Fall 2013 Seminars
Time: Tuesday, 3 December 2013, 5:10 PM (Note change of time!) Place: SC 1310 Speaker: Matthew Smedberg Title: A multisorted approach to the finite decidability problem Abstract: We will use multisorted firstorder logic to show that, if A is a finite algebra with strongly solvable radical tau and A has a term operation which is sensitive to changes within tau at more than a small number of variables, then A cannot belong to any finitely decidable variety. 

Time: Tuesday, 19 November 2013, 4:10 PM Place: SC 1310 Speaker: Chris Conidis Title: Computable Algebra: A Personal Perspective Abstract: I will survey some of my recent results about computable Artinian rings and Euclidean domains, while relating these results to classical (i.e. noncomputable) ring theory. In particular I will show that annihilator ideals play a central role in the theory of Artinian rings, and then construct transfinite Euclidean domains of all cardinalities, answering a question of P. Samuel, Nagata, and others. 

Time: Tuesday, 12 November 2013, 4:10 PM Place: SC 1310 Speaker: Rebecca Steiner Title: Effective Symmetry Breaking Abstract: Symmetry breaking in combinatorics involves coloring the elements of a structure so that there are no nontrivial automorphisms of the structure which respect the coloring. We say that such a coloring distinguishes the structure. We apply computability theory to this notion and show that there is a computable, finitevalence, pointed graph which is distinguished by a 2coloring but not by any computable 2coloring. We also show that if a computable, finitebranching tree has a distinguishing 2coloring, then it must have a 0”computable distinguishing 2coloring. 

Time: Tuesday, 1 October 2013, 4:10 PM Place: SC 1310 Speaker: Ralph McKenzie Title: A perspective on fifty years of work, delight and discovery in general algebra. Abstract: I conceive the talk to be like a ramble through general algebra and related fields of mathematics such as logic, model theory, graph theory and computational complexity. It will be in part a highly personal and biased offering of some of my reflections on personalities, good results and false starts collected over a long career in research. But also, I will strive to convey a convincing picture of a youthful field currently enjoying a vigorous state of healthy development. 

Time: Tuesday, 17 September 2013, 4:10 PM Place: SC 1310 Speaker: Matthew Moore Title: The Definable Principal Subcongruences problem is undecidable Abstract: For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is undecidable. Using this, we present another proof that A. Tarski’s finite basis problem is undecidable. 

Time: Tuesday, 10 September 2013, 4:10 PM Place: SC 1310 Speaker: Alexander Kazda Title: Absorbing subalgebras: Where to find them, and how to use them Abstract: While studying the complexity of the Constraint Satisfaction Problem, Libor Barto and Marcin Kozik discovered the idea of absorption. If B is an absorbing subalegebra of the algebra A, then many kinds of connectivity properties of A are also true for B. This is very useful for proofs by induction, and absorption has since played a role in several other universal algebraic situations. After giving a taste of how absorption works, we would like to talk about our current project (which is a joint work with Libor Barto): How to decide, given an algebra A with finitely many basic operations and some B subalgebra of A, if B absorbs A. 
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