|10am-10:50am||Corey Stone||Euler systems
Abstract: In the 1990s, Kolyvagin introduced Euler systems, which Rubin used to give a simpler proof of the Iwasawa main conjecture, first proven by Mazur and Wiles. The Euler system technique was also used by Kurihara to determine the structure of the first Fitting ideal of certain ideal class groups. In this talk we will describe the Euler system of Gauss sums, briefly outline its use in Kurihara's result, and then discuss work relating the method of Euler systems to a conjecture of Gross.
|11am-11:50am||Robert Won||Categories of graded modules: What they are and what you can do with them
Abstract:What's a graded module? Why should I care? We'll answer these questions as we learn about graded rings, graded modules, and figure out how to do geometry in the absence of a geometric space. I will present a theorem on graded module categories from my thesis, and we'll learn one way to define a functor on a category of graded modules.
|12pm-12:50pm||Jonathan Conder||E6 and the cohomology of abelian fivefolds
Abstract: Some numerical and other evidence points to a mysterious connection between the exceptional Lie algebra E6 and the middle cohomology of certain ample divisors in abelian fivefolds. I will try to explain some of this evidence and describe how I hope to make this connection more explicit.