Employment and Education
Oberlin College
- 2021–24, Professor of Mathematics
- 2019–20 & 2022–23, Chair of Mathematics
- 2015–21, Associate Professor of Mathematics
- 2010–15, Assistant Professor of Mathematics
Michigan State University
- 2008–10, Postdoctoral Intructor, Mentor: Selman Akbulut
University of Texas at Austin
- 2004–07, Postdoctoral Intructor, Mentor: Bob Gompf
University of Maryland at College Park
- 1999–04, Ph.D. in Mathematics, Advisor: Elmar Winkelnkemper
Michigan State University
- 1994–99, B.S. in Mathematics, Mentors: Lee Sonneborn and John Masterson
Publications (Oberlin students in bold)
- (with L. Axon) The end sum of surfaces, accepted in Topology at Infinity of Discrete Groups, Contemporary Mathematics volume in honor of Mike Mihalik, American Mathematical Society, Providence, RI, 2024, 37 pp.
- (with R.M. Young) Cones (Feedback on 106.06), Mathematical Gazette 106 (2022), 549–550.
- (with C. Guilbault and P. Haggerty) Extreme nonuniqueness of end-sum, Journal of Topology and Analysis 14 (2022), 461–503.
- (with J. Li) Artin presentations, triangle groups, and 4-manifolds, Boletín de la Sociedad Matemática Mexicana 28 (2022), 15 pp.
- (with R. Gompf) On uniqueness of end sums and 1-handles at infinity, Algebraic and Geometric Topology 19 (2019), 1299–1339.
- (with J. Metcalf-Burton) Double branched covers of theta-curves, Journal of Knot Theory and Its Ramifications 25 (2016), 9 pp.
- Rational angled hyperbolic polygons, The Mathematics Student 85 (2016), 103–111.
- (with H.E. Winkelnkemper) The explicit algebraic autonomy of Artin Presentation Theory and the Fox Calculus. I, Boletín de la Sociedad Matemática Mexicana 22 (2016), 251–261.
- (with P. Haggerty) Connected sum at infinity and 4-manifolds, Algebraic and Geometric Topology 14 (2014), 3281–3303.
- (with J. Metcalf-Burton, T. Richard, and L. Solus) Borromean rays and hyperplanes, Journal of Knot Theory and Its Applications 23 (2014), 46 pp.
- (with R. Gompf) Orbit spaces of gradient vector fields, Ergodic Theory and Dynamical Systems 33 (2013), 1732–1747.
- (with H. King and L. Siebenmann) Connected sum at infinity and Cantrell-Stallings hyperplane unknotting, Rocky Mountain Journal of Mathematics 42 (2012), 1803–1862.
- (with R. Gompf and J. McCarthy) On fundamental groups of quotient spaces, Topology and Its Applications 159 (2012), 322–330.
- Grade school triangles, American Mathematical Monthly 117 (2010), 673–685.
- (with J. McCarthy) Discreteness and homogeneity of the topological fundamental group, Topology Proceedings 34 (2009), 339–349.
- Gaussian integers and arctangent identities for pi, American Mathematical Monthly 116 (2009), 515–530.
- Torelli actions and smooth structures on 4-manifolds, Journal of Knot Theory and Its Applications 17 (2008), 171–190.
- Artin presentations from an algebraic viewpoint, Journal of Algebra and Its Applications 6 (2007), 355–367.
- Knot theory and the Casson invariant in Artin presentation theory, Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics) 11, no. 4, L. V. Keldysh Memorial Proceedings, Moscow (2005) 119--126 (Russian); English translation in Journal of Mathematical Sciences (New York) 44 (2007), 4446–4450.
- (with H.E. Winkelnkemper) Artin presentations of complex surfaces, Boletín de la Sociedad Matemática Mexicana 10, Special Issue in honor of F. González-Acuña (2004), 63–87.
- (with Henry King) Noncompact codimension 1 real algebraic manifolds, Michigan Mathematical Journal 52 (2004), 361–373.
- Single rational arctangent identities for pi, Pi Mu Epsilon Journal 11 (1999), 1–6.