2. Scholarship
3. Talks

Talks

Below is a list of talks and presentations that I have given over the past several years.  In most cases, there are links to slides. Check out my scholarship overview page for additional information about my research interests. If you are interested in presentations that my undergraduate research students have given, check out my undergraduate research page.

• Discussion of AI in Mathematics. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. October 2026. [Slides]
• My experience teaching at Epsilon Camp. NAU Mathematics and Statistics Teaching Seminar, NAU, Flagstaff, AZ. October 2026.
• When are two things equal? Math on Tap, Mother Road Brewery, Flagstaff, AZ. September 2026. [Slides]
• My academic journey. Parent talk at Epsilon Camp, Logan, UT. July 2026.
• Structure of braid graphs for reduced words in simply-laced Coxeter systems. Seminario di Algebra e Geometria, University of Bologna, Bologna, Italy. April 2026. [Slides]
• In defense of mathematics. 2026 Great Survival Debate, NAU, Flagstaff, AZ. March 2026.
• Friendship Paradox: Your friends, on average, have more friends than you do. Math on Tap, Mother Road Brewery, Flagstaff, AZ. November 2025. [Slides]
• Structure of braid graphs for reduced words in Coxeter groups. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. September 2025. [Slides]
• Structure of braid graphs for reduced words in Coxeter groups. 15th Nordic Combinatorial Conference, Reykjavik University, Iceland. June 2025. [Slides]
• Pattern-avoiding Cayley permutations via combinatorial species. University of Arizona Mathematical Physics & Probability Seminar, UofA, Tucson, AZ. November 2024. [Slides]
• Pattern-avoiding Cayley permutations via combinatorial species. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. November 2024. [Slides]
• Braid graphs in simply-laced triangle-free Coxeter systems are median. CU Lie Theory Seminar. CU Boulder, Boulder, CO. March 2024. [Slides]
• An introduction to species (3 talks). NAU Mathematics Seminar. NAU, Flagstaff, AZ. November 2023.
• Topics in combinatorics. NAU Mathematics and Statistics Putnam Exam Preparation. NAU, Flagstaff, AZ. November 2023.
• Adopting, Adapting and Creating Open Education Resources (panel discussion). NAU Teaching and Learning Center: Faculty Professional Development Opportunities. NAU, Flagstaff, AZ. October 2023.
• Sabbatical Report / Categories of rulesets and games. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. September 2023. [Slides]
• Discussion of Open Educational Resources (OER). NAU Mathematics and Statistics Teaching Seminar, NAU, Flagstaff, AZ. August 2023. [Slides]
• Enumerating signed permutations by reversal distance. University of Iceland Mathematics Seminar. June 2023. [Slides]
• Morphisms of impartial combinatorial games. Virtual Combinatorial Game Theory Seminar. April 2023. [Slides]
• Fundamental homomorphism theorem for impartial combinatorial games (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. March 2023.
• Impartial geodetic convexity achievement & avoidance games on graphs. Combinatorial Game Theory Colloquium IV, S. Miguel, Azores. January 2023. [Slides]
• Some enumeration results for sorting signed permutations by reversals. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. March 2022. [Slides]
• Some enumeration results for sorting signed permutations by reversals. ASU Discrete Mathematics Seminar, ASU, Tempe, AZ. March 2022. [Slides]
• Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes (4 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. November 2021. [Slides for part 1 only]
• Architecture of braid classes in Coxeter systems. AMS Special Session on Interactions between Combinatorics, Representation Theory, and Coding Theory, Joint Mathematics Meetings, Denver, CO. January 2020. [Slides]
• Taxonomy of braid graphs in Coxeter systems of types $A$ and $D$ (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. November 2019.
• Pennies and Paperclips. Flagstaff Festival of Science Math Circles, Coconino High School, Flagstaff, AZ. September 2019.
• What is mathematical inquiry? Plenary talk at 2019 IBL Workshop, Portland, OR. June 2019. [Slides]
• Enhancing Student Engagement and Understanding via Inquiry-Based Learning. The Good Teaching Round Table, Boise State University, Boise, ID. February 2019. [Slides]
• Should you consider graduate school in statistics or mathematics education or mathematics? Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. January 2019.
• Braid shadows in simply-laced Coxeter systems (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. November 2018.
• The Dating Game. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. September 2018.
• What is mathematical inquiry? Plenary talk at 2018 IBL Workshop, DePaul University, Chicago, IL. June 2018. [Slides]
• Experiencing IBL. Plenary talk at 2018 IBL Workshop, DePaul University, Chicago, IL. June 2018.
