About

James McKernan received his Ph.D. from Harvard University in 1991. He was recruited from MIT, where he was a Professor since 2007 and held an endowed chair, Norbert Weiner Professor since 2009. Prior to that, he was a professor at UC Santa Barbara from 1995 to 2007. His work concerns birational geometry, which has won numerous awards. McKernan’s research focuses on algebraic geometry, particularly birational geometry, and he has been recognized with several prestigious honors including the Breakthrough Prize in Mathematics, the Clay Research Award, the Cole Prize in Algebra, and he was an International Congress of Mathematicians Speaker in 2010. He is a Fellow of the Royal Society of the UK.

Research topics

• Mathematics
• Pure mathematics
• Combinatorics
• Sociology
• Pedagogy

Selected publications

• Юрий Геннадьевич Прохоров (к шестидесятилетию со дня рождения)

  Успехи математических наук · 2025-01-01

  articleOpen access

  2025 . - . 80, . 4 (484) ( ) 2 2024 . 60 - , .. . , - .. . , . - . , 1979 . - 18 - . 1981 . - . 1980- , , , - . , . . , . , .

  PublisherOA PDFDOI

• Yurii Gennadievich Prokhorov (on his sixtieth birthday)

  Russian Mathematical Surveys · 2025-01-01

  articleOpen access

  turned 60 years of age.He is widely recognized as one of the global leaders in contemporary birational algebraic geometry.He was born in the town of Orekhovo-Zuevo in Moscow Oblast, in a family of engineers.While still in school, he demonstrated talents for the exact sciences, which in 1979 earned him an invitation to Boarding School No. 18, a physics-mathematics school affiliated with Moscow State University.After graduating successfully in 1981, he enrolled in the Faculty of Mechanics and Mathematics (Mechmat) at Moscow State University (MSU).In the vibrant scientific atmosphere of Mechmat in the early 1980s, Yuri Prokhorov was fortunate to quickly find a mentor, Vasily Alekseevich Iskovskikh, who became his teacher, senior colleague, coauthor, and a kindred spirit in life principles.Thus Yuri joined the famous Soviet algebraic geometry school founded by I. R. Shafarevich.One of the key research fronts during that period concerned birational geometry of special classes of three-dimensional algebraic varieties.These problems became the focus of Prokhorov's work -initially under Iskovskikh's guidance, and later, after his teacher's untimely death, as the informal leader of the vibrant research community now known as the Iskovskikh School.After defending his undergraduate thesis in 1986, Prokhorov continued research under Iskovskikh's supervision in the graduate program at Mechmat, defending his Kandidat dissertation "Geometric properties of Fano varieties" in 1990.

  PublisherOA PDFDOI

• A geometric characterization of toric varieties

  Apollo (University of Cambridge) · 2018-04-01 · 27 citations

  articleOpen access

  We prove a conjecture of Shokurov which characterizes toric varieties using log pairs.

  PublisherOA PDFDOI

• Boundedness of varieties of log general type

  Proceedings of symposia in pure mathematics · 2018-06-01 · 2 citations

  other

  Simons foundation [DMS-1300750, DMS-1265285]; NSF [0701101, 1200656, 1265263]; Simons foundation; Mathematische Forschungsinstitut Oberwolfach; National Science Fund for Distinguished Young Scholars grant from China [11425101]

  PublisherDOI

• Boundedness of varieties of log general type

  Proceedings of symposia in pure mathematics · 2018-01-01 · 6 citations

  other

  We survey recent results on the boundedness of the moduli functor of stable pairs.

  PublisherDOI

• Boundedness of moduli of varieties of general type

  Journal of the European Mathematical Society · 2018-03-05 · 70 citations

  article

  We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.

  PublisherDOI

• Rational curves on algebraic spaces

  Advanced studies in pure mathematics · 2018-10-23

  articleOpen access1st authorCorresponding

  <!-- *** Custom HTML *** --> We prove a conjecture of Starr [11] that the conclusion of bend and break holds for proper algebraic spaces over an algebraically closed field of characteristic zero. The proof uses the minimal model program, rather than reduction modulo $p$ and it even applies to spaces with kawamata log terminal singularities.

  PublisherOA PDFDOI

• Boundedness of varieties of log general type

  arXiv (Cornell University) · 2016-06-24 · 2 citations

  preprintOpen access

  We survey recent results on the boundedness of the moduli functor of stable pairs

  PublisherOA PDFDOI

• Erratum

  Simons symposia · 2016-01-01

  erratumOpen access
  PublisherOA PDFDOI

• Ethics: from negative regulations to fidelity to the event

  ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) · 2015-01-01 · 7 citations

  articleSenior author

Recent grants

• FRG: Collaborative Research: Birational Geometry and Singularities in Zero and Positive Characteristic

  NSF · $106k · 2014–2017

• FRG: Collaborative Research: Birational Geometry and Singularities in Zero and Positive Characteristic

  NSF · $161k · 2013–2015

• Minimal Model Program

  NSF · $294k · 2010–2014

• Boundedness and termination

  NSF · $542k · 2014–2019

• Boundedness and termination

  NSF · $294k · 2012–2015

Frequent coauthors

• Christopher D. Hacon

  University of Utah

  20 shared

• Hong R. Zong

  University of Cambridge

  9 shared

• Morgan V. Brown

  9 shared

• Roberto Svaldi

  University of Utah

  9 shared

• Chenyang Xu

  7 shared

• Yuri Prokhorov

  5 shared

• Paolo Cascini

  5 shared

• Seán Keel

  5 shared

Education

• Bachelor of Arts, Mathematics

  University of Cambridge

• Part III, Mathematics

  University of Cambridge

• PhD, Mathematics

  Harvard University

Awards & honors

• Breakthrough Prize in Mathematics
• Fellow of the Royal Society of UK
• Cole Prize in Algebra
• International Congress of Mathematicians Speaker - 2010
• Clay Research Award