Maryna Viazovska

Maryna Viazovska
Name	Maryna Viazovska
Birth date	1984
Birth place	Kyiv, Ukrainian SSR
Nationality	Ukrainian
Fields	Mathematics
Alma mater	Kyiv National University, Swiss Federal Institute of Technology in Lausanne
Known for	Solution of the sphere packing problem in dimension 8
Awards	EMS Prize, Clay Research Award, New Horizons in Mathematics Prize, Fields Medal

Maryna Viazovska is a Ukrainian mathematician known for solving the sphere packing problem in eight dimensions and for contributions to modular forms, optimization, and discrete geometry. She completed studies in Kyiv and at the École Polytechnique Fédérale de Lausanne and has held positions at institutions including the Institute for Advanced Study, Princeton University, and the Swiss Federal Institute of Technology in Lausanne. Her work connects classical problems studied by John Conway, Neil Sloane, and Henry Cohn with techniques from the theory of modular forms and harmonic analysis.

Early life and education

Viazovska was born in Kyiv during the era of the Ukrainian SSR and attended local schools before studying mathematics at Taras Shevchenko National University of Kyiv (often called Kyiv National University). She pursued graduate studies at the École Polytechnique Fédérale de Lausanne (EPFL), working within programs that involved collaborations with faculty at ETH Zurich, University of Zurich, and research groups linked to the Institute for Advanced Study. During her doctoral training she engaged with topics related to modular forms, the Fourier transform, and problems popularized by John Conway and Neil Sloane in connection with lattice packing.

Academic career and positions

Viazovska has held appointments and affiliations at several leading institutions: postdoctoral and visiting roles at the Institute for Advanced Study, a visiting position at Princeton University, faculty roles at the Swiss Federal Institute of Technology in Lausanne (EPFL), and collaborations with research groups at University of Cambridge, Harvard University, Massachusetts Institute of Technology, and Imperial College London. She has participated in programs run by the Mathematical Sciences Research Institute (MSRI), lectures at the International Congress of Mathematicians, and seminars hosted by the American Mathematical Society and the European Mathematical Society. Her teaching and supervision occurred alongside colleagues from Stanford University, University of California, Berkeley, and Columbia University.

Contributions to mathematics

Viazovska's breakthrough solution of the sphere packing problem in eight dimensions built on conjectures and numerical investigations by Conway and Sloane and on earlier rigorous bounds developed by Henry Cohn, Aubrey de Gray, and Jeffrey Lagarias. She constructed an explicit radial Schwartz function using techniques from the theory of modular forms, quasimodular forms, and the Laplace transform to produce an optimality proof for the E8 lattice packing, connecting to the work of Ernst Witt and the classification of even unimodular lattices. Her methods were extended, in joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Drew S. Lubinsky to prove optimality in twenty-four dimensions for the Leech lattice, drawing on structures studied by John Leech and results related to sporadic simple groups and the Monster group via connections with modular functions. Beyond sphere packing she has contributed to problems in interpolation, energy minimization, and optimization, interfacing with research by Viacheslav Nikulin, Igor Shafarevich, and analysts studying the Poisson summation formula and theta functions. Her explicit constructions introduced new applications of quasi-modular forms and advanced techniques in discrete geometry used by researchers at institutions such as Princeton, Harvard, and Cambridge.

Awards and honors

She received numerous distinctions including the EMS Prize, the Clay Research Award, the New Horizons in Mathematics Prize, and the Fields Medal. Additional recognitions include fellowships and prizes from organizations like the European Mathematical Society, the American Mathematical Society, the International Mathematical Union, and awards conferred by institutions such as EPFL and the Institute for Advanced Study. Her work was highlighted in coverage by the Royal Society, the National Academy of Sciences, and invited addresses at the International Congress of Mathematicians and the European Congress of Mathematics.

Selected publications

- "The sphere packing problem in dimension eight", published in a leading journal; the result built on conjectures formulated by John Conway and Neil Sloane and techniques influenced by Srinivasa Ramanujan and Atle Selberg. - Joint work with Henry Cohn proving optimality in twenty-four dimensions, related to the Leech lattice and studies by John Leech and J. H. Conway. - Papers on interpolation and modular forms that connect to research traditions established by André Weil, Hideki Yukawa, and Serge Lang. - Contributions on energy minimization and discrete analysis interfacing with work by Thomas Hales, László Lovász, and Oded Schramm.

Personal life and outreach

Viazovska has engaged in public outreach through lectures hosted by institutions like the Institute for Advanced Study, public talks at the Royal Institution, and interviews with outlets associated with the European Mathematical Society. She has participated in conferences sponsored by the Clay Mathematics Institute, given talks at the Mathematical Association of America, and contributed to programs encouraging young mathematicians in Ukraine and across Europe. Outside academia she maintains ties to cultural institutions in Kyiv and has been cited in profiles by organizations such as the National Academy of Sciences and media coverage in scientific sections of major outlets.

Category:Ukrainian mathematicians Category:Women mathematicians Category:Fields Medalists