Despite being a math professor, I′m not a "math person," if such a thing even exists. I didn′t decide to study mathematics until pretty late in college, and went from being relatively dismissive of mathematics to completely obsessed in a three-week period. Because of my background, I remember vividly what it is like to be uninterested in math but now understand how much I was missing out. At any level of mathematics, there are beautiful structures that appeal to our natural human desire to solve puzzles and "see how things work." Thinking that you need to spend years studying mathematics in order to appreciate these structures and puzzles is like thinking that you have to learn how to be a professional typesetter in order to enjoy a book.
In the classroom, my primary goal is to entice students to appreciate the mathematics they are learning. Like most things worth doing, math can be difficult. But students far too commonly focus on the difficulty of mathematics, which certainly doesn′t make it any easier to understand. From introductory to advanced classes, I focus on the motivation and relevance of the material in terms of applications either outside or inside of mathematics. I stress the ways that the material confronts our intuition and challenges us to find out "what is really going on," striving constantly to leave my students eager to understand, not just to finish the current homework assignment. It is impossible to learn math without doing math, and if you are going to do math, you might as well love every second of it. Or at least most of them.
Since joining the department in 2004, I′ve most frequently taught Calculus III, Cryptology, and Applied Calculus. I′ve re-designed the Applied Calculus course at Rhodes with Rachel Dunwell, and have offered a number of topics and directed inquiry courses on advanced material. Almost every mathematics course at Rhodes includes material that plays a significant role in my research, so I try to teach as many courses as possible.
Additionally, my research interests involve a lot of examples that need to be computed and understood. Even low-dimensional examples of the objects that I study can be complicated, and computations involving these examples involve a synthesis of geometry, topology, and algebra that can make for a great learning experience for students. I′m very interested in teaching students the skills that they need to perform these computations so that we can try to understand the structures embedded in these computations. I′ve worked with several students at Rhodes (and at other places) and have gotten positive results, and I′m always interested in recruiting more student collaborators. Students at any level are encouraged to inquire further.
I am interested in the geometry and topology of objects with singularities, i.e., objects that have a "smoothness" that breaks down due to sharp corners, edges, or other types of "unsmoothness." Primarily, I study objects called Orbifolds and other objects whose singularities arise from collections of symmetries. Most of my work is differential topology or differential geometry, meaning that I use calculus-like techniques to study the shapes and structures of these singular spaces. However, understanding these objects involves using techniques from many fields of mathematics, including both algebra and analysis. I love being able to work in an area that combines so many different kinds of math.
Currently, I am working with several people to better understand certain collections of invariants for orbifolds, as well as to extend related techniques to more general singular spaces. Recently, I have presented research at the Great Planes Operator Theory Symposium as well as several AMS meetings. I′ve also co-organized an AMS Special Session and Mellon Collaborative Workshop. I have co-authored several research papers with undergraduate students.
OUTSIDE THE CLASSROOM
I grew up in Downriver Detroit, where much of my family still lives. Before coming to Memphis in 2004, I lived in Boulder, Colorado, which I still frequently visit. My twin brother lives in Brooklyn, New York, so I go there often as well. I studied abroad at the Hebrew University of Jerusalem in Israel and participated in a German-American exchange program twice while in high school.
Currently, I live in Midtown with my spouse Lauren, son Heron, and dog Meatball. When I′m pretending to not to think about math, I′m usually listening to or making music. I play bass guitar in a few local Memphis bands and have played in bands pretty consistently since I started high school. I′ll listen to almost anything and love to stretch my ear. The only thing I enjoy better than a good live music performance is a good session of working on mathematics—and I often try to combine these two with varying results.
I am obsessed with zombies in popular culture, think that socks are the most important part of an outfit, and garden in the middle of the night. I love sketch and stand-up comedy, This American Life, web-comics, aimless walks, and road trips. Most of my past roommates and house-mates would tell you that I am the heaviest sleeper they′ve ever met.
Approximating orbifold spectra using collapsing connected sums (with Carla Farsi and Emily Proctor), to appear in the Journal of Geometric Analysis.
The Laurent coefficients of the Hilbert series of a Gorenstein algebra (with Hans-Christian Herbig and Daniel Herden), Experimental Mathematics 30 (2021), 56—75.
Constructing symplectomorphisms between symplectic torus quotients (with Hans-Christian Herbig and Ethan Lawler), Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61 (2020), 581—604.
Hilbert series associated to symplectic quotients by SU2 (with Hans-Christian Herbig and Daniel Herden), International Journal of Algebra and Computation 30 (2020), 1323—1357.
The Hilbert series of SL2-invariants (with Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, and Daniel Herden), Communications in Contemporary Mathematics 22 (2020), 1950017.
Symplectic quotients have symplectic singularities (with Hans-Christian Herbig and Gerald Schwarz), Compositio Mathematica 156 (2020), 613—646.
The Hilbert series and a-invariant of circle invariants (with L. Emily Cowie, Hans-Christian Herbig, and Daniel Herden), Journal of Pure and Applied Algebra 223 (2019), 395—421.
Functional equations for orbifold wreath products (with Carla Farsi), Journal of Geometry and Physics 120 (2017), 37—51.
Symplectic reduction at zero angular momentum (with Joshua Cape and Hans-Christian Herbig), Journal of Geometric Mechanics 8 (2016), 13—34.
On compositions with x^2/(1-x) (with Hans-Christian Herbig and Daniel Herden), Proceedings of the American Mathematical Society 143 (2015), 4583—4596.
When is a symplectic quotient an orbifold? (with Hans-Christian Herbig and Gerald Schwarz), Advances in Mathematics 280 (2015), 208—224.
An impossibility theorem for linear symplectic circle quotients (with Hans-Christian Herbig), Reports on Mathematical Physics 75 (2015), 303—331.
Stratifications of inertia spaces of compact Lie group actions (with Carla Farsi and Markus Pflaum), Journal of Singularities 13 (2015), 107—140.
Gauge-fixing on the lattice via orbifolding (with Dhagash Mehta, Noah S. Daleo, and Jonathan D. Hauenstein), Physical Review D 90 (2014), 054504.
Gamma-extensions of the spectrum of an orbifold (with Carla Farsi and Emily Proctor), Transactions of the American Mathematical Society 366 (2014), 3881—3905.
The Hilbert series of a linear symplectic circle quotient (with Hans-Christian Herbig), Experimental Mathematics 23 (2014), 46—65.
Ph.D., Mathematics, University of Colorado at Boulder