# CMU Algebra and Combinatorics Seminar

## Spring 2016

### Meeting Times

Wednesdays, 4–5pm, in Pearce 203.

### Schedule

 Date Speaker Affiliation Title 1/13 George Grossman Central Michigan University Combinatorial Identities with Fibonacci and Lucas Numbers 1/27 Adam Chapman Michigan State University Linkage of $p$-algebras of prime degree 2/24 Rajesh Kulkarni Michigan State University TBD 3/2 Li Li Oakland University TBD 3/16 Jake Levinson University of Michigan TBD 3/23 David C. Murphy Hillsdale College TBD 3/30 Rachel Karpman University of Michigan TBD 4/6 Amrita Acharyya University of Toledo TBD 4/27 David Clark Grand Valley State University TBD

### Abstracts

Speaker: George Grossman (Central Michigan University)
Title: Combinatorial Identities with Fibonacci and Lucas Numbers
Abstract: In this talk we explore aspects of combinatorial identities. In particular, it is shown that each Fibonacci number, up to sign change, can be represented countably many distinct ways as sum of binomial coefficients. The talk is accessible to graduate and undergraduate students.

Speaker: Adam Chapman (Michigan State University)
Title: Linkage of $p$-algebras of prime degree
Abstract: Quaternion algebras contain quadratic field extensions of the center. Given two algebras, a natural question to ask is whether they share a common field extension. This gives us an idea of how closely related those algebras are to one another. If the center is of characteristic 2 then those extensions divide into two types – the separable type and the inseparable type. It is known that if two quaternion algebras share an inseparable field extension then they also share a separable field extension and that the converse is not true. We shall discuss this fact and its generalization to $p$-algebras of arbitrary prime degree.

Speaker: Rajesh Kulkarni (Michigan State University)
Title: TBD
Abstract: Coming soon …

Speaker: Li Li (Oakland University)
Title: TBD
Abstract: Coming soon …

Speaker: Jake Levinson (University of Michigan)
Title: TBD
Abstract: Coming soon …

Speaker: David C. Murphy (Hillsdale College)
Title: TBD
Abstract: Coming soon …

Speaker: Rachel Karpman (University of Michigan)
Title: TBD
Abstract: Coming soon …

Speaker: Amrita Acharyya (University of Toledo)
Title: TBD
Abstract: Coming soon …

Speaker: David Clark (Grand Valley State University)
Title: TBD
Abstract: Coming soon …