"Fixed Point, Banach Space and Metric Space Theory Workshop"
There will be four 50-minute lectures, interspersed with and followed by time for coffee, refreshments and/or discussion.
Program: Saturday 4/October/2014.
(0) 9:00 am - 9:30 am. Coffee and refreshments, Thackeray 428.
(1) 9:30 am - 10:20 am. Professor Anthony Weston from Canisius College will speak on:
"Finite metric spaces of strictly negative type." (See abstract below.)
(2) 10:30 am - 11:30 am. Coffee and refreshments.
(3) 11:30 am - 12:20 pm. Mr. Zachariah Riel from Kent State University will speak on:
"Operators on L1 which take Lp into Lp."
(4) Lunch. 12:30 pm - 2:30 pm
(5) 2:30 pm - 3:20 pm. Mr. Torrey Gallagher from the University of Pittsburgh will speak on:
"Mean nonexpansive maps: results and open questions."
(6) 3:30 pm - 4:20 pm. Ms. Roxana Popescu from the University of Pittsburgh will speak on:
"Lipschitz mappings and hyperconvex spaces."
(7) 4:30 pm - 5:30 pm. Chris Lennard will speak for a short while about a recently accepted paper, joint with Professors Jared Burns from Seton Hill University and Jeromy Sivek from Temple University, entitled: "A contractive fixed point free mapping on a weakly compact set",
to appear in Studia Mathematica.
This paper came out of a CRDF-supported Summer 2013 research project with Jared and Jeromy, entitled:
"Fixed Point Free Nonexpansive Mappings on Weakly Compact, Convex Sets".
This work also forms part of the doctoral dissertation of Dr. Jeromy Sivek.
Chris' short talk will be followed by some further time for discussions between attendees/participants.
The organizer, Chris Lennard, wishes to thank and/or thank in advance the University of Pittsburgh CRDF Small Grants Program, Tony Weston, Zach Riel, Torrey Gallagher, Roxana Popescu, Carol Miller, LaVerne Kapucensko, Diane Hall, Drew Porvaznik, Melissa Weidman, Carol Olczak, Ivan Yotov, Tammeka Banks, and the University of Pittsburgh Mathematics Department for their support of this workshop.
(1) Professor Anthony Weston: "Finite metric spaces of strictly negative type."
The title of this talk is taken from a paper by Hjorth, Linosek, Markvorsen and Thomassen (Linear Algebr. Appl. 270:255-273) that was published in 1998. Their work has since completely rewired my own understanding of negative type and the related notion of generalised roundness. Negative type was introduced by Schoenberg in order to characterise those metric spaces that embed isometrically into Hilbert spaces. But what of "strict" negative? In this talk I will outline a general theory of metric spaces of "strictly" negative type. Much of the focus will be on finite metric spaces and affine isometries into Euclidean spaces. I may also indicate a connection to one of the fundamental problems of distance geometry: the realisation of graphs in Euclidean spaces.