume of locally symmetric manifolds". Duke Mathematical Journal. 124 (3). Duke University Press. arXiv:math/0111165. doi:10.1215/s0012-7094-04-12432-7. ISSN 0012-7094. S2CID 14272953. Bader, Uri; Furman, Alex; Gelander, Tsachik; Monod, Nicolas (2007). "Property (T) and rigidity for actions on Banach spaces". Acta Mathematica. 198 (1). International Press of Boston: 57–105. arXiv:math/0506361. doi:10.1007/s11511-007-0013-0. ISSN 0001-5962. S2CID 5739931. Breuillard, Emmanuel; Gelander, Tsachik (1 September 2007). "A topological Tits alternative". Annals of Mathematics. 166 (2): 427–474. arXiv:math/0403043. doi:10.4007/annals.2007.166.427. ISSN 0003-486X. S2CID 14859975. Breuillard, E.; Gelander, T. (3 May 2008). "Uniform independence in linear groups". Inventiones Mathematicae. 173 (2). Springer Science and Business Media LLC: 225–263. arXiv:math/0611829. Bibcode:2008InMat.173..225B. doi:10.1007/s00222-007-0101-y. ISSN 0020-9910. S2CID 16029687. Gelander, Tsachik; Karlsson, Anders; Margulis, Gregory (2008). "Superrigidity, generalized harmonic maps and uniformly convex spaces". Geometric and Functional Analysis. 17 (5): 1524–1550. arXiv:math/0606256. Bibcode:2008InMat.173..225B. doi:10.1007/s00039-007-0639-2. S2CID 16029687. Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner (5 October 2010). "Counting arithmetic lattices and surfaces". Annals of Mathematics. 172 (3): 2197–2221. arXiv:0811.2482. doi:10.4007/annals.2010.172.2197. ISSN 0003-486X. S2CID 14172846. Bader, U.; Gelander, T.; Monod, N. (27 October 2011). "A fixed point theorem for L 1 spaces". Inventiones Mathematicae. 189 (1). Springer Science and Business Media LLC: 143–148. arXiv:1012.1488. doi:10.1007/s00222-011-0363-2. ISSN 0020-9910. S2CID 55594695. Abert, Miklos; Bergeron, Nicolas; Biringer, Ian; Gelander, Tsachik; Nikolav, Nikolay; Raimbault, Jean; Samet, Iddo (1 May 2017). "On the growth of $L^2$-invariants for sequences of lattices in Lie groups" (PDF). Annals of Mathematics. 185 (3). arXiv:1210.2961. doi:10.4007/annals.2017.185.3.1. ISSN 0003-486X. S2CID 106398777. Gelander, Tsachik; Levit, Arie (January 2018). "Local rigidity of uniform lattices". Commentarii Mathematici Helvetici. 93 (4): 781–827. arXiv:1605.01693. doi:10.4171/cmh/450. Gelander, Tsachik (2019). "A VIEW ON INVARIANT RANDOM SUBGROUPS AND LATTICES". Proceedings of the International Congress of Mathematicians (ICM 2018). WORLD SCIENTIFIC. pp. 1321–1344. arXiv:1807.06979. doi:10.1142/9789813272880_0099. ISBN 978-981-327-287-3. Fraczyk, Mikolaj; Gelander, Tsachik (January 2023). "Infinite volume and infinite injectivity radius". Annals of Mathematics. 197 (1): 389–421. arXiv:2101.00640. doi:10.4007/annals.2023.197.1.6.

References

Worked examples

Example 1 — a first encounter with Tsachik Gelander

Start with the simplest possible case. Write down what Tsachik Gelander 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 Tsachik Gelander 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 Tsachik Gelander 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 Tsachik Gelander

In research: Tsachik Gelander 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 Tsachik Gelander 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: Tsachik Gelander is common in secondary-school and first-year university syllabi. It links to neighbouring topics Hebrew University of Jerusalem alumni, Israeli mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Tsachik Gelander 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 Tsachik Gelander in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Tsachik Gelander 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 Tsachik Gelander out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tsachik Gelander in simple terms?

Why does Tsachik Gelander 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 Tsachik Gelander?

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 Tsachik Gelander.