Professor Cattani's current research deals mainly with the study of rational hypergeometric functions in several variables and the Hodge theory of algebraic varieties.
Articles
The Structure of Bivariate Rational Hypergeometric Functions (with Alicia Dickenstein and Fernando Villegas), International Mathematics Research Notices (2010)
We describe the structure of all codimension-2 lattice configurations A which admit a stable rational...
Infinitesimal variations of Hodge structure at infinity (with J Fernandez), Geometriae Dedicata (2009)
By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the...
Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations, International Mathematic Research Notices (2008)
The Hard Lefschetz Theorem (HLT) and the Hodge–Riemann bilinear relations (HRR) hold in various contexts:...
Complete intersections in toric ideals (with R Curran and A Dickenstein), Proceedings of the American Mathematical Society (2007)
Counting solutions to binomial complete intersections (with A Dickenstein), Journal of Complexity (2007)
We study the problem of counting the total number of affine solutions of a system...
Other
Asymptotic Hodge theory and quantum products (with Javier Fernandez), Mathematics and Statistics Department Faculty Publication Series (2000)
Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold $X$ one may...
Computing Multidimensional Residues (with Alicia Dickenstein and Bernd Sturmfels), Mathematics and Statistics Department Faculty Publication Series (1994)
Given n polynomials in n variables with a finite number of complex roots, for any...