• Structure of braid graphs for reduced words in Coxeter groups (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. February 2018.
• Open-source course materials for an inquiry-based approach to an introduction to proof course and abstract algebra. The Advancement of Open Educational Resources, Joint Mathematics Meetings, San Diego, CA. January 2018. [Slides]
• Enhancing Student Engagement and Understanding via Inquiry-Based Learning. Creating Meaningful Classroom Activities to Deepen Student Learning, Project NExT Panel Discussion, Joint Mathematics Meetings, San Diego, CA. January 2018. [Slides]
• More combinatorics of genome rearrangements. Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. November 2017.
• An introduction to the combinatorics of genome rearrangements. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. November 2017.
• Proofs Without Words. Guest lecture for MAT 123, NAU, Flagstaff, AZ. October 2017. [Slides]
• The ubiquitous Catalan numbers, part 2. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. October 2017.
• The ubiquitous Catalan numbers, part 1. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. October 2017.
• Impartial achievement and avoidance games for generating finite groups (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. October 2017. [Slides]
• The Futurama Theorem. DePaul Math Club, DePaul University, Chicago, IL. September 2017. [Slides]
• Impartial achievement and avoidance games for generating finite groups. DePaul Mathematical Sciences Colloquium, DePaul University, Chicago, IL. September 2017. [Slides]
• What is mathematical inquiry? Plenary talk at 2017 IBL Workshop, Cal Poly, San Luis Obispo, CA. June 2017. [Slides]
• Jamming the Death Star cafeteria pool table with counterfeit coins: The wonderful world of MAT 220. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. January 2017. Joint with Monika Keindl and Nandor Sieben. [Slides]
• On the size of a braid class of a permutation (3 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. November 2016.
• Transitioning students from consumers to producers. Opening address at the Spring 2016 Joint ArizMATYC and MAA–Southwest Section Conference, Coconino Community College, Flagstaff, AZ. April 2016. [Slides]
• Several representations of my favorite open problem. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. February 2016. [Slides]
• Euler’s characteristic, soccer balls, and golf balls. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. February 2016.
• The mathematics of Boggle logic puzzles. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. January 2016. [Slides]
• Student presentations in calculus: A vehicle for getting students to talk about mathematics. Increasing Student Engagement & Understanding through Active Learning Strategies in Calculus I minicourse, Joint Mathematics Meetings 2016, Seattle, WA. January 2016. [Slides]
• Counting commutation classes of the longest element in the symmetric group. Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. December 2015.
• The Futurama Theorem. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. December 2015. [Slides]
• Explorations of Sylver Coinage (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. December 2015.
• The Kirkman Schoolgirls Problem. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. November 2015. [Slides] [Blog Post]
• Proofs Without Words. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. September 2015. [Slides] [Blog Post]
• Friendship Paradox: Your friends, on average, have more friends than you do. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. September 2015. [Slides] [Blog Post]
• An Iterated Prisoner’s Dilemma. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. April 2015. [Slides]
• Impartial achievement and avoidance games for generating finite groups. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. April 2015. [Slides]
• One step forward, one step back: A puzzle approach to Erdős’ discrepancy problem. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. February 2015. [Slides]
• A discussion about inquiry-based learning (part 2). NAU Mathematics and Statistics Teaching Showcase, NAU, Flagstaff, AZ. January 2015. [Slides]
• A guide-on-the-side approach to calculus. First-Year Calculus: Fresh Approaches for Jaded Students, Joint Mathematics Meetings 2015, San Antonio, TX. January 2015. [Slides]
• Transitioning students from consumers to producers. Teaching Inquiry, Joint Mathematics Meetings 2015, San Antonio, TX. January 2015. [Slides]
• A discussion about inquiry-based learning (part 1). NAU Mathematics and Statistics Teaching Showcase, NAU, Flagstaff, AZ. November 2014. [Slides]
• T-avoiding elements in Coxeter groups (2 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. October 2014.
