Mathematics & Computer Science

Seminars and Colloquia

Monday, April 27, 2015

04:45 pm - 06:00 pm

Logic Seminar, Petr Glivicky (Charles University): "Definability in linear fragments of Peano Arithmetic"

Abstract: In this talk, I will give an overview of recent results on linear arithmetics with main focus on definability in their models. Here, for a cardinal k, the k-linear arithmetic (LAk) is a full-induction arithmetical theory extending Presburger arithmetic by k non-standard scalars (= unary functions of multiplication by distinguished elements). The hierarchy of linear arithmetics lies between Presburger and Peano arithmetics and stretches from tame to wild. I will present a quantifier elimination result for LA1 and give a complete characterisation of definable sets in its models. On the other hand, I will construct an example of a model of LA2 (or any LAk with k at least 2) where multiplication is definable on a non-standard initial segment (and thus no similar quantifier elimination is possible). There is a close connection between models of linear arithmetics and certain discretely ordered modules (as each model of a linear arithmetic naturally corresponds to a discretely ordered module over the ordered ring generated by the scalars) which allows to construct wild (e.g. non-NIP) ordered modules. On the other hand, the quantifier elimination result for LA1 implies interesting properties of the structure of saturated models of Peano arithmetic.

ESC 638

Thursday, April 30, 2015

04:30 pm - 05:30 pm

Anna Haensch (Duquesne, Wes PhD '13): 17 Weird Facts About Science Writing That Will Blow You Away"

Abstract: A group of scientists make a discovery. We can probably all agree that the world deserves to hear about their work, and we can probably also agree that the scientists deserve some recognition. But how does that science make it from the lab bench to the Twitter feed? And what is the likelihood that the information you eventually consume will be intact, interesting, and accurate? As a mathematician with a background in radio, blogging, social media, and podcasting, I will attempt to answer these questions, and more. I will discuss the evolution of a science story from beginning to end, and like much click-bait, this talk might not actually blow you away -- but then again, maybe it will. There's really only one way to find out.

ESC 184 (Woodhead Lounge)