mathematics

Mihnea Popa

Mihnea Popa 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 Mihnea Popa rather than just read about it. In short: Mihnea Popa (born 11 August 1973) is a Romanian-American mathematician at Harvard University, specializing in algebraic geometry. He is known for his work on complex birational geometry, Hodge theory, abelian varieties, and vector bundles.

Key takeaways

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

Reference excerpt

Mihnea Popa (born 11 August 1973) is a Romanian-American mathematician at Harvard University, specializing in algebraic geometry. He is known for his work on complex birational geometry, Hodge theory, abelian varieties, and vector bundles.

Academic career Popa received his bachelor's degree in 1996 from the University of Bucharest. He studied mathematics at the University of California, Los Angeles from 1996 to 1997, and then in 2001 he received his Ph.D. from the University of Michigan under the supervision of Robert Lazarsfeld. His thesis was titled Linear Series on Moduli Spaces of Vector Bundles on Curves. From 2001 to 2005, Popa was a Benjamin Peirce Assistant Professor at Harvard University and from 2005 to 2007 an assistant professor at the University of Chicago. He joined the University of Illinois at Chicago as an associate professor in 2007 and became a full professor in 2011. In 2014 he moved to Northwestern University, and in 2020 he became a professor at Harvard University.

Awards and honors Popa is an honorary member of the Institute of Mathematics of the Romanian Academy. He was an AMS Centennial Fellow in 2005–2007, a Sloan Research Fellow in 2007–2009, and a Simons Fellow in 2015–2016. In 2015 he became a fellow of the American Mathematical Society. In 2018 he was an Invited Speaker at the International Congress of Mathematicians in Rio de Janeiro.

Selected publications Pareschi, Giuseppe; Popa, Mihnea (2003). "Regularity on abelian varieties I". Journal of the American Mathematical Society. 16 (2): 285–302. arXiv:math/0110003. doi:10.1090/S0894-0347-02-00414-9. MR 1949161. S2CID 15351749. Farkas, Gavril; Popa, Mihnea (2005). "Effective divisors on M ¯ g {\displaystyle {\overline {\mathcal {M}}}_{g}} , curves on K3 surfaces, and the slope conjecture". Journal of Algebraic Geometry. 14 (2): 241–267. arXiv:math/0305112. doi:10.1090/S1056-3911-04-00392-3. MR 2123229. S2CID 1659630. Ein, Lawrence; Lazarsfeld, Robert; Mustață, Mircea; Nakamaye, Michael; Popa, Mihnea (2006). "Asymptotic invariants of base loci". Annales de l'Institut Fourier. 56 (6): 1701–1734. arXiv:math/0308116. doi:10.5802/aif.2225. MR 2282673. S2CID 33125067. Lazarsfeld, Robert; Popa, Mihnea (2010). "Derivative complex, BGG correspondence, and numerical inequalities for compact Kähler manifolds". Inventiones Mathematicae. 182 (3): 605–633. arXiv:0907.0651. Bibcode:2010InMat.182..605L. doi:10.1007/s00222-010-0269-4. MR 2737707. S2CID 667056. Popa, Mihnea; Schnell, Christian (2013). "Generic vanishing theory via mixed Hodge modules". Forum of Mathematics, Sigma. 1 e1: Paper No. e1, 60 pp. arXiv:1112.3058. doi:10.1017/fms.2013.1. MR 3090229. S2CID 26554421. Popa, Mihnea; Schnell, Christian (2014). "Kodaira dimension and zeros of holomorphic one-forms". Annals of Mathematics. 179 (3): 1109–1120. arXiv:1212.5714. doi:10.4007/annals.2014.179.3.6. MR 3171760. S2CID 8073319. Popa, Mihnea (2016). "Kodaira–Saito vanishing and applications". L'Enseignement mathématique. 62 (1): 49–89. arXiv:1407.3294. doi:10.4171/LEM/62-1/2-5. MR 3605809. S2CID 32670893. Positivity for Hodge modules and geometric applications, in Proceedings of Symposia in Pure Mathematics, Vol. 97, Part I, Algebraic Geometry: Salt Lake City 2015, pp. 555–584. arXiv:1605.08093 Mustață, Mircea; Popa, Mihnea (2019). "Hodge Ideals". Memoirs of the American Mathematical Society. 262 (1268): v+80 pp. arXiv:1605.08088. doi:10.1090/memo/1268. ISBN 978-1-4704-3781-7. MR 4044463. S2CID 119700627.{{cite journal}}: CS1 maint: periodical has ISBN (link) Popa, Mihnea; Schnell, Christian (18 October 2016). "Viehweg's hyperbolicity conjecture for families with maximal variation". Inventiones Mathematicae. 208 (3). Springer Science and Business Media LLC: 677–713. arXiv:1511.00294. doi:10.1007/s00222-016-0698-9. ISSN 0020-9910. S2CID 34920237. Pareschi, Giuseppe; Popa, Mihnea; Schnell, Christian (19 May 2017). "Hodge modules on complex tori and generic vanishing for compact Kähler manifolds". Geometry & Topology. 21 (4). Mathematical Sciences Publishers: 2419–2460. arXiv:1505.00635. doi:10.2140/gt.2017.21.2419. ISSN 1364-0380. S2CID 20275751. Mustață, Mircea; Popa, Mihnea (2020). "Hodge Ideals for -Divisors, -Filtration, and Minimal Exponent". Forum of Mathematics, Sigma. 8 e19. Cambridge University Press (CUP). doi:10.1017/fms.2020.18. ISSN 2050-5094. S2CID 218780383.

References

External links Homepage Mihnea Popa publications indexed by Google Scholar

Illustrations

Worked examples

Example 1 — a first encounter with Mihnea Popa

Start with the simplest possible case. Write down what Mihnea Popa 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 Mihnea Popa 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 Mihnea Popa 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 Mihnea Popa

In research: Mihnea Popa 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 Mihnea Popa 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: Mihnea Popa is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1973 births, 20th-century American mathematicians, 20th-century Romanian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mihnea Popa 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 Mihnea Popa in 20 minutes

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

Frequently asked questions

What is Mihnea Popa in simple terms?

Why does Mihnea Popa 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 Mihnea Popa?

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 Mihnea Popa.