Logan Hoehn (curso)

Logan Hoehn is an Associate Professor in the Department of Computer Science & Mathematics at Nipissing University.

Logan was born and raised in Saskatoon, Saskatchewan, Canada. He attended the University of Saskatchewan, where his initial interest in computer science gradually grew into a keen enthusiasm for mathematics. After completing a semester in the Math in Moscow program, he graduated with a BSc honors degree in Mathematics and Computer Science.

Logan obtained his MSc and PhD degrees in Mathematics from the University of Toronto. One semester before completing his PhD, he took on a Visiting Assistant Professor position at the University of Alabama at Birmingham for two years.

Logan's research interests include continuum theory, low-dimensional topology, and topology and dynamics in the plane. His most notable results in continuum theory are the construction of a non-chainable continuum with span zero (2011), and (joint with Lex Oversteegen) the characterization of the pseudo-arc as the unique hereditarily indecomposable continuum with span zero, which completed the classification of homogeneous plane continua (2016).

CURSO:

Folding maps and hereditarily indecomposable continua

In many central open problems of interest in continuum theory, hereditarily indecomposable continua play a key part. For instance, in the classification of hereditarily equivalent continua all that remains is the case of hereditarily indecomposable continua, and the still unsolved classification of homogeneous tree-like continua is equivalent to the classification of homogeneous hereditarily indecomposable continua. In recent work on homogeneous continua in the plane, a new tool for the study of hereditarily indecomposable continua emerged, namely folding maps.

A folding map between two graphs is a generalization of the concept of a "crooked" map between two arcs. In this course, we will introduce the notion of a folding map, and develop some of the basic theory associated with folding maps. We will explain their role in the study of hereditarily indecomposable continua, in particular in developing new characterizations of the pseudo-arc.

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