Alexander Andreyevich Logunov

Alexander Andrejewitsch Logunow ( Russian Александр Андреевич Логунов , English transcription Alexander Logunov) is a Russian mathematician who deals with harmonic analysis , potential theory and geometric analysis.

Logunow received his doctorate in 2015 from the University of St. Petersburg with Viktor Chawin (О граничных свойствах гармонических функций, English On boundary properties of harmonic functions ). He works at the Chebyshev Mathematics Laboratory at the University of Saint Petersburg and at Tel Aviv University.

Logunow received the Clay Research Award in 2017 with Yevgenia Malinnikova for the introduction of novel geometrical-combinatorial methods for the study of elliptic eigenvalue problems . Among other things, he proved an upper bound for the Hausdorff measure of the nodal area of eigenfunctions of the Laplace operator on compact smooth manifolds and lower bounds (conjectures by Yau and Nadirashvili). For 2018 he received the Salem Prize . For 2020/21 he received the EMS Prize .

Fonts

• Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure , Annals of Mathematics, Volume 187, 2018, pp. 221-239, Arxiv
• with Eugenia Malinnikova: On ratios of harmonic functions , Adv. Math. 274 (2015), 241-262, Arxiv
• with Eugenia Malinnikova: Ratios of harmonic functions with the same zero set , Geom. Funct. Analysis, Volume 26, 2016, pp. 909-925, Arxiv
• Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture , Annals of Mathematics, Volume 187, 2018, S. Annals of Mathematics, Volume 187, 2018, pp. 241-263, Arxiv
• with Eugenia Malinnikova : Nodal sets of Laplace eigenfunctions: estimates of the Hausdorff measure in dimension two and three , 2016, Arxiv

Web links

• mathnet.ru

Individual evidence

1. ↑ Alexander Andrejewitsch Logunow in the Mathematics Genealogy Project (English)
2. ^ Clay Research Award 2017
3. ↑ Salem Prize 2018
4. ↑ EMS price, entry Logunov