Anvar R. Mavlyutov: Curriculum Vitae

• Mailing address: Department of Mathematics, Oklahoma State University, Stillwater, OK, 74075.
• Phone: (405)-744-6540
• Email: mavlyutov@math.okstate.edu
• Date of Birth: 25 August 1971

Education

• B.S. in Mathematics, Novosibirsk State University, Russia, 1992.
• M.S. in Mathematics, Novosibirsk State University, Russia, 1994.
• Ph.D. in Mathematics, University of Massachusetts at Amherst, 2000 (Thesis advisor: David A. Cox, Amherst College; thesis title: Toric Geometry and Mirror Symmetry).

Appointments

Clay Mathematics Institute, USA, Liftoff Research Fellow, June – August 2000.
Max-Planck-Institut für Mathematik, Bonn, Research Member, September 2000 – August 2001, and  May – August 2003.
Indiana University, Bloomington, Zorn Assistant Professor, August 2001 – December 2003.
Isaac Newton Institute for Mathematical Sciences, Cambridge, Research Member, programme “The Higher Dimensional Complex Geometry”, June – July, 2002.
University of Oxford, Mathematical Institute, England, EPSRC Postdoctoral Fellow, December 2003 – August 2004
Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France, Research Member,  June 15 –  August 15 in 2004 and 2005.
Oklahoma State University, Stillwater, Tenure-Track Assistant Professor, August 2004 -- present

Research interests

Algebraic Geometry and Mirror Symmetry:  Calabi-Yau varieties and mathematics related to them.

Publications and preprints

Cohomology of rational forms and a vanishing theorem on toric varieties, Journal für die reine und angewandte Mathematik (Crelle's Journal), to appear.
Embedding of Calabi-Yau deformations into toric varieties, Mathematische Annalen333  (2005), 45–65.
Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varietiesInventiones Mathematicae, 157 (2004), 621–633.
• (with Lev Borisov) String cohomology of Calabi-Yau hypersurfaces via Mirror SymmetryAdvances in Mathematics, 180 (2003), Issue 1, 355–390.
Nef complete intersections in toric varieties, preprint in progress.
On the chiral ring of Calabi-Yau hypersurfaces in toric varieties, Compositio Mathematica, 138 (2003), Issue 3, 289–336.
Approximation by smooth curves near the tangent cone, Journal of Algebra, Volume 266, Issue 1, (2003), 154–161.
“The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map” in
Advances in Algebraic Geometry Motivated by Physics
, Contemp. Math., 276
, Amer. Math. Soc., Providence, RI, 2001, 199–227.
Semiample hypersurfaces in toric varieties, Duke Mathematical Journal, 101 (2000), 85–116.
Cohomology of complete intersections in toric varieties, Pacific J. of Math., 191 (1999), no 1, 133–144.
Stable nilpotent algebras of degree 3, Sibirsk. Mat. Zh. 40 (1999), no. 1, 91–101; translation in Siberian Math. J. 40 (1999), no. 1, 76–84.
Nilpotency of degree 3 that is stable in some class of algebras, Sibirsk. Mat. Zh. 39 (1998), no. 6, 1336–1337;
translation in Siberian Math. J. 39 (1998), no. 6, 1153–1154.
• (with A. Z. Anan’in) Stability of nilpotence of the third degree , Sibirsk. Mat. Zh. 35 (1994), no. 3, 480–494;
translation in Siberian Math. J. 35 (1994), no. 3, 426–438.

Selected talks

• “Embedding of Calabi-Yau deformations into toric varieties”, Conference on Geometry and Topology of Quotients,  December 2002,  University of Arizona, Tucson.
• “Deformations of Calabi-Yau hypersurfaces”, Isaac Newton Institute for Mathematical Sciences, June 2002, Cambridge, UK.
• “Recent developments in string cohomology”, EAGER annual conference 2001 at Sophus Lie conference center, Nordfjordeid, Norway.
• “Cohomology ring of semiample hypersurfaces and nef complete intersections, and String Cohomology of orbifolds”, Oberwolfach meeting on Combinatorial Convexity and Algebraic Geometry, January 2001, Mathematisches Forschungsinstitut Oberwolfach, Germany.
• “The chiral ring of Calabi-Yau hypersurfaces, the roots of An and a generalization of the monomial-divisor mirror map”, Workshop on Algebraic Geometry and Physics, International school for advanced studies, Trieste, Italy, October 2000 (also presented in the Oberseminar at the Max-Planck-Institut and in “Mathematical Challenges of the 21st century”, UCLA, 2000.)
• “Mirror Symmetry, cohomology and the chiral ring of Calabi-Yau hypersurfaces in toric varieties”, the AMS meeting (special session “Enumerative geometry in physics”), April 2000.
• “Geometry of semiample hypersurfaces in toric varieties”, Valley Geometry Seminar, November 1998, University of Massachusetts at Amherst.
• “Cohomology of complete intersections in toric varieties”, Midwest Algebraic Geometry Conference, November 1997, Notre Dame, Indiana.

Grants and Awards

• Summer 2004 and 2005, Dean's incentive grant.
• Summer 2000, Liftoff program of the Clay Mathematics Institute for the new Ph.D. recipients in the U.S.
• Fall 1998, Graduate Fellowship, University of Massachusetts at Amherst.
• Summer research grant, 1997, 1998, 1999.
• 1993–1995, a grant for graduate studies in Russia from the American Mathematical Society.

Teaching

Oklahoma State University, Stillwater
 
  Fall 2006: Calculus I
   Spring 2006: Algebra II (graduate course)
   Fall 2005: Algebra I (graduate course) and Calculus I
   Spring 2005: Linear Algebra
   Fall 2004: Calculus I and Number Theory.
Indiana University, Bloomington
   Fall 2003: Finite Mathematics and Calculus III,
   Spring 2003: Introduction to differential geometry and Calculus I, 
   Fall 2002: Algebraic Geometry (graduate course) and Calculus I,
   Spring 2002: Finite Mathematics,
   Fall 2001: Calculus I.
University of Massachusetts, Amherst
   Instructor, Calculus I and II, 1997-2000; Review sessions for graduate qualifying exams, 1996-1999.