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seminars:alge

The Algebra Seminar

Unless stated otherwise, the seminar meets Tuesdays in room WH-100E at 2:50 p.m. There will be refreshments served at 4:00 in room WH-102.

Organizers: Alex Feingold and Hung Tong-Viet

To receive announcements of seminar talks by email, please join the seminar's mailing list.

Fall 2019

• August 27
Organizational meeting
• September 3
Casey Donoven (Binghamton University)
Automata acting on Fractal Spaces

Abstract: A self-similar set is a set that is a union of scaled copies of itself. Through iterated labeling of the $n$ copies, $n^2$ subcopies, and so on, we create a correspondence between infinite sequences over an n letter alphabet and points in the self-similar set. Automata act naturally on infinite sequence, and I will explore groups of homeomorphisms of semi-similar sets induced by automata. I will focus on two examples, the unit interval and Julia set associated to the map $z^2+i$. An important tool in the construction of the automata is the approximation of these self-similar sets as finite graphs.

• September 10
Matt Evans (Binghamton University)
BCK-algebras and generalized spectral spaces

Abstract: Commutative BCK-algebras are the algebraic semantics of a non-classical logic. Mimicing the construction of the spectrum of a commutative ring (or Boolean algebra or distributive lattice), we can construct the spectrum of a commutative BCK-algebra.

A topological space is called *spectral* if it is homeomorphic to the spectrum of some commutative ring, and *generalized spectral* if it is homeomorphic to the spectrum of a distributive lattice with 0.

In this talk I will briefly discuss Hochster's characterization of spectral spaces, and then show that the spectrum of a commutative BCK-algebra is generalized spectral.

• September 17
Jonathan Doane (Binghamton University)
Dualizing Kleene Algebras

Abstract: It is well-known that the class of Boolean algebras is “generated” by the two element chain $F<T$ equipped with negation $\neg F:= T$, $\neg T:=F$. When we include an uncertainty element $F<U<T$, along with negation $\neg U: =U$, we generate the class of Kleene algebras. Of course, there is a famous correspondence between Boolean algebras and Boolean topological spaces, named Stone duality; this leads us to wonder if we can somehow represent Kleene algebras by topological spaces as well. In fact, Stone duality is but an application of a more general theory of dual equivalences between categories. In this talk, we will utilize this theory to construct a dual equivalence between the categories of Kleene algebras and certain topological spaces.

• September 24
David Biddle (Binghamton University)
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• October 1
No Classes (University)
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• October 8
Ben Brewster (Binghamton University)
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• October 15
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• October 22
Eran Crockett (Binghamton University)
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• October 29
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• November 5
Luise Kappe (Binghamton University)
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• November 12
Dikran Karagueuzian (Binghamton University)
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• November 19
Zach Costanzo (Binghamton University)
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• November 26
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• December 3
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