Logic Seminar Abstracts |
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Title: Algebras with small <R,S>-minimal sets Speaker: Keith Kearnes Affiliation: CU Time: 3pm, Monday, January 24 Location: Math 220 Abstract: This is a talk about the local structure of finite algebras. The theorem proved is a characterization of those finitely generated varieties of algebras whose members are covered by local approximations of size at most k for some fixed finite k. Title: Algebras with small <R,S>-minimal sets Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, January 31 Location: Math 220 Abstract: Continuation. Title: An easy test for congruence modularity. Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, February 28 Location: Math 220 Abstract: If an equationally definable class of algebras is congruence modular, then it has a commutator theory extending the theory for groups. The usual way of establishing that an equationally definable class of algebras is congruence modular is to exhibit Day terms for the class. I will describe a new method recently discovered by Topaz Dent, Agnes Szendrei and me. Title: The Paris-Harrington Theorem: an introduction to "natural" incompleteness Speaker: Everett Piper Affiliation: CU Time: 3pm, Monday, March 14 Location: Math 220 Abstract: The first "natural" instance of PA-incompleteness, discovered by Jeff Paris and Leo Harrington, will be discussed. I will sketch their original proof and mention some of the interesting Ramsey-type combinatorics involved. I will also give an updated model-theoretic proof due to Bovykin. Title: Progress on the classification of groups of finite Morley rank with a split BN-pair of Tits rank 1 Speaker: Josh Wiscons Affiliation: CU Time: 3pm, Monday, March 28 Location: Math 220 Abstract: After a brief introduction to groups of finite Morley rank (fMr), we review the current state of the classification of the infinite simple ones and indicate the connection with BN-pairs. We then focus on the analysis of split BN-pairs of Tits rank 1 with the goal of presenting a recent result that classifies, as PSL(2,F), all simple groups of fMr of odd type with a split BN-pairs of Tits rank 1, (B,N,U), for which U is without involutions and B/U is (nontrivial and) abelian.
The study of groups of fMr employs techniques from both group theory
and model theory, but we wish to give fair warning that at least 99%
of this talk will be group-theoretic.
Title: Progress on the classification of groups of finite Morley rank with a split BN-pair of Tits rank 1 Speaker: Wiscons Affiliation: CU Time: 3pm, Monday, April 4 Location: Math 220 Abstract: Continuation. |
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