Oct

1

Thu

October 1, 2015, 12:33 pm

No events

No events at this time. … (link: http://www.hawaii.edu/calendar/manoa-math/2015/10)

Oct

2

Fri

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.

Oct

14

Wed

The Packing Constant in l^2, l^p, a Class of Orlicz Functions and its Relationship to Totally Bounded

Link to Master’s project

**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.

## University of Hawaiʻi at Mānoa