• Open problems with monetary rewards. 2014 Northern Arizona University High School Math Day, NAU, Flagstaff, AZ. October 2014. [Slides]
• Open problems with monetary rewards. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. October 2014. [Slides]
• What is MAT 220? Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. October 2014. [Slides]
• Mathematics as a Creative Endeavor. Is Mathematics Communication?, Liberal Studies Town Hall, NAU, Flagstaff, AZ. September 2014. Joint with Terry Blows. [Slides]
• Creating Independent Learners. NAU Fall 2014 Tutor Training. NAU, Flagstaff, AZ. August 2014. Joint with Ellie Kennedy. [Slides]
• Soup to Nuts: My Approach to IBL. Plenary talk at 2014 IBL Workshop, Portland, OR. August 2014. [Slides] [Blog Post]
• Inquiry-Based Education in Mathematics: Models, Methods, and Effectiveness for Higher Education. Workshop on Innovations in Higher Education Mathematics Teaching, Cardiff University, Cardiff, Wales. July 2014. [Slides] [GitHub Repository]
• A Pentagon of Assessments. 12th Annual Assessment Fair, NAU, Flagstaff, AZ. April 2014. Joint with B. Beaudrie and B. Boschmans.
• Tried & True Practices for IBL & Active Learning. Project NExT Panel Discussion, Joint Mathematics Meetings, Baltimore, MD. January 2014. [Slides] [Blog Post]
• An Iterated Prisoner’s Dilemma. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. October 2013. [Slides] [Blog Post]
• The nim-values of combinatorial games on groups respect parity (3 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. September-October 2013.
• Proofs without Words. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. September 2013. [Slides] [Blog Post]
• Lumberjack Mathematics Center Poster. Showcase at the President and Provost Speaker Series, NAU, Flagstaff, AZ. September 2013. Joint with B. Beaudrie and B. Boschmans.
• Introduction to Inquiry-Based Learning. NAU Department of Mathematics & Statistics Teaching Showcase, NAU, Flagstaff, AZ. August 2013. [Slides] [Summary of IBL Research by Laursen, et. al] [Engaging in Dialogue with Students Handout] [Blog Post]
• Implementing IBL in an Introduction to Proof Course. Legacy of R.L. Moore Conference, Austin, TX. June 2013. [Slides] [Blog Post] [Video]
• Teaching Strategies for Improving Student Learning. Michigan Project NExT Panel Discussion, 2013 Spring MAA Michigan Section Meeting, Lake Superior State University, Sault Ste. Marie, MI. May 2013. [Slides] [Blog Post]
• Games on Groups. Omaha Area Math Teachers Circle, University of Nebraska at Omaha, Omaha, NE. April 2013. [Blog Post]
• Impartial games for generating groups. Cool Math Talks, University of Nebraska at Omaha, Omaha, NE. April 2013. [Slides] [Blog Post]
• A diagrammatic representation of the Temperley-Lieb algebra. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. February 2013. [Slides] [Blog Post]
• The Stargate Switch. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. February 2013. [Slides] [Blog Post]
• Using IBL as an assessment strategy. Project NExT Alternative Assessment Techniques Panel Discussion, Joint Mathematics Meetings, San Diego, CA. January 2013. [Slides] [Blog Post]
• Conjugacy and reducibility in Coxeter groups (5 talks). Algebra, Combinatorics, Geometry, and Topology Seminar (ACGT), NAU, Flagstaff, AZ. October-November 2012.
• The Futurama Theorem and some refinements. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. November 2012. [Slides] [Blog Post]
• Euler’s characteristic, soccer balls, and golf balls. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. November 2012. [Slides] [Blog Post]
• Inquiry-Based Learning Panel Discussion. MAA Section Meeting, Butler University, Indianapolis, IN. October 2012. [Slides] [Blog Post]
• Designing Inquiry-Based Learning Experiences. NAU Faculty Development Workshop, NAU, Flagstaff, AZ. October 2012. [Slides] [Blog Post]
• Inquiry-Based Learning: What, Why, and How? ArizMATYC Conference, Yavapai College, Prescott, AZ. October 2012. [Slides] [Blog Post]
• Inquiry-Based Learning: What, Why, and How? UA Mathematics Instructional Colloquium, University of Arizona, Tucson, AZ. October 2012. [Slides] [Blog Post]
• An open problem of the symmetric group. Friday Afternoon Mathematics Undergrad Seminar (FAMUS), NAU, Flagstaff, AZ. September 2012. [Slides] [Blog Post]
• Effective and efficient grading for an IBL course. Legacy of R.L.Moore Conference, Austin, TX. June 2012. [Slides] [Blog Post]
• Permutation Puzzles. Omaha Area Math Teachers Circle, University of Nebraska at Omaha, Omaha, NE. February 2012. [Slides]
• The Futurama Theorem. UNO Mathematics Colloquium, University of Nebraska at Omaha, Omaha, NE. February 2012. [Slides]
• Collaborative peer review between two IBL number theory courses. Scholarship of Teaching and Learning in Collegiate Mathematics, Joint Mathematics Meetings 2012, Boston, MA. January 2012. [Slides]
• The Futurama Theorem. PSU Mathematics Seminar, Plymouth State University, Plymouth, NH. December 2011. [Slides] [Blog Post]
• What can you do with a degree in mathematics? PSU Mathematics Association Panel Discussion, Plymouth State University, Plymouth, NH. November 2011.
