Seminar za algebro

Sreda, 14. novembra 2012, ob 10. uri v Plemljevem seminarju, Jadranska 19/III, Ljubljana

Sreda, 7. novembra 2012, ob 10. uri v Plemljevem seminarju, Jadranska 19/III, Ljubljana

Sreda, 24. oktobra 2012, ob 10. uri v Plemljevem seminarju, Jadranska 19/III, Ljubljana

There are several conjectures in the theory of algebraic cycles relating groups of algebraic cycles, on the one hand, with values of certain zeta functions, on the other. One well known example is the Dirichlet Class number formula relating the units group and class group with the value at 0 of the Dedekind zeta function. \zeta_K^*(0)=-R_Kh_K/w_k Several people have formulated general conjectures generalizing this formula. In this talk we will describe some work on algebraic cycles on Abelian surfaces and K3 surfaces which is motivated by trying to prove these conjectures in some special cases.

I will be talking about groups that occur as a central quotient and how we determine if a group is capable. To this end we will look at the epicenter of a group and how we can compute it. The talk will be expository in nature.

In the latest developments in the theory of skew lattices, the study of distributivity has been one of the main topics. Furthermore, the largest classes of examples of such algebras are distributive. Unlike what happens in lattices, the properties of cancellation and distributivity are independent for skew lattices. In the past two years a group of mathematicians have worked on this topic (namely K. Cvetko-Vah, J. Leech, M. Spinks and M. Kinyon). In this talk we will discuss several aspects of distributivity in the absence of commutativity, review the recent results by Kinyon and Leech on these matters and have an insight on the coset structure of those algebras that satisfy this property.