TeachingFor more information on my experiences and views on teaching, here is my teaching statement.
- Linear Algebra. Course materials for students can be found on Canvas.
- Calculus III (Fall 2018, Fall 2019)
- (TA) Calculus III (Fall 2019)
- (TA) Differential Equations (Spring 2019). This
involved working with other instructors to co-develop
curriculum to be used in a weekly recitation session.
- Associate Convenor for College Algebra and Trigonometry (AY 2017-2018). Responsible for coordinating 4 (spring) - 12 (fall) sections of Math 103, writing quizzes, improving curriculum, making decisions regarding grading, and running weekly course meetings with all of the instructors.
- College Algebra and Trigonometry (Fall 2016, Fall 2017)
- (TA) Mini-Course: An Introduction to Knotted Surfaces
in Four-Space (Summer 2017). This mini-course was a
part of the Southeast
Undergraduate Mathematics Workshop at Georgia
- (TA) Mini-Course: An Introduction to Knot Theory
(Summer 2017). This mini-course was a part of All
Girls/All Math, a summer camp for high school
girls at UNL.
- Geometry Matters (Spring 2017). This is a course
for elementary education majors.
- Contemporary Mathematics (Summer 2016)
- College Algebra (Fall 2015, Spring 2016)
- (TA) Calculus II (Fall 2014, Summer 2015)
- (TA) Calculus I (Spring 2015)
ResearchI am interested in low-dimensional topology and geometric topology, particularly trisections of smooth 4-manifolds. Trisection diagrams for (from left to right) T2xS2, S2x(T2#T2), T2xT2, and S2xT2 are displayed at the top of the page; each of these comes from an algorithmic construction I developed for trisecting closed orientable surface bundles over surfaces. For more details, here is my research statement.
- Crawford, L., Ponomarenko, V., Steinberg, J., Williams, M. Accepted Elasticity in Local Arithmetic Congruence Monoids, Results in Mathematics 66 (2014), pp 227-245.
- Trisecting Surface Bundles over Surfaces (Slides), AMS Special Session on Women in Topology, Joint Mathematics Meetings (January 2019)
- An Introduction to Trisections and Surface Bundles,
University of Iowa topology seminar (October 2018)
- Trisecting an S2 Bundle over RP2,
Session on Connections Between Trisections of
4-manifolds and Low-dimensional Topology, Boston,
MA (April 2018)
- Knot Theory and Beyond, Great Plains Alliance talk at Benedictine College (April 2018)
- Surface Bundles over Surfaces, Winter
Trisectors Meeting, University of Georgia
- What are Trisections of 4-Manifolds?, Nebraska Wesleyan University math club (October 2017)
- Knot Theory and Beyond, Creighton University Mathematics Undergraduate Conference (October 2017)