(Pantev): I will explain how essential information about the structure of symplectic manifolds is captured by algebraic data, and specifically by the non-commutative mixed Hodge structure on the cohomology of the Fukaya category. As application we obtained complete classification of skew-symmetric cluster algebras by the growth rate (finite, polynomial, or exponential). More exactly, we proved conjecture by Derksen and Owen that a connected quiver with at least three vertices whose mutation class is finite either corresponds to a triangulated bordered surface or is of one of eleven exceptional types. We classify all finite classes of mutation equivalent quivers. Any skew-symmetric cluster algebra defines a class of mutation equivalent quivers. Mutations of clusters of skew-symmetric cluster algebra induce mutations of quivers. Generators of cluster algebra are collected into clusters that mutate one into another. (Shapiro): Cluster algebras were introduced by Fomin and Zelevinsky to create an algebraic framework for total positivity and canonical bases in In another direction, we discuss how ACM bundles produce subvarieties of X that are not cut out properly on X by a subvariety of projective space. We discuss work of Kleppe, Chiantini-Madonna and Kumar-Rao-Ravindra in this direction. Recent theorems indicate that ACM bundles of small rank should not exist on hypersurfaces of large dimension. We will discuss constructions of such ACM bundles. Indecomposable ACM bundles of rank >1 exist on any smooth hypersurface. (Rao): An Arithmetically Cohen Macaulay vector bundle on a hypersurface X of projective space is a bundle E for which $H^i(X,E(a))=0$ for any integer a and any i between 1 and dim(X)-1. Generalization of this result in birational geometry. In this talk we will discuss the proof of his theorem and talk about a higher dimensional Royden showed that the converse is true if $X$ and $Y$ both have genus $g\geq 2$. If $X\to Y$ is an isomorphism between Riemann surfaces the induced map $H^0(Y, 2K_Y)\to H^0(X, 2K_X)$ will actually be a linear isometry with respect to the canonical norms. (Chi): Given a Riemenn surface $X$ there is a canonical norm on its space of holomorphic quadratic differentials $H^0(X, 2K_X)$. In the case of Fano toric varieties, we show how their deformations induce deformations Calabi-Yau hypersurfaces. In our construction the toric variety is embedded into a higher dimensional toric variety where the image is given by a complete intersection toric ideal in Cox homogeneous coordinates. We will show how Altmann's construction can be extended using a categorical quotient presentation of a subvariety of a toric variety. Rational points vs zero cycles of degree one in stable A^1-homotopyĬluster Algebras and Quiver GrassmanniansĪbstracts (Mavlyutov): In the 90's, Klaus Altmann constructed deformations of affine toric varieties as complete intersections in another toric variety using Minkowski sums of polyhedra. Stable cohomology of Hurwitz spaces and arithmetic applicationsĪlgebraic bounds on analytic multiplier ideals Geometric Langlands and non-abelian Hodge theoryĮlementary modular representation theory (Colloquium)Ĭlassical conjectures on algebraic cycles Geometric Langlands Duality and its classical limit OSU/UM/UIC weekend algebraic geometry workshop at U Michigan (in honor of the retirement of I. Varieties with quasi projective universal cover Great Lakes Geometry Conference 2011 in OSU Geometry of general curves via degenerations and deformationsį-theory GUTs: Particle Physics from Algebraic Geometry Universal Polynomials for Severi Degrees of Toric Surfaces On the derived structure of the moduli of A-branesĬonstructing moduli spaces of objects with infinite automorphisms (see also Chi's talk in Differential Geometry seminar) Pluricanonical spaces and their canonical distance structures OSU/UM/UIC weekend algebraic geometry workshop at UIC Time/Location: Tuesdays 4:30pm/CH240 (unless otherwise noted)Ĭomplete intersection toric ideals with applications to deformations of toric and Calabi-Yau varieties Ohio State University Algebraic Geometry Seminar
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