Ilia Zharkov

Assistant Professor

Office Location: Cardwell Hall 110

Office Phone: 785-532-0589

Departmental Fax: 785-532-0546

Mailing Address:

138 Cardwell Hall

Mathematics Department

Kansas State University

Manhattan, KS 66506 USA

Email: zharkov AT then you guess right

Teaching:

• Fall 2005: Math 136. Differential Geometry
• Spring 2005: Math 21b. Linear Algebra and Differential Equations
• Fall 2004: On leave to UW Madison
• Spring 2004: On leave to MSRI
• Fall 2003: Math 273x. Toric Varieties and Applications

• Algebraic and differential geometry

  I study various structures on Calabi-Yau manifolds related to mirror symmetry from the geometric point of view. In particular, this includes homological mirror symmetry, Strominger-Yau-Zaslow conjecture and a link between these two provided by the metric collapse and its algebraization via non-archimedean geometry. Recently I have a strong inlcination towards tropical geometry. More generally, I am interested in geometry arising from any kind of dualities in string theory.

Diploma		Moscow Institute of Physics and Technology	1994
Ph.D.		University of Pennsylvania (Thesis advisor: Ron Donagi )	2000

Publications and preprints:

• (with Grigory Mikhalkin), Tropical curves, their Jacobians and Theta functions, preprint, [math.AG/0612267].
• (with Christian Haase), Integral affine structures on spheres: complete intersections, Int. Math. Res. Not. 2005, no. 51, 3153--3167, [math.AG/0504181].
• Limiting behavior of local Calabi-Yau metrics , Adv. Theor. Math. Phys. 8 (2004), no. 3, 395-420, [math.AG/0304116].
• (with Christian Haase), Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces II, preprint 2003, [math.AG/0301222].
• (with Christian Haase), Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I, preprint 2002, [math.AG/0205321].
• Theta functions for indefinite polarizations, J. Reine Angew. Math. 573 (2004), 95--116, [math.AG/0011112].
• Torus fibrations of Calabi-Yau hypersurfaces in toric varieties , Duke Math. J., 101 (2000), no. 2, 237--257, [math.AG/9806091].
• (with Igor Chubarov), On indecomposable representations of quantum $SL_q(2)$, Vestnik M.I.Ph.T., 1995.

Miscellaneous

In my free time I like to do serious expeditional caving, work on my ultimate driving machine or travel with my family.

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Last modified: 12/10/06