October 1, 2015, 12:33 pm
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Speaker: Ken-ichi Kuga (Chiba University)
Title: Wild Topologies and Formalization
Many wild spaces appear in low-dimensional topology where naive
geometric intuition fails to hold. It is therefore desirable to formalize mathematical arguments dealing with those wild phenomena.
One basic theorem in this field of geometric topology is the Bing
shrinking theorem. In this talk, after introducing some of those interesting wild spaces
including the Alexander’s horned sphere, I will explain one of Bing’s original shrinking argument which constructs a counter-intuitive, hence wild,
involution of the 3-dimensional sphere. Then I will explain our formalization of the Bing shrinking theorem using the proof-assistant COQ,
and also our future plan of formalizing geometric topology especially in
dimension 4.
The Packing Constant in l^2, l^p, a Class of Orlicz Functions and its Relationship to Totally Bounded
Abstract. In this paper we will be discussing in further detail papers about the packing constant of the unit sphere in the space l^2, l^p written by Rankin, and a class of Orlicz functions given by Cleaver. In both the l^2 and l^p cases, the packing constant has been found however we will see in a paper written by Cleaver, the packing constant is not easily found for Orlicz spaces. In each case we will relate the packing constant to coverings, and thus relating packing spheres to compactness in metric spaces.