Logic Seminar Abstracts |
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Title: Automorphism groups of finite free algebras. Speaker: Keith Kearnes Affiliation: CU Time: 3pm, Monday, September 13 Location: Math 220 Abstract: It has been known since the mid-1970's that a group G is representable as the automorphism group of a 2-generated free algebra if and only if G has an involution. For a long time it was unknown whether every finite group with an involution is representable as the automorphism group of a finite 2-generated free algebra, but in 1996 Steven Tschantz proved that Z4 is not so representable. In this talk, I will explain why the Mathieu simple groups and the Suzuki simple groups are not representable as automorphism groups of finite, 2-generated, free algebras. Title: Automorphism groups of finite free algebras. Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, September 20 Location: Math 220 Abstract: A continuation of the previous talk. Title: Automorphism groups of finite free algebras. Speaker: Kearnes Affiliation: CU Time: 3pm, Monday, September 27 Location: Math 220 Abstract: A continuation of the previous talk. Title: Scissor congruence/dissection on smooth planar bodies. Speaker: Daniel Champion Affiliation: CU Time: 3pm, Monday, October 18 Location: Math 220 Abstract: Scissor congruence has been studied since ancient times. In particular, it is well known that any polygon is scissor congruent to a square of equal area. Also, it has been proven that two convex bodies A, A' are scissor congruent iff their boundaries are scissor congruent (Dubins et al. 1963). I will present an extension to these results by proving that any planar region bounded by a smooth simple closed curve (not necessarily convex) is not scissor congruent to a square (or any polygon). I will also discuss several interesting generalizations to this result, which are made possible by my method of proof. Title: Scissor congruence/dissection on smooth planar bodies. Speaker: Daniel Champion Affiliation: CU Time: 3pm, Monday, October 25 Location: Math 220 Abstract: A continuation of the previous talk. Title: Proofs without syntax. Speaker: John Fuhrmann Affiliation: CU Time: 3pm, Monday, November 1 Location: Math 220 Abstract: In ordinary propositional logic, a proof is a finite sequence of propositions having the property that each is deducible from the preceding propositions using specified rules of inference. Dominic Hughes (Stanford) has a new formulation in which combinatorial propositions are special labeled graphs and proofs are graph homomorphisms. In a series of talks, I will explain how to encode ordinary propositions into labeled graphs and prove soundness and completeness theorems for combinatorial propositional logic. Title: Proofs without syntax. Speaker: John Fuhrmann Affiliation: CU Time: 3pm, Monday, November 15 Location: Math 220 Abstract: A continuation of the previous talk. |
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