mathematics

Jan Philip Solovej

Jan Philip Solovej 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 Jan Philip Solovej rather than just read about it. In short: Jan Philip Solovej (born 14 June 1961) is a Danish mathematician and mathematical physicist working on the mathematical theory of quantum mechanics. He is a professor at University of Copenhagen.

Key takeaways

Jan Philip Solovej belongs to mathematics; place it in that map before memorising details.
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Reference excerpt

Jan Philip Solovej (born 14 June 1961) is a Danish mathematician and mathematical physicist working on the mathematical theory of quantum mechanics. He is a professor at University of Copenhagen.

Biography Solovej obtained his Ph.D. in 1989 from Princeton University with the thesis on "Universality in the Thomas-Fermi-von Weizsäcker Model of Atoms and Molecules" supervised by Elliott H. Lieb. As a post-doctoral researcher, he went to the University of Michigan in 1989/90 and to the University of Toronto in 1990. In 1991 (and 2003/04) he was a member at the Institute for Advanced Study. From 1991 to 1995, he was Assistant Professor in the Department of Mathematics at Princeton University. From 1995 to 1997, he was a research professor at the University of Aarhus. Since 1997, he is professor in the Department of Mathematics at the University of Copenhagen. Since 2016, he is also leader of VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH). He is President of European Mathematical Society during 2023-2026. He is Editor in Chief of Journal of Mathematical Physics (since 2019). He is married and has two children.

Recognition In 2021, he received the Henri Poincaré Prize from the International Association of Mathematical Physics, "for outstanding contributions to the analysis of quantum many-body problems ranging from the electronic structure of large atoms to the Lee-Huang-Yang asymptotics of the ground state energy of dilute Bose gases". He was an invited speaker at the International Congress of Mathematicians in 2022, an invited speaker at the European Congress of Mathematics in 1996 and 2004, and a plenary speaker at the International Congress on Mathematical Physics in 1991, 2003 and 2021. Solovej is a member of the Royal Danish Academy of Sciences and Letters (elected 2000) and of the Academia Europaea(elected 2020). He was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to the rigorous analysis of quantum systems, particularly many-body systems".

Works Solovej deals with mathematical questions in atomic physics (large atoms and molecules in the Thomas-Fermi model and the Hartree-Fock method), solid-state physics (the Bose-Einstein condensate, Bogoliubov transformation, quantum dot, Heisenberg model and others) and in many-body quantum mechanics (the stability of matter, the Lieb-Thirring inequality and others). He is co-author, together with Elliott H. Lieb, Robert Seiringer, and Jakob Yngvason, of a monograph on the mathematics of the Bose gas. In 1995, with Elliott H. Lieb and Michael Loss, he proved the stability of matter in magnetic fields. In 2003, he established the ionization conjecture for atoms within the Hartree-Fock theory, namely the excess charge, the ionization energy and the radius of an atom are uniformly bounded independently of the nuclear charge. Related questions for many-body Schrödinger equation remain open, which are Problems 9, 10, 11 of the Simon problems on Schrödinger operators. In 2012, with Rupert L. Frank, Christian Hainzl and Robert Seiringer, he derived the Ginzburg-Landau theory from the BCS theory. In 2014, with Elliott H. Lieb, he proved Wehrl's conjecture on the mininimum entropy of quantum spin systems. In 2020, with Søren Fournais, he proved the Lee-Huang-Yang conjecture on the ground state energy of dilute Bose gases.

Selection of publications Solovej, Jan Philip (1991). "Proof of the ionization conjecture in a reduced Hartree-Fock model". Inventiones Mathematicae. 104 (1). Springer: 291–311. doi:10.1007/bf01245077. hdl:2027.42/46574. Lieb, Elliott H.; Loss, Michael; Solovej, Jan Philip (1995). "Stability of Matter in Magnetic Fields". Physical Review Letters. 75 (6). American Physical Society (APS): 985–989. arXiv:cond-mat/9506047. doi:10.1103/physrevlett.75.985. Solovej, Jan (2003). "The ionization conjecture in Hartree–Fock theory". Annals of Mathematics. 158 (2): 509–576. arXiv:math-ph/0012026. doi:10.4007/annals.2003.158.509. "The Mathematics of the Bose Gas and its Condensation". Oberwolfach Seminars. Vol. 34. Springer. 2005. doi:10.1007/b137508. Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip (2012). "Microscopic derivation of Ginzburg-Landau theory". Journal of the American Mathematical Society. 25 (3). American Mathematical Society (AMS): 667–713. arXiv:1102.4001. doi:10.1090/s0894-0347-2012-00735-8. Lieb, Elliott H.; Solovej, Jan Philip (2014). "Proof of an entropy conjecture for Bloch coherent spin states and its generalizations". Acta Mathematica. 212 (2). International Press of Boston: 379–398. arXiv:1208.3632. doi:10.1007/s11511-014-0113-6. Fournais, Søren; Solovej, Jan Philip (1 November 2020). "The energy of dilute Bose gases". Annals of Mathematics. 192 (3). doi:10.4007/annals.2020.192.3.5. Fournais, Søren; Solovej, Jan Philip (2023). "The energy of dilute Bose gases II: the general case". Inventiones mathematicae. 232. Springer. arXiv:2108.12022. doi:10.1007/s00222-022-01175-0.

References

External links "Homepage of Jan Philip Solovej". "Jan Philip Solovej". Google Scholar.

Illustrations

Worked examples

Example 1 — a first encounter with Jan Philip Solovej

Start with the simplest possible case. Write down what Jan Philip Solovej 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 Jan Philip Solovej 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 Jan Philip Solovej 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 Jan Philip Solovej

In research: Jan Philip Solovej 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 Jan Philip Solovej 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: Jan Philip Solovej is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, Academic staff of the University of Copenhagen, Danish scientist stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Jan Philip Solovej 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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Frequently asked questions

What is Jan Philip Solovej in simple terms?

Jan Philip Solovej (born 14 June 1961) is a Danish mathematician and mathematical physicist working on the mathematical theory of quantum mechanics. He is a professor at University of Copenhagen.

Why does Jan Philip Solovej 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 Jan Philip Solovej?

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 Jan Philip Solovej.