ANDREY TODOROV Professor of Mathematics B.A., Ph.D., Moscow State University

Phone: Office: Office Hours: On Leave Email: todorov_at_ucsc_dot_edu

RESEARCH INTERESTS

The research interests of Andrey Todorov are in the field of Algebraic Geometry. He is interested in the study of moduli of K3 surfaces, Calabi Yau manifolds and Hyper-Kahler manifolds and its relations to Mathematical Physics (String Theory) and Number Theory. More specifically Todorov’s research focuses on the following topics:

The Geometric Quantization of the Moduli space of polarized Calabi Yau manifolds and its relation with the Qunatum Independence Background in String Theory.

The generalization of the Dedekind Eta Function to higher dimension, its relation with the regularized determinants of CY metrics and with the algebraic notion of the discriminants.

The functional analogue of Shafarevich’s conjecture about finiteness of families of CY manifolds over Riemann surfaces with fix points of degeneration.

Generalization of Picard-Lefschetz theory of vanishing cycles, its relation with the notion of a large radius limit in string theory, theory of mixed Hodge structures and its applications to moduli problems of algebraic manifolds.

The relation between Rational Conformal Field Theories, K3 surfaces and CY manifolds admitting CM structures.

Lagrangian Fibrations of Hyper-Kahler manifolds and the topological classification of Hyper-Kahler manifolds.

SELECTED PUBLICATIONS

Igor Frenkel and A. Todorov: Complex Counterpart of Chern-Simons-Witten Theory and Holomorphic Linking. Preprint. math.AG/0502169

A. Todorov: Quantum Background Independence and Witten Geometric Quantization of the Moduli of CY Threefolds. Accepted for publication to Communications of Methematical Physics. math.AG/0004043

J. Bass and A. Todorov: The analogue of Dedekind eta function for CY manifolds I.  Journal fur die reine und angewandte Mathematik (Crelles Journal), v. 599, 61-96 (2006).

B. Lian, A. Todorov, and Shing-Tung Yau: Maximal Unipotent Monodromy for Complete Intersection CY Manifolds. Amer. Journal of Mathematics, v. 127, 1-50 (2005).

K. Liu, A. Todorov, Shing-Tung Yau, and K. Zuo: Shafarevich Conjecture for CY Manifolds I, Quarterly Journal of Pure and Applied Mathematics, v. 1 (2005).

A. Todorov: Local and Global Theory of the Moduli of Polarized Calabi-Yau Manifolds, Journal Revista Matematica Iberoamericana, v. 19, 1-43 (2003).

M. Schonbek, A. Todorov, and J. Zubelli: Geodesic Flows on Diffeomorphisms of the Circle, Grassmanians, and the Geometry of the Periodic KdV Equation. Adv. Theor. Math. Physics, v. 4, 1027-1090 (2000).

J. Jorgenson and A. Todorov: Ample Divisors, Automorphic Forms and Shafarevich Conjecture,  Mirror Symmetry IV, ed. Shing-Tung Yau, AMS Studies in Advanced Mathematics, 361-381. (2000).

J. Jorgenson and A. Todorov: Analytic Discriminant for Polarized K3 Surfaces Mirror Symmetry III, ed. Shing-Tung Yau, AMS Studies in Advanced Mathematics, 211-261. (1999).

J. Jorgenson and A. Todorov: Enriques Surfaces, Analytic Discriminant and Borcherds PSI Function. Comm. In Mathe, Physics, v. 191, 249-264 (1996)

J. Jorgenson and A. Todorov: A Conjectured Analogue of the Dedekind Eta Function for K3 Surfaces. Math. Research Notes,  v. 2, 359-376 (1995).

A. Todorov: Instanton Moduli as a Novel Map from Tori to K3 Surfaces, Invent. Math, v. 257, (1992).

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