På the International Congress of Basic Science, Beijing mottok Andrii Bondarenko, Kristian Seip og Nina Holden alle Frontiers of Science Awards.

Se her for mer informasjon om Frontier of Science Award

The Viggo Brun Prize for 2022 is awarded to:

Nina Holden

for her exceptionally deep and broad contributions to probability theory, especially for her work on random surfaces and quantum gravity in two dimensions.

Nina Holden (born 1986) is a Norwegian mathematician with MSc from the University of Oslo in 2010 and PhD from the Massachusetts Institute of Technology in 2018. She is currently a Post-Doc at ETH Zürich and has accepted a position as Associate Professor at the Courant Institute of Mathematical Sciences, New York University, starting in fall 2022. In 2021 Nina Holden was honored with the Maryam Mirzakhani New Frontiers Prize.

Holden’s research field is probability theory. She has successfully pursued an impressive number of topics: Liouville Quantum Gravity (LQG), Schramm–Loewner evolutions (SLE), random planar maps, statistical physics, data reconstruction, graphons, fine properties of Brownian motion, the Schelling model, and more. Her results are of theoretical nature, but have important implications in theoretical physics (conformal field theory, string theory, the understanding of gravity), as well as real-world phenomena such as phase transitions for random systems. Her proofs involve a wide variety of different techniques and ideas.

Holden’s perhaps most remarkable achievement, for which she was awarded the Maryam Mirzakhani New Frontiers Prize, concerns the convergence of uniform random planar triangulations (URPT) to LQG. Physicists have believed, since at least the 1980s, that if one takes an appropriate limit of large number of vertices of the URPT, one should obtain some form of convergence to LQG. In other words, just as discrete random walks converge to continuum random paths of Brownian motion, it should be the case that discrete random surfaces converge to continuum random surfaces.

In joint work with Xin Sun, Holden establishes this fact in a very precise way. They prove that if uniformly random planar triangulations are embedded in the plane via the so called Cardy embedding, then the embedded map converges to LQG. This result and various ramifications span six publications, with several co-authors, that are noteworthy in their own right and that have been published or accepted for publication in highest level journals such as Memoirs of the American Mathematical Society, Annales de l’Institut Henri Poincaré and Acta Mathematica.

In addition to the monumental results related to the Cardy embedding, Holden also has several other impressive achievements, in particular within the broad subject of conformal probability, from which we give some samples:

In “A distance exponent for Liouville quantum gravity”, with E. Gwynne and X. Sun, Probability Theory and Related Fields (2018), she has made some of the most important progress on the still somewhat mysterious problem of understanding distance functions on Liouville quantum gravity surfaces.

The paper “SLE as a mating of trees in Euclidean geometry”, with X. Sun, Communications in Mathematical Physics (2018), explains a fundamental property of the scaling limit of a uniformly random spanning tree, namely that it is in some sense determined by the structure of the graph itself.

The paper “An almost sure KPZ relation for SLE and Brownian motion”, with E. Gwynne and J. Miller, Annals of Probability (2020), provides a very general way to understand dimensions of random fractals arising in conformal probability, many related to statistical physics models.

In “Brownian motion correlation in the peanosphere for κ > 8”, with E. Gwynne, J. Miller and X. Sun, Annales de l’Institut Henri Poincar ́e (2017), an answer is given to a fundamental question asked by Miller and Sheffield in one of their papers.

The paper “Conformal welding for critical Liouville quantum gravity”, with E. Powell, Annales de l’Institut Henri Poincaré (2021), solves a problem about SLE and the conformal welding theory of LQG surfaces by extending the γ < 2 theory to the critical γ = 2 case.

In “Dimension transformation formula for conformal maps into the complement of an SLE curve”, with E. Gwynne and J. Miller, Probability Theory and Related Fields (2019), a formula is proved relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLE curve.

Outside of conformal probability, Holden has solved, in “How round are the complementary components of planar Brownian motion?”, with S. Naçu, Y. Peres,and T. S. Salisbury, Annales de l’Institut Henri Poincaré (2019), one of the more fundamental questions about the complementary components of planar Brownian motion, namely the extent to which they tend to be “round”, that is, have area on the same order of the square of their diameter. In the well-cited and recognized “Sparse exchangeable graphs and their limits via graphon processes”, with C. Borgs, J. T. Chayes and H. Cohn, Journal of Machine Learning Research (2018), so–called graphons are studied, which constitute an approach to large dense graphs. In addition, Holden has obtained interesting results on trace reconstruction problems for random strings and deletion probabilities in “Trace reconstruction with varying deletion probabilities”, with L. Hartung and Y. Peres, Analytic Algorithmics and Combinatorics (ANALCO) (2018), and in “Subpolynomial trace reconstruction for random strings and arbitrary deletion probability”, with R. Pemantle and Y. Peres, Conference On Learning Theory (COLT) (2018). The problems in this area involve the extent to which one can recover information about a string of characters when some of the characters have been randomly removed.

In conclusion, Holden’s research record is truly astonishing, with papers of exceptional depth and breadth published in first class journals, and she has very rapidly established herself as one of the leading researchers in probability theory at highest international level.

The board of the Norwegian Mathematical Society and the Norwegian National Committee for Mathematics has on February 27, 2022 issued the following statement concerning the invation of Ukraine and the upcoming ICM and IMU General Assembly:

«Mathematicians in Norway have been looking forward to celebrating mathematics this summer with people from around the world in Saint Petersburg, a city with a long and important tradition in mathematics. We strongly condemn the Russian government’s brutal invasion of Ukraine and we support IMU’s decision not to hold the 2022 International Congress of Mathematicians (ICM 2022)  in Saint Petersburg. 
Our thoughts are with our colleagues and the people in Ukraine suffering from the ongoing war and also with our colleagues and the people in Russia who are protesting against these unlawful actions of their government.»

«Norske matematikere har sett fram til å feire matematikk i sommer sammen med mennesker fra hele verden i Sankt Petersburg, en by med lange og viktige matematiske tradisjoner.  Vi fordømmer på det sterkeste den russiske regjeringens brutale invasjon av Ukraina og vi støtter IMUs avgjørelse om å ikke avholde den internasjonale matematikkongressen i Sankt Petersburg.  
Våre tanker er med våre kolleger og det ukrainske folk som lider under den pågående krigen og også med våre kolleger og alle i Russland som protesterer mot disse ulovlige handlingene begått av deres styresmakter.»

Yours sincerely,

Hans Z. Munthe-Kaas

President of the Norwegian Mathematical Society

Vi ber om at alle som ønsker å avholde Abelsymposium 2023 sender en skisse til mailto:nmf@matematikkforeningen.no innen 1. september 2023.

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