CUNY Graduate Center
Room 6417
Fridays 2:00-3:30pm
Organized by:
Joel David Hamkins
Roman Kossak
Russell Miller
Philipp Rothmaler
Hans Schoutens
Spring 2018
March 30
Seminar cancelled
Spring Break.
February 23
Dimitris Tsementzis
Rutgers University
Univalent Foundations and Set Theory
Abstract
The Univalent Foundations is a proposed foundation for mathematics that takes as primitive a notion of space (rather than a notion of set). I will introduce the basic concepts of the Univalent Foundations from first principles, and give an overview of a class of formal systems, called Homotopy Type Theories, that can be used to formalize these basic notions. I will then describe how to construct a model of set theory in the Univalent Foundations, explain the consequences of the construction, and discuss several open problems. In the process, I will demonstrate the implementation of everything I talk about in a proof assistant.
February 16
Andrei Morozov
Sobolev Institute of Mathematics
Infinite time Blum-Shub-Smale machines: a computability for analysis
Abstract
We study a concept of computability over the reals based on Blum-Shub-Smale machines working in infinite time (ITBM). We give some characterizations of this computability, prove some its properties, and discuss its adequacy to classical analysis. This is joint work with Peter Koepke.
February 9
Andrew Brooke-Taylor
University of Leeds
Products of CW complexes
Abstract
CW complexes are the topological spaces of choice for algebraic topology, but the product (as topological spaces) of two CW complexes need not be a CW complex. In the 1940s and 50s Whitehead and Milnor gave sufficient conditions for the product to be a CW complex, and in the 70s and 80s Liu and Tanaka gave characterisations of those pairs of CW complexes whose product is a CW complex, under the assumption of set-theoretic axioms such as CH. In this talk I will present a new characterisation of the pairs of CW complexes whose product is a CW complex, valid in any model of set theory (ie, without any such extra set-theoretic assumptions). Whilst I have stripped the set theory away from the assumptions on the universe, the characterisation is with reference to a cardinal that may not be familiar to non-set theorists: the bounding number.
February 2
Seminar cancelled
MathFest conference at the Graduate Center.