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The soul of an SO(4) action on the 8-sphere. [LaTeX source]

Welcome to my homepage, feel free to browse the various tabs above for the actual contents of the website.

Useful Links

More will be added as I find them!

My Research

My primary research area is Riemannian geometry with a focus on orbifolds, manifolds with density, group actions and spaces with positive curvature.

My Thesis: Riemannian Orbifolds with Non-Negative Curvature

Orbifold Biquotients of SU(3) Diff. Geom. Appl. 42 (2015), 54-76 (arXiv version arXiv:1401.7565 [math.DG])

On Geometry and Topology of 4-Orbifolds (preprint) arXiv:1411.1700 [math.DG]

On Poincare Duality for Orbifolds Topology Appl. 219 (2017) 9-16 (arXiv version arXiv:1502.03384 [math.AT])

On the Geometry of Riemannian Manifolds with Density (preprint) arXiv:1602.08000 [math.DG] (with W. Wylie)

The Weighted Connection and Sectional Curvature for Manifolds with Density (preprint) arXiv:1707.05376 [math.DG] (with L. Kennard and W. Wylie)


I've also dabbled in other fields.

On a Certain Cooperative Hat Game (preprint) arXiv:1407.4711 [math.CO] (with J. Kariv and C. van Alten)

Connectedness of Two-Sided Group Digraphs (to appear: Involve) arXiv:1705.05827 [math.CO] (with P. Chikwanda, C. Kriloff, Y.T. Lee, T. Sandow and G. Smith)

LaTeX Resources

What is LaTeX?

LaTeX is the preferred method of most mathematicians for typing up mathematics. It offers a wide array of capabilities for making both equations and figures.

What software to use?

There are a large number of LaTeX editors and several distributions. The most popular distribution for Windows is MiKTeX, for other operating systems (but also work on Windows) check out TeX Live. For editors my personal preference is TeXstudio which works for all major operating systems, but there are many other great options out there.

If you prefer to have your stuff in the cloud, you can also use shareLaTeX or overleaf.

How to learn LaTeX?

Once again, there are many great options available for free online, such as the wikibooks LaTeX page.

Graphics in LaTeX

There are a lot of ways to include graphics in LaTeX files, my personal preference is to use the TikZ Package. This package has a lot of capabilities, I have used it to draw commutative diagrams, plot functions and draw 3-d pictures. While the complete manual is over a thousand pages long, the tools for the most common uses can be learned very quickly. Additionally, there are hundreds of examples available online.

About Me

I received my B.S. in Mathematics from St. Joseph's University in 2009. There I did my undergraduate honors thesis "New Results in Exponential Families" under the direction of Paul Klingsberg.

I received my Ph.D. in Mathematics from the University of Pennsylvania in 2014 under the direction of Wolfgang Ziller.

Outside if mathematics, I enjoy reading, programming, hiking, skiing, photography and Magic: the Gathering.