Logan C. Hoehn

Tools and demonstrations

• Lights Out
• 15 Puzzle
• 2x2 Linear Transformations
• Linear Transformations of an image
• Complex Function Graph

Course notes

Selected talks

• The problem of Nadler and Quinn on accessible points of arc-like continua. STDC24, University of North Carolina, Charlotte NC (Mar 6, 2024). [slides (pdf)]
• Accessibility of points in plane embeddings of arc-like continua. STDC23, Rhodes College, TN (Mar 15, 2023, virtual). [slides (pdf)]
• Combinatorial folding maps and hereditarily indecomposable continua. STDC22, Baylor University, Waco TX (Mar 12, 2022, virtual). [slides (pdf)]
• Folding maps on graphs and hereditarily indecomposable continua. STDC21, Murray State University, Murray KY (May 14, 2021, virtual). [slides (pdf)]
• Hereditarily equivalent continua in the plane. STDC19, University of Alabama, Birmingham AL (Mar 15, 2019). [slides (pdf)]
• Hereditarily indecomposable weakly chainable continua. Summer Topology Conference 2018, Western Kentucky University, Bowling Green KY (Jul 18, 2018). [slides (pdf)]
• Graphs in the study of 1-dimensional continua and span. Workshop on graphs and continua theory, University of Pittsburgh, Pittsburgh PA (Sep 2, 2017). [slides (pdf)]
• A new example of a tree-like continuum with a fixed-point-free self-map. Summer Topology Conference 2016, Leicester University, Leicester, England (Aug 4, 2016). [slides (pdf)]
• Workshop on homogeneous plane continua. STDC16, Baylor University, Waco TX (Mar 9, 2016). [slides (pdf)]
• A complete classification of homogeneous plane continua. Summer Topology Conference 2015, National University of Ireland, Galway, Ireland (Jun 25, 2015). [slides (pdf)]
• Paths in Euclidean space. Summer Topology Conference 2014, College of Staten Island CUNY, Staten Island NY (Jul 23, 2014). [slides (pdf)]
• Isotopies of compact sets in the plane. STDC14, University of Richmond, Richmond VA (Mar 15, 2014). [slides (pdf)]
• A weakly mixing, but not mixing, map on a dendrite. STDC13, CCSU, New Britain CT (Mar 25, 2013). [slides (pdf)]
• An alternative to the Euclidean path length in the plane. STDC12, UNAM, Mexico City (Mar 24, 2012). [slides (pdf)]
• Uncountable collections of pairwise disjoint non-chainable tree-like continua in the plane. STDC11, UT Tyler, Tyler TX (Mar 19, 2011). [slides (pdf)]
• Course on chainable continua and Lelek's problem. V Taller Estudiantil de Teoria de Continuos y sus Hiperespacios, Universidad Autonoma de Guerrero, Acapulco Mexico (Nov 25--27, 2010). [introductory problems (pdf)]
• A non-chainable continuum with span zero. STDC10, MSU, Starkville MS (Mar 19, 2010). [slides (pdf)]
• A counterexample for Lelek's problem in continuum theory. Southern Wisconsin Logic Colloquium, UW Madison, Madison WI (Nov 17, 2009).
• Chain covers of graphs. Lloyd Roeling Mathematics Conference, UL Lafayette, Lafayette LA (Oct 30, 2009).
• A construction of a compact metric space from a compact Hausdorff space. Nipissing Topology Workshop, Nipissing University, North Bay ON (May 22, 2009). [notes (pdf)]
• Span zero vs. surjective span zero. STDC09, UF, Gainesville FL (Mar 7, 2009). [slides (pdf)]

Publications

• (with Ammerlaan, Andrea) Planarity of compactifications of R with arc-like remainder. Preprint. [arXiv]
• (with Anušić, Ana) Accessibility of countable sets in plane embeddings of arc-like continua. Preprint. [arXiv]
• (with Ammerlaan, Andrea; Anušić, Ana) The Nadler-Quinn problem on accessible points of arc-like continua. Preprint. [arXiv]
• (with Ammerlaan, Andrea; Anušić, Ana) The Nadler-Quinn problem for simplicial inverse systems. Fund. Math. 267 (2024), 157-180. [arXiv]
• (with Ammerlaan, Andrea; Anušić, Ana) Radial departures and plane embeddings of arc-like continua. Houston J. Math, to appear. [arXiv]
• (with Hernández-Gutiérrez, R.) Smooth fans that are endpoint rigid. Applied General Topology 24 (2023), no. 2, 407-422. [arXiv]
• (with Oversteegen, L.G.; Tymchatyn, E.D.) Shortest paths in arbitrary plane domains. Canadian Journal of Mathematics 74 (2022), no. 2, 349-367. DOI. [pdf]
• (with Oversteegen, L.G.; Tymchatyn, E.D.) A canonical parameterization of paths in Rⁿ. Houston J. Math. 46 (2020), no. 2, 465-489. [pdf]
• (with Oversteegen, L.G.) A complete classification of hereditarily equivalent plane continua. Adv. Math. 368 (2020), 8 pp.
• (with Pacheco-Juárez, Yaziel) Dendroids with a low homogeneity degree. Topology Appl. 277 (2020), 11 pp.
• (with Oversteegen, L.G.; Tymchatyn, E.D.) Extension of isotopies in the plane. Trans. Amer. Math. Soc. 372 (2019), no. 7, 4889-4915. [pdf]
• Hereditarily indecomposable continua. CMS Notes 51 (2019), no. 4, 12-13.
• (with Hernández-Gutiérrez, R.) A fixed-point-free map of a tree-like continuum induced by bounded valence maps on trees. Colloq. Math. 151 (2018), no. 2, 305-316. [pdf]
• (with Oversteegen, L.) Characterizations of the pseudo-arc. In Problems in Continuum Theory, in memory of Sam B. Nadler Jr.. Topology Proc. 52 (2018).
• (with Acosta, Herardo; Pacheco-Juárez, Yaziel) Homogeneity degree of fans. Topology Appl. 231 (2017), 320-328. [pdf]
• (with Oversteegen, L.G.) A complete classification of homogeneous plane continua. Acta Math. 216 (2016), no. 2, 177-216. [pdf]
• (with Mouron, C.) Hierarchies of chaotic maps on continua. Ergodic Theory Dynam. Systems 34 (2014), no. 6, 1897-1913. [pdf] [corrections]
• (with Oversteegen, L.G.; Tymchatyn, E.D.) Continuum theory. In Klaas Pieter Hart, Jan van Mill and Petr Simon (Eds.) Recent Progress in General Topology III (2013).
• An uncountable family of copies of a non-chainable tree-like continuum in the plane. Proc. Amer. Math. Soc. 141 (2013), no. 7, 2543-2556. [pdf]
• (with Bartošová, D.; Hart, K.P.; van der Steeg, B.) Lelek's problem is not a metric problem. Topology Appl. 158 (2011), no. 18, 2479-2484.
• A non-chainable plane continuum with span zero. Fund. Math. 211 (2011), no. 2, 149-174. [pdf]
• (with Karassev, A.) Equivalent metrics and the spans of graphs. Colloq. Math. 114 (2009), no. 1, 135-153. [pdf]

Preprints

• (with Oversteegen, L.G.; Tymchatyn, E.D.) Shortest paths in arbitrary plane domains. (submitted)