TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, Millersville University, and West Chester University

Speakers Fall 2024

    Sep 2024: NO TGTS this month
  4 Oct 2024: Ron Umble, Millersville University
  1 Nov 2024: Jeremy Brazas, West Chester University

TGTS is a regional mathematics seminar/colloquium. We meet at 4:30
p.m. on the first Friday of each month during the academic year (with
some exceptions, as noted in the schedule above).  The public is
cordially invited to attend.

Next Talk

Date/Time: 1 November 2024, 4:30pm ET
 Location: Room 158, 25 University Ave, West Chester, PA 19383
  Parking: Visitor Parking is available behind the Sykes Student Union and is closest to the math department.
  (google maps)
     Zoom: https://wcupa.zoom.us/j/93351748930?pwd=EWWW5srJ8OpV7ONB6QT3bo2CRrZJQH.1
  Speaker: Jeremy Brazas, West Chester University
    Title: Unwinding paths in the plane to form an R-tree

 Abstract: When you unwind all paths in a graph up to
backtracking, you end up forming a tree that serves as the universal
covering space of the graph. In the same way, we can unwind paths in a
more complicated one-dimensional space like the Sierpinski
Carpet. However, in this case, we end up forming a space called an
R-tree, which serves as a kind of generalized universal covering space.
 
In this talk, I'll survey the evidence that one should also be able to
define a suitable notion of "thin" or "one-dimensional" homotopy that
makes it possible to unwind all paths in the plane (up to
one-dimensional backtracking) to form an R-tree. For instance, a 2010
result of Berestovskii-Plaut shows this is achievable if one restricts
to rectifiable paths. We'll also discuss a few fundamental open
questions related to covering maps and R-trees that would be answerable
if one could decide whether or not an unwinding construction is possible
for all paths in the plane. In the second half of the talk, I'll
introduce an intricate new planar construction that resulted from ten
years of effort and allowed us to solve this problem in 2023. This work
is joint with Greg Conner, Curtis Kent, and Paul Fabel.

Past Seminars

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