astronomy

Kari Vilonen

Kari Vilonen is a astronomy 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 Kari Vilonen rather than just read about it. In short: Kari Kaleva Vilonen (born 1955) is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.

Key takeaways

Kari Vilonen belongs to astronomy; place it in that map before memorising details.
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Reference excerpt

Kari Kaleva Vilonen (born 1955) is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.

Education He received in 1983 his Ph.D from Brown University under Robert MacPherson with thesis The Intersection Homology D-module on Hypersurfaces with Isolated Singularities.

Career From 1983 to 1986 was a C. L. E. Moore instructor at the Massachusetts Institute of Technology, on leave in 1984–1985 at the Mathematical Sciences Research Institute in Berkeley, California. Afterward, Vilonen was a Benjamin Pierce Assistant Professor at Harvard University from 1986 to 1989. From 1989 to 2000 he was a faculty member at Brandeis University, rising to the rank of Professor in 1996. After that, he was a professor at Northwestern University, and then a professor at the University of Helsinki from 2010 to 2015. Starting in 2015, Vilonen has been a professor at the University of Melbourne in Australia. In 2002, with Dennis Gaitsgory and Edward Frenkel, he proved the geometrical Langlands conjecture for curves over finite fields. In 2004, Vilonen, Mark Goresky, Dennis Gaitsgory and Edward Frenkel were awarded a multimillion dollar grant from the Defense Advanced Research Projects Agency (DARPA) to work on a project aimed at establishing links between the Langlands program and dualities in quantum field theory. Later, Frenkel wrote, "We felt like we were in uncharted territory: no mathematicians we knew had ever received grants of this magnitude before." The funds were used to coordinate the work of dozens of mathematicians with the goal of making a concerted effort in a significant area of research. In 2007, with Ivan Mirković, he published "Geometric Langlands duality and representations of algebraic groups over commutative rings", which proved the geometric Satake equivalence, a geometric version of the Satake isomorphism. In 2013, Vilonen received a Humboldt Prize. In 2014, he was awarded a Simons Fellowship from the Simons Foundation. In 2020, the Australian Research Council awarded Vilonen an Australian Laureate Fellowship, their highest award to an individual. This five year grant will allow him to address questions about real groups, algebraic objects which describe the basic symmetries occurring in nature.

Awards and keynote addresses Vilonen was a Guggenheim Fellow for the academic year 1997/98. In 1998 he was an Invited Speaker with talk Topological methods in representation theory at the International Congress of Mathematicians in Berlin. In 2004 he was elected a member of the Finnish Academy of Science and Letters.

Selected publications MacPherson, Robert; Vilonen, Kari (1986). "Elementary construction of perverse sheaves". Inventiones Mathematicae. 84 (2). Springer Science and Business Media LLC: 403–435. Bibcode:1986InMat..84..403M. doi:10.1007/bf01388812. ISSN 0020-9910. S2CID 120183452. Mirković, I; Uzawa, T; Vilonen, K (1992). "Matsuki correspondence for sheaves". Inventiones Mathematicae. 109 (1): 231–245. Bibcode:1992InMat.109..231M. doi:10.1007/BF01232026. S2CID 120058836. Vilonen, K (1994). "Perverse sheaves and finite-dimensional algebras". Trans. Amer. Math. Soc. 341 (2): 665–676. doi:10.1090/S0002-9947-1994-1135104-3. Frenkel, E; Gaitsgory, D; Kazhdan, D; Vilonen, K (1998). "Geometric realization of Whittaker functions and the Langlands conjecture". J. Amer. Math. Soc. 11 (2): 451–484. arXiv:alg-geom/9703022. doi:10.1090/S0894-0347-98-00260-4. Schmid, Wilfried; Vilonen, Kari (1998). "Two geometric character formulas for reductive Lie groups". J. Amer. Math. Soc. 11 (4): 799–867. arXiv:math/9801081. Bibcode:1998math......1081S. doi:10.1090/S0894-0347-98-00275-6. Mirković, I; Vilonen, K (1999). "Perverse sheaves on affine Grassmannians and Langlands duality". arXiv:math/9911050. Vilonen, Kari (2000). "Geometric methods in representation theory by K. Vilonen". In J. Adams; D. Vogan (eds.). Representation theory of Lie groups. IAS/Park City Mathematics Series 8. American Mathematical Society. pp. 241–290. arXiv:math/0410032. Bibcode:2004math.....10032V. Schmid, Wilfried; Vilonen, Kari (2000). "Characteristic Cycles and Wave Front Cycles of Representations of Reductive Lie Groups". The Annals of Mathematics. 151 (3). JSTOR: 1071. arXiv:math/0005305. Bibcode:2000math......5305S. doi:10.2307/121129. ISSN 0003-486X. JSTOR 121129. S2CID 3002170. Frenkel, E.; Gaitsgory, D.; Vilonen, K. (31 December 2001). "On the geometric Langlands conjecture". Journal of the American Mathematical Society. 15 (2). American Mathematical Society (AMS): 367–417. doi:10.1090/s0894-0347-01-00388-5. ISSN 0894-0347. Frenkel, E; Gaitsgory, D; Vilonen, K (2002). "On the geometric Langlands conjecture". J. Amer. Math. Soc. 15 (2): 367–417. doi:10.1090/S0894-0347-01-00388-5. Mirković, Ivan; Vilonen, Kari (1 July 2007). "Geometric Langlands duality and representations of algebraic groups over commutative rings". Annals of Mathematics. 166 (1). Annals of Mathematics, Princeton U: 95–143. arXiv:math/0401222. doi:10.4007/annals.2007.166.95. ISSN 0003-486X. Schmid, Wilfried; Vilonen, Kari (2011). "Hodge theory and the unitary representations of reductive Lie groups". Frontiers in Mathematical Sciences. International Press. pp. 397–420. arXiv:1206.5547. Bibcode:2012arXiv1206.5547S. Kashiwara, Masaki; Vilonen, Kari (1 September 2014). "Microdifferential systems and the codimension-three conjecture". Annals of Mathematics. 180 (2): 573–620. arXiv:1209.5124. doi:10.4007/annals.2014.180.2.4. ISSN 0003-486X. S2CID 56382698.

References

Illustrations

Worked examples

Example 1 — a first encounter with Kari Vilonen

Start with the simplest possible case. Write down what Kari Vilonen claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Kari Vilonen 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 Kari Vilonen 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 Kari Vilonen

In research: Kari Vilonen appears in astronomy 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 Kari Vilonen 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: Kari Vilonen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, Academic staff of the University of Helsinki, Academic staff of the University of Melbourne, so understanding it makes those chapters shorter.
In everyday life: Look for Kari Vilonen 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 Kari Vilonen in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kari Vilonen means in your own words.
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Frequently asked questions

What is Kari Vilonen in simple terms?

Kari Kaleva Vilonen (born 1955) is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.

Why does Kari Vilonen matter?

Because it connects several astronomy 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 Kari Vilonen?

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 Kari Vilonen.