Joaquin Diaz-Boils
The algebra seminar this semester will run on Tuesdays and Thursdays, 4:30-5:30 p.m. in Morton 313. The speaker for the first seven weeks will be Professor Joaquin Diaz-Boils of the Pontifical Catholic University of Ecuador (PUCE) , Quito, Ecuador. He will be dictating a CRA workshop sponsored by the Ohio University Mathematics Department and the College of Arts & Sciences.
Title: Categorical models of Computation
Abstract: We study the different approaches to the Theory of Computation given from Category Theory, including abstract algebraic points of view of Recursion as well as Complexity Theory. This will encompass mainly two different kinds of characterizations: the explicit ones, introduced by the Montreal school, and based on the existence of a Natural Numbers Object in a certain category, and the purely algebraic that considers partiality, initiated by the group of Calgary. If time allows it, we will study the Kleene concept of Realizability from a categorical point of view. Along the sessions we will see several different characterizations of computable function classes, sometimes more than one for a certain class, and important and singular recursion schemes such as the safe recursive. Some of the authors whose articles will be examined in some extent are: Robin Cockett, Martin Hofmann, Martin Hyland, Joachim Lambek, Gordon Plotkin, Philip Scott, Leopoldo Román and Noson Yanofsky.
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