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Events happening on March 8, 2016

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Mar. 08, 2016 11am (MATH 350)	Number Theory Joseph H. Silverman (Brown University) X A divisibilty sequence is a sequence of integers W_1,W_2,... with the property that if m divides n, then W_m divides W_n. Classical divisibility sequences include a^n-b^n, Fibonacci and Lucas sequences, and elliptic divisibility sequences. These tend to grow rapidly, and their behavior modulo p is quite interesting. After surveying these sequences, I will move on to higher dimensional analogues such as gcd(a^n-1,b^n-1), which tend to grow slowly, and faster growing Divisor Divisibility Sequences that Katherine Stange, Patrick Ingram, and I have recently been studying. Despite their elementary-seeming nature, divisibility sequences arise in many areas of mathematics due to their intrinsic definition in terms of arithmetic intersections on arithmetic groups. Along the way I will describe many open questions whose easy statements belie their depth. Divisibility Sequences
Mar. 08, 2016 12:10pm (MATH …	Kempner Paul Horn (University of Denver) X Graphs are a mathematical abstraction of networks, which on their most basic level capture objects and their relationships. Although graphs are discrete objects, there turns out to be many striking analogies between them and Riemannian manifolds. Most famous of these are the relationships between the spectra of the Laplace operator on graphs and the spectra of the Laplace-Beltrami operator on a manifold. Recent work, however, has attempted to bring other ideas from the world of geometry into the graph setting – notably by trying to introduce notions of curvature on graphs. In this talk, I will describe some of my work in this area and how it reflects a rich interplay between the local structure of a graph, the behavior of random walks on graphs, and more global geometric properties of a graph. The Geometry of Graphs
Mar. 08, 2016 1pm (MATH 220)	Andrew Maurer (University of Georgia) X Lie superalgebras can be defined abstractly as an associative ZZ/(2)-graded algebra with the usual commutator operation. It turns out the bracket structure respects the grading. When studying the representation theory of Lie superalgebras, we may use the tools provided by support varieties. This involves taking Spec of the cohomology ring modulo its nilradical. As in the theory of Lie algebras, our study begins with complex Lie superalgebras. Quickly, we encounter a problem in that the cohomology ring is finite dimensional as a complex vector space, and thus support varieties are points. This may be remedied by using Hochschild's relative cohomology, which have much more interesting, and much more elusive, support varieties. In this talk I will speak about some results concerning so-called classical Lie superalgebras, with particular emphasis on cohomology relative to its even Lie subsuperalgebra. (Relative) Cohomology and Support Varieties and Lie Superalgebras
Mar. 08, 2016 2pm (MATH 350)	Lie Theory Marcelo Aguiar (Cornell) X Consider an arrangement of linear hyperplanes integral with respect to a given lattice. The lattice gives rise to a torus and the arrangement to a subdivision of the torus. We are interested in the combinatorics of this subdivision. We will describe questions and results for particular lattices associated to root systems and arrangements associated to graphs. This is joint work in progress with Swee Hong Chan. Integral hyperplane arrangements Sponsored by the Meyer Fund
Mar. 08, 2016 4pm (Math 220)	Shawn Burkett (CU Boulder) X A central idea in group theory is to study a group by studying homomorphic images into families of groups in which a lot of information is already known. For example, given a group action, one gets a homomorphism of the acting group into the symmetric group on the elements of the set being acted on. The permutation representation so acquired may contain significant information about the acting group. Extending this idea, if a group G acts on a k-vector space V, one gets a homomorphism of G into GL(V), called a linear representation. That is, each element of G acts as an invertible linear transformation on V. Linear transformations have many invariants, one being the trace. If we compose the linear representation with the trace map, one obtains a map from G to k, called a k-character. In this talk, we will discuss the basics of linear representation theory and character theory in great detail, providing all necessary information to introduce supercharacter theories of finite groups. Character Theory of Finite Groups

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