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Askold Khovanskii – Home Address – University Address 605-22 Walmer Road 40 St

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Date of Revision April 2021 A BIOGRAPHICAL INFORMATION 1 PERSONAL { Askold Khovanskii { Home address { University address 605-22 Walmer Road 40 St. George Street Toronto, ON, Toronto, ON, Canada M5R 2W5 Canada M5S 2E4 (416)926-8572 (416)978-4868 2 DEGREES { Russian Doctoral degree { 1988 Steklov Mathematical Institute, Moscow { Newton Polyhedra and Fewnomials { Ph.D. { 1973 Steklov Mathematical Institute, Moscow { Representability of Functions in Quadratures { M.S. { 1970 { Moscow State University, Moscow { Superpositions of Holomorphic Functions with Radicals 3 EMPLOYMENT Since 1996 July { Full Professor at the University of Toronto, Canada Since 1991 { Professor of the Moscow Independent University 1995, January - June { Visiting Professor, University of Toronto, Canada 1994, January - June { Visiting Professor, University of Toronto, Canada 1993, January - June { Visiting Professor, University of Minnesota, USA 1992, July { Visiting Professor, University Paris-7, France 1992, March { Visiting Professor, University of Maryland, USA 1992, February { Visiting Professor, University of Bern, Switzerland 1992, January { Visiting Professor, Mittag-Leffler Institute, Sweden 1991, April { Visiting Professor, University Paris-7, France 1991, May { Visiting Professor, University of Dijon, France 1991, June { Visiting Professor, Ecole Polytechnic, France 1990, April { Visiting Professor (Distinguished Ordway visitor), University of Minnesota, Twin Cities, USA 1990, March { Scholar, Harvard University, USA 1981, spring { Visiting Professor, IHES, Bures-sur-Yvette, France 1976{2014 { Institute for System Studies of the Academy of Sciences of Russia Main scientific staff member, member of Scientific Committee 1973{1976 { Institute of Applied Mathematics of the Academy of Sciences of the USSR, Junior scientific staff member 1 4 HONOURS 2020 Fellow of Royal Canadian Society 2017 International Conference \Galois Meets Newton: Algebraic and Geometric aspects of Singularity Theory" celebrating the 70th birthday of Prof. Askold Khovanskii, Weizmann Institute of Science, Israel 2014 Jefferey–Williams Prize for outstanding contributions to mathematical research in Canada 2012 International Conference dedicated to the 65-th anniversary of Askold G. Khovanskii \Algebra and Geometry", Higher School of Economics, Independent University of Moscow, Moscow, Russia 2012 A meeting of Bourbaki's seminar (France) was devoted to the theoty of Okounkov bodies developed by Kaveh-Khovanskii and Lazarsfeld-Mustata. 2007 Two issues of the Moscow Mathematical Journal (V. 7, NN 2{3) were dedicated to Askold Georgievich Khovanskii on the occasion of his 60th birthday 1984 A meeting of Bourbaki's seminar (France) was devoted to Khovanskii's theory of fewnomials 1983 International Congress of Mathematicians in Warszawa. \Fewnomials and Pfaff manifolds". Invited 45-Minute Speaker in Section 1978 A short talk at the International Congress of Mathematicians Helsinki, Finland 5 PROFESSIONAL AFFILIATION AND ACTIVITIES { Editor in Chief of the Arnold Mathematical Journal, the Institute of Mathematical Science at Stony Brook, USA, and by Springer Verlag, Germany. { Fellow of Royal Canadian Society. { Chair of the Scientific Committee of International conference \Contemporary mathe- matics" marking the 80th birthday of Vladimir Arnold, National Research University Higher School of Economics, Moscow, Russia, 2017. { Member of Canadian Mathematical Society. { Member of Moscow Mathematical Society (1994{1998 and 2010{2016 member of Boarding Committee). { Member of American Mathematical Society. { Series Editor of \Moscow Lectures", Springer Berlin Heidelberg. { Member of Editorial Board of the Russian Mathematical Surveys. { Member Dissertation Council (mathematics) of the National Research University Higher School of Economics since 2018. { Member of Scientific Committee of the Independent Moscow University. { Member of Boarding Committee of the Journal \Functional Analysis and Other Mathematics" till January 1, 2013. 2 { Member of Editorial Board of the Moscow Mathematical Journal. { Member of the Board of Experts Foundation for the Advancement of Theoretical Physics and Mathematics \BASIS". 2018{2020. { Jury member of the contest \Young Russian Mathematics", 2015{2020. { Member of the Scientific Committee and Local Organization Committee of Confer- ence Legacy of Vladimir Arnold, Fields Institute, Toronto, Canada. 2013{2014. { Jury member of the Simons contest. 2011. { Member of the Program Committee of the Conference \Polynomial Computer Al- gebra", Euler International Mathematical Institute, St. Petersburg, Russia. 2011{ 2021. { Jury member of the Dinastia contest. 