Aleksandr Logunov (mathematician)
{{Short description|Russian mathematician (born 1989)}}
Aleksandr Andreyevich Logunov (Russian: Александр Андреевич Логунов, 5 December 1989) is a Russian mathematician, specializing in harmonic analysis, potential theory, and geometric analysis.
Logunov received his Candidate of Sciences (PhD) in 2015 from the Saint Petersburg State University under Viktor Petrovich Havin (Виктор Петрович Хавин, 1933–2015) with thesis (О граничных свойствах гармонических функций, On boundary properties of harmonic functions).{{MathGenealogy|id=215071 }} He works at the Chebyshev Mathematics Laboratory of the Saint Petersburg State University and at the University of Tel Aviv.
Logunov received, jointly with Eugenia Malinnikova, the 2017 Clay Research Award for their introduction of novel geometric-combinatorial methods for the study of elliptic eigenvalue problems.{{Cite web|url=http://www.claymath.org/aleksandr-logunov-and-eugenia-malinnikova|title=Aleksandr Logunov and Eugenia Malinnikova | Clay Mathematics Institute|website=www.claymath.org|access-date=2017-07-12|archive-date=2018-01-11|archive-url=https://web.archive.org/web/20180111111601/http://www.claymath.org/aleksandr-logunov-and-eugenia-malinnikova|url-status=dead}} He proved, among other results, an estimate (from above) for Hausdorff measures on the zero sets of Laplace eigenfunctions defined on compact smooth manifolds and an estimate (from below) in harmonic analysis and differential geometry that proved conjectures by Shing-Tung Yau and Nikolai Nadirashvili. In 2018 he received the Salem Prize[https://www.ams.org/journals/notices/201901/rnoti-p113.pdf Salem Prize 2018] and in 2020 the EMS Prize of the European Mathematical Society.{{Cite web|url=https://8ecm.si/prizes|title=8th European Congress of Mathematics|website=8th European Congress of Mathematics}} For 2021 he received the Breakthrough Prize in Mathematics – New Horizons in Mathematics.{{Cite web|url=https://breakthroughprize.org/News/60|title=Breakthrough Prize – Winners Of The 2021 Breakthrough Prizes In Life Sciences, Fundamental Physics And Mathematics Announced|website=breakthroughprize.org}}
Selected publications
- {{cite journal
| title=Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
| date=2018
| arxiv=1605.02587
| journal=Annals of Mathematics
| volume=187
| issue=1
| pages=221–239
| doi=10.4007/annals.2018.187.1.4| last1=Logunov
| first1=Alexander
| s2cid=119170110
}}
- with Eugenia Malinnikova: {{cite journal
| title=On ratios of harmonic functions
| journal=Advances in Mathematics
| volume=274
| date=2015
| pages=241–262
| arxiv=1402.2888
| doi=10.1016/j.aim.2015.01.009 | doi-access=free| last1=Logunov
| first1=Alexander
| last2=Malinnikova
| first2=Eugenia
}}
- with Eugenia Malinnikova: {{cite journal
| title=Ratios of harmonic functions with the same zero set
| journal=Geometric and Functional Analysis
| volume=26
| date=2016
| pages=909–925
| arxiv=1506.08041
| doi=10.1007/s00039-016-0369-4 | doi-access=free| last1=Logunov
| first1=Alexander
| last2=Malinnikova
| first2=Eugenia
| issue=3
}}
- {{cite journal
| title=Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture
| date=2018
| arxiv=1605.02589
| journal=Annals of Mathematics
| volume=187
| issue=1
| pages=241–262
| doi=10.4007/annals.2018.187.1.5| last1=Logunov
| first1=Alexander
| s2cid=119176697
}}
- with Eugenia Malinnikova: {{cite book
| contribution=Nodal sets of Laplace eigenfunctions: estimates of the Hausdorff measure in dimensions two and three
| date=2018
| arxiv=1605.02595
| title=50 Years with Hardy Spaces
| series=Operator Theory: Advances and Applications
| volume=261
| pages=333–344
| doi=10.1007/978-3-319-59078-3_17 | doi-access=free| last1=Logunov
| first1=Alexander
| last2=Malinnikova
| first2=Eugenia
| isbn=978-3-319-59077-6
}}
References
External links
- [http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=100666 mathnet.ru]
{{authority control}}
{{DEFAULTSORT:Logunov, Aleksandr (mathematician)}}
Category:Saint Petersburg State University alumni
Category:Differential geometers