Alex Eskin

from Wikipedia, the free encyclopedia

Alexander "Alex" Eskin , Russian Алексей Олегович Еськин , transcription Alexei Olegowitsch Jeskin, (born May 19, 1965 in Moscow ) is a Russian-born American mathematician who deals with geometric group theory, ergodic theory and dynamic systems (billiards), Lie groups busy with applications in number theory.

He studied mathematics at the University of California, Los Angeles (Bachelor's degree 1986), then physics at the Massachusetts Institute of Technology until 1989 . In 1991 he studied mathematics at Stanford University and received his doctorate in 1993 from Princeton University under Peter Sarnak ( Counting lattice points on homogeneous varieties ). In 1993/94 he was a postdoc at the Institute for Advanced Study . He was then at the University of Chicago , first as a Dickson Instructor, from 1997 as Associate Professor and from 1999 as Professor.

Among other things, he dealt with the dynamics and geometry of Teichmüller rooms , geometric group theory, ergodic theory in Lie groups and billiards in rational polygons .

In 1992/93 he was a Sloan Research Fellow and from 1997 to 2002 a Packard Fellow. In 2007 he received the Clay Research Award , particularly for collaborative work with David Fisher and Kevin Whyte, which demonstrated the rigidity of groups that are quasi-isometric to the three-dimensional solvable Lie group Sol. In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( quasi-isometric rigidity of solvable groups with David Fisher) and in 1998 in Berlin ( counting problems and semisimple groups ). He is a Fellow of the American Mathematical Society ; in 2011 he was elected to the American Academy of Arts and Sciences and in 2015 to the National Academy of Sciences . For 2020 he was awarded the Breakthrough Prize in Mathematics . He received it for the proof of the magic wand theorem with the late Maryam Mirzakhani from the dynamics of modular spaces of Abelian differentials.

Works (selection)

  • with Curtis McMullen : Mixing, counting, and equidistribution in Lie groups. Duke Math. J. 71 (1993) no. 1, 181-209.
  • with Shahar Mozes , Nimish Shah : Unipotent flows and counting lattice points on homogeneous varieties. Ann. of Math. (2) 143 (1996) no. 2, 253-299.
  • Quasi-isometric rigidity of non-uniform lattices in higher rank symmetric spaces. J. Amer. Math. Soc. 11 (1998), no. 2, 321-361.
  • with Grigori Margulis , Shahar Mozes: Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture. Ann. of Math. (2) 147 (1998) no. 1, 93-141.
  • with Andrei Okounkov : Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials. Invent. Math. 145 (2001), no. 1, 59-103.
  • with Howard Masur , Anton Zorich : Moduli spaces of abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants. Publ. Math. Inst. Hautes Études Sci. No. 97 (2003): 61-179.
  • with David Fisher : Quasi-isometric rigidity of solvable groups. Proceedings of the International Congress of Mathematicians. Volume III, 1185-1208, Hindustan Book Agency, New Delhi, 2010.
  • with David Fisher, Kevin Whyte : Coarse differentiation of quasi-isometries I: Spaces not quasi-isometric to Cayley graphs. Ann. of Math. (2) 176 (2012), no. 1, 221-260. II: Rigidity for Sol and lamplighter groups. Ann. of Math. (2) 177 (2013), no. 3, 869-910.
  • with Maxim Kontsevich , Anton Zorich: Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow. Publ. Math. Inst. Hautes Études Sci. 120 (2014), 207-333.
  • with Maryam Mirzakhani : Invariant and stationary measures for the SL (2, R) action on Moduli space. , Publ. Math. IHES, Volume 127, 2018, pp. 95-324, Arxiv
  • with Simion Filip, Alex Wright: The algebraic hull of the Kontsevich – Zorich cocycle , Annals of Mathematics, Volume 188, 2018, pp. 281-313

Web links

Individual evidence

  1. ↑ mathnet.ru
  2. ↑ Curriculum Vitae from Eskin, University of Chicago, accessed October 25, 2018
  3. ↑ Alex Eskin in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  4. ↑ Abstracts of his work on his homepage , laudation at the Clay Research Institute ( Memento from November 3, 2013 in the Internet Archive )
personal data
SURNAME Eskin, Alex
ALTERNATIVE NAMES Eskin, Alexander (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH May 19, 1965
PLACE OF BIRTH Moscow