Research
See my Publications/Presentations
Toric Gometry and Resolution of Singularities
My graduate research area is algebraic geometry, with a focus on toric geometry. Lately, I have been working with different resolutions of toric orbifolds of the form C^3/G, and studying the deformations of the tangent sheaf of these resolutions. I have also been looking at the relationship to the conformal field theory of the orbifold, in the context of the McKay correspondence. My recent work has also led me to a careful study of the G-Hilbert scheme, which is a particular resolution of this orbifold. A poster describing some of this work can be seen here. In the future, I hope to continue working in a related area, using toric geometry to examine the predictions of string theory, and looking at other problems using the tools of combinatorial algebraic geometry.
Combinatorial Games
I have recently been very interested in the study of combinatorial games, and ways that they can be varied to lead to interesting outcomes. I have worked with a number of undergraduate students on this topic, and presented talks on it at local seminars. The Honors Theses I have advised in this area are:
James Welsh: The Effects of Non-standard Turn Order in Domineering
Honors Thesis advised Fall 2015-Fall 2016: submitted in January 2017.
Research presented at both Thesis Day and Iona Scholar’s Day 2017.
Robert Cox: Implementation of Analysis Software for N-player Combinatorial Games
Honors Thesis, co-advised with Walter Krawec Fall 2017: submitted in December, 2017.
Large Scale Data Analysis
After attending a professional development conference in 2017, I became familiar with the ways different statistical methods, dimension reduction algorithms, and machine learning techniques are used to visualize and explore relationships among data. These methods allow exploration of any number of questions, and provide fertile ground for my own research and for undergraduate research projects. With the wealth of data available online, there are many interesting areas to be explored and analyzed. The Honors Thesis I have advised in this area is:
Willow Lopez-Silvers: Race as a Factor of Degree Attainment at the Secondary Level
Honors Thesis advised Spring 2019-Fall 2020: submitted in January 2021.
Research presented at Thesis Day and Iona Scholar’s Day 2021, UConn Math Continued Conference 2020, and MAA Metro NY Section meeting.
Writing Activities and Mathematics Pedagogy
Since coming to Iona, I have also become more interested in mathematical pedagogy, and doing research in the Scholarship of Teaching and Learning. My main focus has been on the benefits of writing in freshman-level mathematics courses. I use writing in all of my math courses, and have been collecting data demonstrating their effectiveness at engaging students, and measuring understanding of the relevant material. I also am collaborating on a project looking at how students’ evaluations of their peer's arguments change over time, and how evaluating peer work can help students to become stronger problem solvers and better communicators themselves.