mathematics

Mircea Mustață

Mircea Mustață 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 Mircea Mustață rather than just read about it. In short: Mircea Immanuel Mustață ([mir.'tʃa musˈta.t͡sə]; born 1971) is a Romanian-American mathematician, specializing in algebraic geometry. Background Mustață was born in Romania.

Key takeaways

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

Reference excerpt

Mircea Immanuel Mustață ([mir.'tʃa musˈta.t͡sə]; born 1971) is a Romanian-American mathematician, specializing in algebraic geometry.

Background Mustață was born in Romania. He received a bachelor's degree in 1995 and a master's degree the following year, both from the University of Bucharest. For his doctorate, Mustață moved to the United States, obtaining his PhD from UC Berkeley in 2001. His thesis, Singularities and Jet Schemes, was advised by David Eisenbud. A Clay Research Fellow during 2001–04, Mustață held postdoc positions at the University of Nice Sophia Antipolis (Fall 2001), the Isaac Newton Institute (Spring 2002), and Harvard University (2002–04). Since 2004, when he became an associate professor, Mustață has been on the faculty of the University of Michigan in Ann Arbor. He was made a full professor by Michigan in 2008. In fall 2006, he was at the Institute for Advanced Study. From 2006 to 2011, he held a five-year Packard Fellowship. Mustață was an invited speaker at the 2004 European Mathematical Congress in Stockholm and at the 2014 International Congress of Mathematicians in Seoul. His doctoral students include Fields medalist June Huh.

Research Mustață's research deals with a wide range of topics in algebraic geometry, including:

various invariants of singularities of algebraic varieties, such as minimal log discrepancies, log canonical thresholds, multiplier ideals, Bernstein–Sato polynomials and F-thresholds ... resolutions of singularities, jet schemes, D-modules or positive characteristic methods ... birational geometry, asymptotic base loci and invariants of divisors, and toric varieties.

Selected publications

Ein, Lawrence; Lazarsfeld, Robert; Mustaţă, Mircea; Nakamaye, Michael; Popa, Mihnea (2006). "Asymptotic invariants of base loci". Annales de l'Institut Fourier. 56 (6): 1701–1734. arXiv:math/0308116. Bibcode:2003math......8116E. doi:10.5802/aif.2225. S2CID 33125067. Ein, Lawrence; Mustaţă, Mircea (2009). "Jet schemes and singularities". Algebraic geometry—Seattle 2005. Part 2. Proceedings of Symposia in Pure Mathematics. Vol. 80. Providence, RI: American Mathematical Society. pp. 505–546. arXiv:math/0612862. doi:10.1090/pspum/080.2/2483946. ISBN 978-0-8218-4703-9. MR 2483946. S2CID 14119380. Budur, Nero; Mustaţă, Mircea; Saito, Morihiko (2006). "Bernstein-Sato polynomials of arbitrary varieties". Compositio Mathematica. 142 (3): 779–797. arXiv:math/0408408. Bibcode:2004math......8408B. doi:10.1112/s0010437x06002193. S2CID 6955564. Mustaţă, Mircea; Payne, Sam (2005). "Ehrhart polynomials and stringy Betti numbers". Mathematische Annalen. 333 (4): 787–795. arXiv:math/0504486. Bibcode:2005math......4486M. doi:10.1007/s00208-005-0691-x. S2CID 119118251. Mustaţă, Mircea; Takagi, Shunsuke; Watanabe, Kei-ichi (2004). "F-thresholds and Bernstein-Sato polynomials". In Laptev, Ari (ed.). European Congress of Mathematics: Stockholm, June 27-July 2, 2004. European Mathematical Society. pp. 341–364. arXiv:math/0411170. Bibcode:2004math.....11170M. ISBN 978-3-03719-009-8. Ein, Lawrence; Mustaţǎ, Mircea (2004). "Inversion of adjunction for local complete intersection varieties". American Journal of Mathematics. 126 (6): 1355–1365. arXiv:math/0301164. Bibcode:2003math......1164E. doi:10.1353/ajm.2004.0044. S2CID 17363166. Mustaţǎ, Mircea; Popa, Mihnea (2016). "Hodge ideals". arXiv:1605.08088 [math.AG].

Personal life Mustață currently resides in Ann Arbor, Michigan, with his wife, Olga, and daughter, Maya. His hobbies include hiking, reading, and playing board games.

References

External links "Interview with Research Fellow Mircea Mustata" (PDF). claymath.org. 2007.

Worked examples

Example 1 — a first encounter with Mircea Mustață

Start with the simplest possible case. Write down what Mircea Mustață 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 Mircea Mustață 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 Mircea Mustață 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 Mircea Mustață

In research: Mircea Mustață 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 Mircea Mustață 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: Mircea Mustață is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1971 births, 21st-century American mathematicians, 21st-century Romanian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mircea Mustață 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 Mircea Mustață in 20 minutes

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

Frequently asked questions

What is Mircea Mustață in simple terms?

Mircea Immanuel Mustață ([mir.'tʃa musˈta.t͡sə]; born 1971) is a Romanian-American mathematician, specializing in algebraic geometry. Background Mustață was born in Romania.

Why does Mircea Mustață 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 Mircea Mustață?

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 Mircea Mustață.