The graduate student seminar meets from 3:30 to 5:00 pm Thursdays in Goldsmith somewhere. Want to give a talk? Email Matt Cordes at mcordes@etc... for details.
We prove formally that dividing by two is possible, then consider dividing by three (which is harder). No background will be assumed beyond a standard undergraduate mathematics education. Some previous knowledge of division assumed.
The card game SET serves as an excellent model for the ﬁnite geometry AG(4,3). Using that model, previous researchers have found partitions of AG(4,3) into 4 disjoint maximal caps along with a distinguished point/card. We define a new geometric object, a demicap - a maximal cap can be written as the union of two disjoint demicaps. We will present results about these demicaps, which provide insight into the maximal cap partitions of AG(4,3).
In an effort to answer the question "What does a random group look like?" Gromov introduced the density model of random groups. I will present a proof of the surprising result that a typical random group is either trivial or Gromov hyperbolic.
Abstract: The Thurston norm is a pseudonorm on the second homology of three manifolds. It can be used to study fibrations and foliations, but difficult to compute. Recently, Ozsvath and Szabo proved Heegaard-Floer homology detects the Thurston norm. In my talk I will define the norm and discuss concrete examples and applications.
The title says it all. We will look at some locally nilpotent recursion operators on a polynomial ring, analyze how fast they make their kill, and derive consequences about the dimension of the operator algebra itself. Serendipitous applications to Hecke algebras on spaces of modular forms modulo p found in the wild.