Maryna Viazovska

Maryna Viazovska, Oberwolfach 2013

Maryna Viazovska ( Ukrainian Марина Сергіївна В'язовська / Maryna Serhijiwna Wjasowska ; * 1984 , Ukrainian SSR ) is a Ukrainian mathematician. In 2016 she achieved a scientific breakthrough in the theory of the closest packing of spheres .

Career

Viazovska studied at the National Taras Shevchenko University of Kiev with a candidate degree in 2010 (corresponding to a doctorate). In 2007 she received her diploma at the University of Kaiserslautern in Gerhard Pfister (calculation of Weierstrass semigroup of singularities of space curves) and was in 2013 at the University of Bonn in Don Zagier Dr. rer. nat. PhD (modular functions and special cycles). As a post-doctoral student , she was at the Humboldt University in Berlin . At the end of 2016 she became an assistant professor (tenure track) and in 2018 she received a full professorship at the École polytechnique fédérale de Lausanne (EPFL) in Lausanne. Here she holds the chair for number theory at the Institute for Mathematics.

In her doctoral thesis she dealt with modular forms and analytical number theory . Further areas of work are approximation of functions and discrete geometry , she also published in solid state physics ( superconductors ).

In 2013, together with Andrij Bondarenko and Danylo Radchenko , she proved a conjecture by Jacob Korevaar and J. L. H. Meyers about the existence of spherical t-designs . In 2013 Bondarenko received the Vasil A. Popov Prize for Approximation Theory for this. A spherical t-design is a set of N points on the unit sphere in d dimensions such that the mean of each polynomial of degree on the points is equal to the mean of the polynomial on the unit sphere. ${\displaystyle \leq t}$

In 2016 she announced a proof that the packing to the root system of the exceptional Lie group is the closest packing of spheres (not only among lattice packings , but also among non-lattice packings ) in eight dimensions and soon afterwards with colleagues just as much proof for the Leech lattice in 24 Dimensions. The proof had been sought for a long time. For the assumption that these lattices were optimal in their respective dimensions, extensive numerical support was available, in particular through upper limits for optimal spherical packing by Noam Elkies and Henry Cohn from 2003, who showed especially for dimensions 8 and 24 that the E8- or Leech grids come very close to the bounds, which was further supported by numerical calculations by Cohn and Abhinav Kumar. After the assessment by Elkies and Cohn, a search was made for suitable auxiliary functions from whose existence a proof should follow. Viazovska's proof uses the theory of modular shapes and, according to Peter Sarnak, is convincing and surprisingly simple. ${\displaystyle E_{8}}$

In 2016 she received the French Salem Prize and in 2017 both the Clay Research Award and the European Prize in Combinatorics and the SASTRA Ramanujan Prize (in 2019 she was a member of its award committee). For 2018 she received a New Horizons in Mathematics Prize and for 2019 both the Ruth Lyttle Satter Prize and the Fermat Prize . For 2020/21 she received the EMS Prize .

Fonts

• With Andriy Bondarenko, Danylo Radchenko: Optimal asymptotic bounds for spherical designs. In: Annals of Mathematics. Second Series, Volume 178, 2013, 443-452, Arxiv.
• The sphere packing problem in dimension 8. , Annals of Mathematics, Volume 185, 2017, pp. 991-1015, Preprint 2016, Arxiv.
• With Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko: The sphere packing problem in dimension 24. , Annals of Mathematics, Volume 185, 2017, pp. 1017-1033, Preprint 2016, Arxiv.

Web links

Commons : Maryna Viazovska  - collection of images, videos and audio files

• Homepage Humboldt University Berlin
• Gil Kalai's blog to prove Viazovska
• David de Laat, Frank Vallentin: A Breakthrough in Sphere Packing: The Search for Magic Functions. Nieuw Archief voor Wiskunde, September 2016, Arxiv.
• Henry Cohn: A conceptual breakthrough in sphere packing. Notices AMS, February 2017, PDF.
• Clay Research Award 2017

Individual evidence

1. ^ German digital library
2. ^ Nil Şahin: Singularity theory and Arf rings. Dissertation, Middleast Technical University, 2012, p. 102 (citation of Viazovska's thesis), PDF.
3. ↑ Maryna Viazovska in the Mathematics Genealogy Project (English)
4. ↑ 11 professors appointed at both ETHs. Swiss Ministry of Education, December 9, 2016.
5. ^ Andrea Testa: Maryna Viazovska promoted to Full Professor . August 1, 2018 ( epfl.ch [accessed on August 12, 2020]).
6. ^ Chair of Number Theory
7. ↑ 2013 - Seventh Prize Recipient. Andriy Bondarenko. ( Memento of the original from October 31, 2015 in the Internet Archive ) Info: The archive link was automatically inserted and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
8. ^ H. Cohn, N. Elkies: New upper bounds on sphere packings I. In: Annals of Mathematics. Volume 157, 2003, pp. 689-714, PDF.
9. ↑ Erica Klarreich: Sphere Packing Solved in Higher Dimensions. A Ukrainian mathematician has solved the centuries-old sphere-packing problem in dimensions eight and 24. In: Quanta Magazine. March 30, 2016.
10. ↑ EMS Prize for Viazovska