Abelian Varieties and Curves

Elham Izadi将工作的问题所产生的霍奇代数的阿贝尔品种和曲线与他们有关。她将使用对应关系产生具体的家庭的曲线在阿贝尔品种。对于阿贝尔品种与行动的虚二次领域，她开发了一个具体的方法，使用家庭的曲线，变形和专业化，和霍奇束的边界线性系统。她将为学生们组织一个研究小组，研究这个项目产生的基本问题。在过去，利用这样的研究小组，她已经成功地使妇女到格鲁吉亚大学，这项研究是在代数几何领域，其主要研究对象是代数簇。这些是经典定义为多项式的同时零点集。阿贝尔簇和阿贝尔曲线是特殊的代数簇，在数学的许多领域都有应用，包括数论和编码理论。经典上，它们出现在阿贝尔，雅可比和黎曼等人的工作中，他们开发了模形式理论。它们为代数几何中的重要定理（如霍奇定理）提供了理想的实验场所。这些都是深刻的acquitures与深远的影响，研究代数簇。 他们最初制定的形式问题的霍奇，然后重新制定和纠正的其他人包括一些最伟大的数学家的这个世纪，如格罗滕迪克。

Elham Izadi will work on questions resulting from the Hodge conjectures for abelian varieties and curves related to them. She will use correspondences to produce concrete families of curves in abelian varieties. For abelian varieties with actions of imaginary quadratic fields, she develops a concrete approach using families of curves, deformations and specializations, and Hodge bundles at the boundaries of linear systems. She will run a research group for students on elementary questions resulting from this project. In the past, using such research groups, she has been successful in bringing women to the University of Georgia.This research is in the field of algebraic geometry, whose main objects of study are algebraic varieties. These are classically defined as the sets of simultaneous zeros of polynomials. Abelian varieties and curves are special algebraic varieties with applications in many areas of mathematics including number theory and coding theory. Classically they appear in the work of Abel, Jacobi and Riemann among others, who developed the theory of modular forms. They make ideal testing grounds for important conjectures in algebraic geometry such as the Hodge conjectures. These are deep conjectures with far reaching consequences for the study of algebraic varieties. They were originally formulated in the form of questions by Hodge, then reformulated and corrected by others including some of the greatest mathematicians of this century such as Grothendieck.