• The prisoner of Benda and the Futurama Theorem. Mathematics Forum, Gordon College, Wenham, MA. November 2011. [Slides] [Blog Post]
• Diagram algebras as combinatorial tools for exploring Kazhdan-Lusztig theory. Dartmouth Combinatorics Seminar, Dartmouth College, Hanover, NH. October 2011. [Slides]
• Mendeley: Reference manager meets social networking. PSU Faculty Workshop Days, Plymouth State University, Plymouth, NH. August 2011.
• Mendeley: Reference manager meets social networking. Spotlight on Faculty Using Technology 2011, Plymouth State University, Plymouth, NH. March 2011. [Prezi]
• Diagram algebras and applications to Kazhdan-Lusztig theory. CU Algebraic Lie Theory Seminar, University of Colorado, Boulder, CO. March 2011. [Slides]
• Within $\epsilon$ of independence: An attempt to produce independent proof-writers via an IBL approach in a real analysis course. Getting Students Involved in Writing Proofs, Joint Mathematics Meetings 2011, New Orleans, LA. January 2011. [Slides]
• Technology Sampler. Issues for Early Career Mathematicians in Academia, 2010 MAA MathFest, Pittsburgh, PA. August 2010. [Slides]
• On an open problem of the symmetric group. PSU Mathematics Seminar, Plymouth State University, Plymouth, NH. April 2010. [Slides]
• A diagrammatic representation of the Temperley–Lieb algebra. Hudson River Undergraduate Mathematics Conference, Keene State College, Keene, NH. April 2010. [Slides]
• Using wikis to enhance collaboration. PSU Spotlight on Faculty Using Technology 2010, Plymouth State University, Plymouth, NH. April 2010. [Slides]
• On the cyclically fully commutative elements of Coxeter groups. 2010 Joint Mathematics Meetings, San Francisco, CA. January 2010. [Slides]
• On an open problem of the symmetric group. KSC Mathematics Seminar, Keene State College, Keene, NH. February 2009. [Slides]
• A diagrammatic representation of an affine $C$ Temperley–Lieb algebra. MAA Project NExT-YMN Poster Session, Joint Mathematics Meeting 2009, Washington, DC. January 2009. [Poster]
• Diagram calculus for the Temperley–Lieb algebra. Fall 2008 Northeastern Section Meeting of the MAA, Bentley University, Waltham, MA. November 2008. [Slides]
• A diagrammatic representation of an affine $C$ Temperley–Lieb algebra. Thesis Defense, University of Colorado, Boulder, CO. May 2008. [Slides]
• Diagram calculus for the Temperley–Lieb algebra. Job Talk, Plymouth State University, Plymouth, NH. February 2008. [Slides]
• Diagram algebras and Kazhdan-Lusztig polynomials. NAU Mathematics and Statistics Colloquium, NAU, Flagstaff, AZ. January 2008. [Slides]
• Weak star reducibility in Coxeter groups. Algebraic Lie Theory Seminar, University of Colorado, Boulder, CO. November 2007.
• The Temperley–Lieb Algebras of Types $A$ and $B$ and Their Associated Diagram Algebras. Slow Pitch Colloquium, University of Colorado, Boulder, CO. October 2007. [Slides]
• Diagram Calculus for the Temperley–Lieb Algebra. Graduate Student Combinatorics Conference, University of Washington Seattle, WA. April 2007. [Slides]
• 10 Things I Wish I Would Have Known Before I Started Teaching. Graduate Teacher Program Workshop, University of Colorado, Boulder, CO. November 2006. [Slides]
• Introduction to finite reflection groups. Coxeter Groups Seminar, University of Colorado, Boulder, CO. October 2006.
• Diagram calculus for the Temperley–Lieb algebra. Slow Pitch Colloquium, University of Colorado, Boulder, CO. October 2006.
• Classification of the FC-finite Coxeter groups. Slow Pitch Colloquium, University of Colorado, Boulder, CO. October 2006.
• Cell complexes for arrangements with group actions. NAU Mathematics & Statistics Colloquium, NAU, Flagstaff, AZ. May 2000.
• A cell complex for configuration space. MAA Southwest Section Meeting, Arizona State University, Tempe, AZ. April 2000.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.