My main area of mathematical research interest is

**knot theory**; specifically, I am interested
in the relationships among

*knot theory*,

*low-dimensional topology*,

*combinatorics*, and

*graph theory*. My areas of research focus are

the relationships among properties of knot and link diagrams (e.g. sigma-adequacy and sigma-homogeneity), polynomial invariants of knots and links (e.g. the Kauffman polynomial), and polynomial invariants of graphs (e.g. the Tutte polynomial).
the relationships between the structure of families of
link diagrams and bounds on the
hyperbolic volume of the link complement.
I am also interested in the

**Scholarship of Teaching and Learning (SoTL)**. I am currently exploring

how student mathematics anxiety and attitudes change over the course of the semester in a liberal arts mathematics course;
how students respond to reading/writing assignments about intelligence mindsets, learning theory, and effective thinking strategies in a liberal arts mathematics course; and
how students beliefs about mathematics change over the course of the semester, what resources students use (and when and how often they use them) to help them learn and how this changes over the course of the semester, and how student perceptions of an active learning pedagogy and textbook change over the course of the semester in Honors Calculus I.
#### Research and Scholarship Statement

#### Papers and Preprints:

*Sigma-adequate link diagrams and the Tutte polynomial.* (Submitted) ArXiv Version.
*Semi-adequate closed braids and volume*, Topology
and its Applications, **198** (2016), 1-21. ArXiv Version.
*Combinatorics of link diagrams and volume*, Journal of Knot Theory and
Its Ramifications, Vol. 24, No. 1 (2015), 1550001 (21 pages). ArXiv Version.
Vertex-magic edge labeling games on graphs with cycles (with Erika L. C. King), *Journal of Combinatorial
Mathematics and Combinatorial Computing*, **78** (2011), 75-96, 05C57 (05C78).
#### Grants Awarded:

”Adopting an Open Source Active Learning Honors Calculus I Text”

The Provost's Open Educational Resources Grant (Awarded March 08, 2017)

University of Connecticut (Internal Grant)

”Using Preview Readings and Technology in an Active Learning Calculus Course”

The Provost's Academic Plan Mini Grant Competition (Awarded December 05, 2016)

University of Connecticut (Internal Grant)

”Using Student Posters to Enhance Student Learning on a Group Project for Honors Calculus II”

Center for Excellence in Teaching and Learning Small Grant (Awarded November 17, 2016)

University of Connecticut (Internal Grant)
#### Grant Applications:

”Adopting an Open Source Active Learning Honors Calculus Text”

CLAS Innovative Education in Science Grant (Applied October 01, 2016)

University of Connecticut (Internal Grant)
#### Honors and Awards:

Red 2015 MAA Project NExT Fellow (Summer 2015 to Summer 2016)

Dissertation Completion Fellowship (Summer 2014)

Research Assistantship (Summer 2012, Fall 2011, Summer 2011, Fall 2010)

Phi Beta Kappa (Spring 2008)

Sigma Xi Scientific Research Society (Spring 2008)

Robert L. Bienert Memorial Prize in Mathematics (Spring 2008)

Sutherland Prize in the Natural Sciences (Spring 2008)

Irving Bentsen Prize in Math and Computer Science (Spring 2006)
#### Research Experience (Undergraduate):

Honors Project in Mathematics (September 2007 to April 2008)
Hobart and William Smith Colleges, Geneva, NY

**Thesis:** A Vertex-Magic Edge Labeling Game for Graphs with Cycles

**Advisor:** Erika L. C. King

Research Experience for Undergraduates (REU) (June 2007 to July 2007)
Central Michigan University, Mount Pleasant, MI

**Topic:** Distance Regular Cayley Graphs

**Advisor:** Ken W. Smith