Scholarship

      Research interests: Geometric topology, knot theory, 3-manifolds, hyperbolic geometry

      Research Articles:

1. Average crosscap number of a 2-bridge knot, Moshe Cohen, Thomas Kindred, Adam M. Lowrance, Patrick D. Shanahan, Cornelia A. Van Cott, Preprint arXiv:2501.03099 (2025).
2. On the nonorientable 4-genus of double twist knots, Jim Hoste, Patrick D. Shanahan, and Cornelia A. Van Cott, Journal of Knot Theory and its Ramifications, 32.5 (2023).
3. Crosscap number and epimorphisms of two-bridge knot groups, Jim Hoste, Patrick D. Shanahan, and Cornelia A. Van Cott, Journal of Knot Theory and its Ramifications, 30.4 (2021).
4. Remarks on Suzuki's epimorphism number, Jim Hoste, Joshua Ocana Mercado, and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications, 28.9 (2019).
5. Finite n-quandles of torus and two-bridge links, Alissa S. Crans, Jim Hoste, Blake Mellor, and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications, 28.3 (2019).
6. An enumeration process for racks, Jim Hoste and Patrick D. Shanahan, Mathematics of Computation, 88 no. 317 (2019).
7. Links with finite n-quandles, Jim Hoste and Patrick D. Shanahan, Algebraic & Geometric Topology, 17.5 (2017).
8. Involutory quandles of (2,2,r)-Montesinos links, Jim Hoste and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications, 26.3 (2017).
9. Twisted Alexander polynomials of 2-bridge knots, Jim Hoste and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications 22.1 (2013).
10. Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots, Jim Hoste, Scott Garrabrant, and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications 21.9 (2013).
11. Epimorphisms and boundary slopes of 2-bridge knots, Jim Hoste and Patrick D. Shanahan, Algebraic & Geometric Topology, 10.2 (2010).
12. Drawing a triangle on the Thurston model of hyperbolic space, Curtis Bennett, Blake Mellor, and Patrick D. Shanahan, Mathematics Magazine, 83 (2010).
13. Boundary slopes of 2-bridge links determine the crossing number, Jim Hoste and Patrick D. Shanahan, Kobe Journal of Mathematics, 24 (2007).
14. Computing boundary slopes of 2-bridge links, Jim Hoste and Patrick D. Shanahan, Mathematics of Computation, 76 no. 259 (2007).
15. Remarks on some hyperbolic invariants of 2-bridge knots Jim Hoste and Patrick D. Shanahan, Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences, World Sci. Pub. Series on Knots and Everything (2005).
16. Commensurability classes of twist knots, Jim Hoste and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications 14.1 (2005).
17. A formula for the A-polynomial of twist knots, Jim Hoste and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications 13.12 (2004).
18. Trace fields of twist knots, Jim Hoste and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications, 10.4 (2001).
19. Cyclic Dehn surgery and the A-polynomial, Patrick D. Shanahan, Topology and Its Applications, 108 (2000).
20. Three-dimensional representations of punctured torus bundles, Brian Mangum and Patrick D. Shanahan, Journal of Knot Theory and its Ramifications 6.6 (1997).

      Books:

1. Complex Analysis: A First Course with Applications 3rd ed., Dennis G. Zill and Patrick D. Shanahan, Jones and Bartlett Learning, Boston (2015).
2. Student Study Guide to Accompany Complex Analysis: A First Course with Applications 3rd ed., Patrick D. Shanahan, Jones and Bartlett Learning, Boston (2015).
3. Student Study Guide to Accompany A First Course in Complex Analysis with Applications 2nd ed., Patrick D. Shanahan, Jones and Bartlett Publishers, Boston (2010).
4. A First Course in Complex Analysis with Applications 2nd ed., Dennis G. Zill and Patrick D. Shanahan, Jones and Bartlett Publishers, Boston (2009).
5. A First Course in Complex Analysis with Applications, Dennis G. Zill and Patrick D. Shanahan, Jones and Bartlett Publishers, Boston (2003).