2010{2014. { Consultant of Committee on Translations from Russian and Other Slavic Languages, AMS. 2008{2009. { Chair of \Math in Moscow Scholarship Selection Committee", AMS. 2007{2008. { Member \Math in Moscow Scholarship Selection Committee", AMS. 2006{2007, 2008{2009. { Jury member of the Pierre Deligne and Dinastia contest. 2006{2009. { Jury member of the Pierre Deligne contest. 2005. { Member of Editorial Board of the PHASIS Publishing House, 1995{2003. { Member of Scientific Programme Committee of the International Scientific Confer- ence \New Geometry and Nature", Kazan, Russia. 2003. { Member of the Program Committee of the Conference Conference in Honor of Vladimir Arnol'd at the Fields Institute. 1997. { Member of Boarding Committee of the \Functional Analyzes Its Applications". 1994{2005. { Member of Boarding Committee of the \The Selecta Mathematica Sovietica". 1991{ 1994. B ACADEMIC HISTORY 6 A RESEARCH ENDEAVOURS I started the topological Galois theory in my PhD. My theory gives the strongest results about unsolvability of algebraic and differential equations in finite terms and provides the topological reasons for such unsolvability. I am one of the creators of the Newton polyhedra theory. I discovered connec- tions between the geometry of Newton polyhedra and the theory of toric vari- eties, results that are now used in both algebraic geometry and combinatorics. I computed many discrete invariants of singularities and of complete intersections using Newton diagrams and Newton polyhedra. This experience in a polyhedral geometry allowed me to prove (jointly with M. Prokhorov) a longstanding con- jecture about absence of a group generated by reflections with a fundamental domain of finite volume in a multidimensional hyperbolic space. Along the same 3 lines is the well known combinatorial analogue of the Riemann-Roch theorem discovered by Pukhlikov and me. It provided the first multidimensional general- ization of the Euler-MacLaurin formula and initiated a broad and very fruitful activity in the geometric community. I also created so called, fewnomial theory. It develops a category of transcenden- tal varieties reminiscent of algebraic geometry. Besides the real algebraic vari- eties, this category contains, for example, graphs of logarithmic and exponential functions. Among applications of this theory, there are my multidimensional version of the classical rule due to Descartes and the solution by Varchenko and me of the Hilbert-Arnold problem about a uniform bound on the number of zeros of abelian integrals. Also Wilkes solution of the longstanding Tarsky problem heavily uses my fewnomials theory. Another area to a large extent motivated by my fewnomials is the recent theory of O-minimal sets. In 1984 I gave an invited talk about this theory at the International Congress of Mathematicians in Warsaw. In the last years together with others I developed the theory of Newton-Okounkov bodies, which provides a new powerful connection between algebra and geome- try. For example, applying it in one direction one can derive a general theorem about systems of algebraic equations from a simple geometric inequality known even to Ancient Greeks. Applying it again in the opposite direction one can derive from this theorem the famous very hard to prove Alexandrov-Fenchel geometric inequality. C SCHOLARLY AND PROFESSIONAL WORK 11 Invited Lecture a. General meetings ∗ 2019 Canadian Mathematical Society Winter Meeting, Convexity in Algebraic Geometry and Symplectic Geometry Session. Toronto. 2019. ∗ Sessions of Moscow Mathematical Society. 2017. ∗ 2016 Canadian Mathematical Society Winter Meeting, Combinatorial Algebraic Geometry Scientific Session, Niagara Falls. 2016. ∗ 2014 Canadian Mathematical Society Winter Meeting, Jeffery-Williams Prize and Lecture, Hamilton. 2014. ∗ 6th European Congress of Mathematics, Mini-symposium, Krakov, Poland. 2012. ∗ Sessions of Moscow Mathematical Society. 2011. ∗ Joint meeting of the St.Petersburg Mathematical Society & the Section of the House of Scientists. St.Petersburg, Russia. 2010. ∗ Sessions of Moscow Mathematical Society. 2008. ∗ Sessions of Moscow Mathematical Society. 2007. ∗ Incorporating 57th British Mathematical Colloquium & 47th British Applied Mathematics Colloquium, Liverpool, UK. 2005. ∗ Sessions of Moscow Mathematical Society. 2004. ∗ Conference of Canadian Mathematical Society, Ottawa. 2002. ∗ Sessions of Moscow Mathematical Society. 2002 4 ∗ Conference of Canadian Mathematical Society, Kingston. 1998. ∗ Sessions of Moscow Mathematical Society. 1997. ∗ Sessions of Moscow Mathematical Society. 1996. ∗ Conference of Canadian Mathematical Society, Toronto. 1995. ∗ Sessions of Moscow Mathematical Society. 1995. ∗ Sessions of Moscow Mathematical Society.1994. ∗ Congress of Singularities, France. 1991. ∗ Sessions of Moscow Mathematical Society and Petrovsky Seminar. 1990. ∗ Sessions
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