Employment and Education
Oberlin College
- 2021–23, 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 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.