### About

I am a Ph.D. Candidate at the University of Nebraska-Lincoln, working with Dr. Alex Zupan and Dr. Mark Brittenham. I earned my B.A. in mathematics from Willamette University, and my M.A. in mathematics from UNL. For more details, here is my CV.Starting in Fall 2020, I will be a Lecturer at Christopher Newport University.

### Teaching

For more information on my experiences and views on teaching, here is my teaching statement.Current:

- 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 Tech.*

- (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)

- Wakefield, N., Kelley, C.,
**Williams, M.**, Haver, M., Seminario-Romero, L., Huben, R., Marks, A., & Prahl, S. (2019).*Coordinated Calculus*. Open Educational Resource. Available from https://mathbooks.unl.edu/Calculus/.

### Research

I am interested in low-dimensional topology and geometric topology, particularly trisections of smooth 4-manifolds. Trisection diagrams for (from left to right)*T*x

^{2}*S*,

^{2}*S*x

^{2}*(T*#

^{2}*T*),

^{2}*T*x

^{2}*T*, and

^{2}*S*x

^{2}*T*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.

^{2}Publications:

- 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 S*, AMS Special Session on Connections Between Trisections of 4-manifolds and Low-dimensional Topology, Boston, MA (April 2018)^{2}Bundle over**RP**^{2}

*Knot Theory and Beyond*, Great Plains Alliance talk at Benedictine College (April 2018)*Surface Bundles over Surfaces*, Winter Trisectors Meeting, University of Georgia (February 2018)

*What are Trisections of 4-Manifolds*?, Nebraska Wesleyan University math club (October 2017)*Knot Theory and Beyond*, Creighton University Mathematics Undergraduate Conference (October 2017)