June Huh

June Huh (* 1983 in California ) is a South Korean-American mathematician.

Life

Huh was born in California, where his parents studied, and grew up in Seoul , where his father taught statistics and his mother taught Russian literature. He studied from 2002 at Seoul National University with a bachelor's degree in physics and astronomy in 2007 and a master's degree in mathematics in 2009. Due to a poorly graded math test in elementary school, Huh initially did not think of becoming a mathematician, but wanted to be a poet and then become a science journalist. The turning point came after he attended a lecture by Heisuke Hironaka , who during his time as a visiting professor in Seoul recognized his talent, made friends with him and supervised his thesis. Huh was accepted for graduate studies (thanks to a recommendation from Hironaka) at the University of Illinois at Urbana-Champaign in 2009 and received his doctorate in 2014 under Mircea Mustata at the University of Michigan , where he had been since 2010 (dissertation: Rota's conjecture and positivity of algebraic cycles in permutohedral varieties ). He was then a Clay Fellow at the Clay Mathematics Institute , Veblen Fellow at Princeton University and at the Institute for Advanced Study , of which he was visiting professor in 2017 and of which he is a member (2018). He has also been a visiting researcher at the Korea Institute for Advanced Study (KIAS) since 2015 .

plant

He deals with applications of combinatorics in algebraic geometry and combinatorial geometry. As a mathematician, Huh is mostly self-taught, apart from the three years in which he was a student of Hironaka , who mainly taught him in his specialty (theory of singularities in algebraic geometry). As a student in 2010, he proved the 1968 conjecture of Ronald C. Read (and Hoggar) in graph theory through a combination of insights from graph theory and algebraic geometry. It says that the coefficients of the chromatic polynomial of a graph form a unimodal sequence ( i.e. the terms of the sequence rise to a maximum and then fall), which even has the property of being log-concave (i.e. ). Soon after, with Karim Adiprasito and Eric Katz , he was able to prove a generalization of Read's conjecture from graphs to matroids , the Rota conjecture (established by Gian-Carlo Rota and Welsh in 1971). Then the coefficients of the chromatic polynomial of matroids form a log-concave sequence. Huh and Katz recognized that behind it was the Hodge theory of algebraic geometry, which was transferred to combinatorial objects , more precisely the Hodge-Riemann relations , and were thus able to prove the Rota conjecture for special ( realizable ) matroids. With the help of Adiprasito, the complete proof was achieved in 2015. Adiprasito recognized in particular that for the proof, in addition to the Hodge-Riemann relations, two other properties had to be shown ( heavy Lefschetz theorem and Poincaré duality ), which together with these the Kähler -Package , and that a combinatorial proof of Peter McMullen's difficult Lefschetz theorem should prove all three properties. Huh also sees the Hodge theory behind other log-concave sequences in various areas of mathematics (see Lefschetz package ). ${\displaystyle a_{i+1}a_{i-1}\leq a_{i}^{2}}$

Honors

Huh is invited speaker at the International Congress of Mathematicians 2018 in Rio de Janeiro (Combinatorial applications of the Hodge-Riemann relations). He is a Clay Fellow and received the Blavatnik Award.

Fonts

• with Eric Katz: Log-concavity of characteristic polynomials and the Bergman fan of matroids, Mathematische Annalen, Volume 354, 2012, pp. 1103-1116. Arxiv
• Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs, J. American Math. Soc., Volume 25, 2012, pp. 907-927, Arxiv
• The maximum likelihood degree of a very affine variety, Compos. Math., Vol. 149, 2013, pp. 1245-1266.
• Milnor numbers of projective hypersurfaces with isolated singularities, Duke Mathematical Journal, Volume 163, 2014, pp. 1525-1548
• with Bernd Sturmfels : Likelihood Geometry, in: Combinatorial Algebraic Geometry, Lecture Notes in Mathematics 2108, Springer 2014, pp. 63–117
• h-vectors of matroids and logarithmic concavity, Adv. Math., Volume 270, 2015, pp. 49-59
• Positivity of Chern classes of Schubert cells and varities, Journal of Algebraic Geometry, Volume 25, 2016, pp. 177-199. Arxiv
• with Farhad Babaee: A tropical approach to a generalized Hodge conjecture for positive currents, Duke Math. J., Volume 166, 2017, pp. 2749-2813
• with Adiprasito, Katz: Hodge theory of matroids, Notices AMS, Volume 64, January 2017, pp. 26-30, pdf
• with Botong Wang: Lefschetz classes on projective varieties, Proceedings of the American Mathematical Society, Volume 145, 2017, pp. 4629-4637. Arxiv
• with Botong Wang: Enumeration of points, lines, planes, etc., Acta Mathematica, Volume 218, 2017, pp. 297-317. Arxiv
• Tropical geometry of matroids, Current Developments in Mathematics 2016, International Press, 2018, pp. 1–46
• with Karim Adiprasito, Eric Katz: Hodge theory for combinatorial geometries, Annals of Mathematics, 2018, Arxiv
• Combinatorial applications of the Hodge-Riemann relations, Proc. ICM 2018, Arxiv

literature

• Matthew Baker: Hodge theory in combinatorics, Bulletin of the American Mathematical Society, Volume 55, 2018, pp. 57-80, online

Web links

• Homepage
• Kevin Hartnett, A Path Less Taken to the Peak of the Math World, Quanta Magazine , June 27, 2017
• June Huh explains the g conjecture , numberphile

Individual evidence

1. ↑ June Huh in the Mathematics Genealogy Project (English)
2. ↑ Adiprasito Huh, Katz, Hodge Theory of Matroids, Notices AMS, January 2017, p. 26
3. ↑ Blavatnik Award to Huh