mathematics

Henri Moscovici

Henri Moscovici 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 Henri Moscovici rather than just read about it. In short: Henri Moscovici (born 5 May 1944) is a Romanian-American mathematician, specializing in non-commutative geometry and global analysis. Moscovici received his undergraduate degree in 1966 and his doctorate in 1971 at the University of Bucharest under the supervision of Gheorghe Vrânceanu.

Key takeaways

Henri Moscovici belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of Henri Moscovici from memory before moving on to harder problems.

Reference excerpt

Henri Moscovici (born 5 May 1944) is a Romanian-American mathematician, specializing in non-commutative geometry and global analysis. Moscovici received his undergraduate degree in 1966 and his doctorate in 1971 at the University of Bucharest under the supervision of Gheorghe Vrânceanu. From 1966 to 1971 Moscovici was an assistant at Politehnica University of Bucharest, from 1971 to 1975 at the Institute of Mathematics of the Romanian Academy and from 1975 to 1977 at the Institute of Atomic Physics in Măgurele, and from 1977 at the INCREST in Bucharest. In 1978 he left for the United States, where he was a visitor at the Institute for Advanced Study in Princeton, New Jersey. In 1980 he joined the Ohio State University, where he held the Alice Wood Chair in Mathematics; he is now a Professor Emeritus there. Moscovici does research on representation theory, global analysis, and non-commutative geometry, in which he has collaborated with, among others, Alain Connes, since the two met at the Institute for Advanced Study in 1978. With Connes he proved in 1990 a refinement of the Atiyah–Singer index theorem. As recounted by Connes in a 2021 interview, Moscovici became his greatest collaborator. In 1990 he was Invited Speaker with talk Cyclic cohomology and invariants of multiply connected manifold at the International Congress of Mathematicians in Kyoto. He has advised 14 Ph.D. students, including András Némethi. In 2001, he received the Ohio State University Distinguished Scholar Award. In 1995 he was a Guggenheim Fellow. From 1999 to 2000 he was at Harvard University as a scholar of the Clay Mathematics Institute. In 2003, he was awarded the Romanian National Order of Faithful Service, Commander rank. A conference in his honor was held at the Hausdorff Center for Mathematics in Bonn in 2009. He was elected a Fellow of the American Mathematical Society in 2012.

Selected publications Connes, Alain; Moscovici, Henri (1982). "The L2-Index Theorem for homogeneous spaces of Lie groups". Annals of Mathematics. 115 (2): 291. doi:10.2307/1971393. JSTOR 1971393. Barbasch, Dan; Moscovici, Henri (1983). "L2-index and the Selberg trace formula". Journal of Functional Analysis. 53 (2): 151–201. doi:10.1016/0022-1236(83)90050-2. (See Selberg trace formula.) Connes, Alain; Moscovici, Henri (1990). "Cyclic cohomology, the Novikov conjecture and hyperbolic groups". Topology. 29 (3): 345–388. doi:10.1016/0040-9383(90)90003-3. (See Novikov conjecture.) Connes, Alain; Gromov, Mikhael; Moscovici, Henri (1993). "Group cohomology with Lipschitz control and higher signatures". Geometric and Functional Analysis. 3 (1): 1–78. doi:10.1007/BF01895513. MR 1204787. S2CID 15060588. Connes, Alain; Moscovici, Henri (1995). "The local index formula in noncommutative geometry". Geometric and Functional Analysis. 5 (2): 174–243. doi:10.1007/BF01895667. MR 1334867. (also at doi:10.1007/978-3-0348-9102-8_4) Connes, Alain; Moscovici, Henri (1998). "Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem". Communications in Mathematical Physics. 198 (1): 199–246. arXiv:math/9806109. Bibcode:1998CMaPh.198..199C. doi:10.1007/s002200050477. S2CID 15238820. Connes, Alain; Moscovici, Henri (1999). "Cyclic Cohomology and Hopf Algebras". Letters in Mathematical Physics. 48: 97–108. doi:10.1023/A:1007527510226. S2CID 117855160. (See Hopf algebra.) Connes, Alain; Moscovici, Henri (2000). "Cyclic Cohomology and Hopf Algebra Symmetry". Letters in Mathematical Physics. 52: 1–28. doi:10.1023/A:1007698216597. S2CID 117908037. Connes, Alain; Moscovici, Henri (2004). "Rankin-Cohen brackets and the Hopf algebra of transverse geometry". Moscow Mathematical Journal. 4 (1): 111–130. doi:10.17323/1609-4514-2004-4-1-111-130. S2CID 3001698. (See Rankin–Cohen bracket.) Connes, Alain; Moscovici, Henri (2008), "Type III and spectral triples", Traces in number theory, geometry and quantum fields, Aspects of Mathematics, vol. E38, Wiesbaden: Friedr. Vieweg, pp. 57–71, arXiv:math/0609703, MR 2427588 Connes, Alain; Moscovici, Henri (2014). "Modular curvature for noncommutative two-tori". Journal of the American Mathematical Society. 27 (3): 639–684. arXiv:1110.3500. doi:10.1090/S0894-0347-2014-00793-1. MR 3194491. S2CID 1517221.

References

External links Henri Moscovici publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Henri Moscovici

Start with the simplest possible case. Write down what Henri Moscovici 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 Henri Moscovici 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 Henri Moscovici 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 Henri Moscovici

In research: Henri Moscovici 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 Henri Moscovici 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: Henri Moscovici is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century American mathematicians, 20th-century Romanian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henri Moscovici 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 Henri Moscovici in 20 minutes

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Frequently asked questions

What is Henri Moscovici in simple terms?

Why does Henri Moscovici 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 Henri Moscovici?

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 Henri Moscovici.