Wednesdays, 4:00–5:00pm, in Pearce 328.
Webpages from previous semesters: 

Date  Speaker  Affiliation  Title 
9/3  Meera Mainkar  Central Michigan University  Anosov Lie algebras and algebraic units in number fields 
9/10  Ben Salisbury  Central Michigan University  The GindikinKarpelevich formula and combinatorics of crystals 
9/17  Sunil Chebolu  Illinois State University  Group Algebras and Circulant Bipartite Graphs 
9/24  Travis Scrimshaw  University of California, Davis  Crystal Structure For Rigged Configurations and the Filling Map 
10/1  Andrzej Dudek  Western Michigan University  On Ramseytype problems for sequences and permutations 
10/8  
10/15  Gabriel Feinberg  Haverford College  TBD 
10/22  Jordan Webster  Mid Michigan Community College  TBD 
10/29  Pete Vermeire  Central Michigan University  TBD 
11/5  Bruce Sagan  Michigan State University  TBD 
11/12  
11/19  
11/26  
12/3 
Speaker: Meera Mainkar (Central Michigan University)
Title: Anosov Lie algebras and algebraic units in number fields
Abstract: In the theory of dynamical systems, Anosov diffeomorphisms are an important class of dynamically interesting diffeomorphisms of Riemannian manifolds. The study of Anosov diffeomorphisms on nilmanifolds (compact quotients of simply connected nilpotent Lie groups) leads to interesting algebraic and arithmetic problems related to Lie algebras. In particular, this relates to very special algebraic units in number fields. We study the classification of Anosov Lie algebras by studying the properties of these algebraic units.
Speaker: Ben Salisbury (Central Michigan University)
Title: The GindikinKarpelevich formula and combinatorics of crystals
Abstract: The GindikinKarpelevich formula computes the constant of proportionality for the intertwining integral between two induced spherical representation of a $p$adic reductive group $G$. The righthand side of this formula is a product over positive roots (with respect to the Langlands dual of $G$) which may also be interpreted as a sum over a crystal graph. The original interpretation as a sum is due to BrubakerBumpFriedberg and BumpNakasuji where $G = \mathrm{GL}_{r+1}$, in which vertices of the crystal graph are parametrized by paths to a specific vector in the graph according to a pattern prescribed by a reduced expression of the longest element of the Weyl group of $G$. I will explain this rule, explain how it may be translated into a statistic on the Young tableaux realization of the same crystal graph, and discuss its generalization to the affine KacMoody setting where the notion of the longest element of the Weyl group no longer makes sense. This is joint work with KyuHwan Lee, SeokJin Kang, and Hansol Ryu.
Speaker: Sunil Chebolu (Illinois State University)
Title: Group Algebras and Circulant Bipartite Graphs
Abstract: Let $p$ be a prime number. We characterise the group algebras over fields in which every nontrivial unit has order $p$. This characterization and some related results gave answers to some basic questions about circulant bipartite graphs. I will discuss these results which are part of a recent joint work (arXiv:1404.4096) with Keir Lockridge and Gail Yamskulna.
Speaker: Andrzej Dudek (Western Michigan University)
Title: On Ramseytype problems for sequences and permutations
Abstract: Ramsey theory can loosely be described as the study of structure which is preserved under finite decomposition. A classical Ramsey theorem states that in any $r$coloring of the edges of a sufficiently large complete graph, one will always find a monochromatic complete subgraph.
In this talk, we discuss analogous results for sequences and permutations. In particular, we study the behavior of the following function $f(r,X)$, which is the length of the shortest sequence $Y$ such that any $r$coloring of the entries of $Y$ yields a monochromatic subsequence that also preserves the order of $X$.
Speaker: Travis Scrimshaw (University of California, Davis)
Title: Crystal Structure For Rigged Configurations and the Filling Map
Abstract: Rigged configurations are combinatorial objects which arise from statistical mechanics, and they are in bijection with classically highest weight elements in a tensor product of the vector representation of finite dimensional nonexceptional affine crystals called KirillovReshetikhin crystals. Schilling has shown there exists a classical crystal structure on rigged configurations in simplylaced affine type. I will present a classical crystal structure on rigged configurations for all affine types using virtual crystals. Furthermore I will present an extension of the socalled "filling map," introduced in recent work by Okado, Sakamoto, and Schilling for affine type D, to all nonexceptional affine types. This is joint work with Anne Schilling.
Speaker: Gabriel Feinberg (Haverford College)
Title: TBD
Abstract: Coming soon …
Speaker: Jordan Webster (Mid Michigan Community College)
Title: TBD
Abstract: Coming soon …
Speaker: Pete Vermeire (Central Michigan University)
Title: TBD
Abstract: Coming soon …
Speaker: Bruce Sagan (Michigan State University)
Title: TBD
Abstract: Coming soon …