My primary research interest is geometric analysis.



This picture illustrates the ``resolution blowup,'' a technique which can be used to resolve conical singularities. This technique was introduced in my doctoral dissertation, completed in 2006 at Stanford University under the supervision of Professor Rafe Mazzeo.

What is "geometric analysis?" It is an area of mathematics which incorporates both differential geometry and analysis. The mathematical models which describe our universe and its natural phenomena often involve both geometry and analysis, and the mathematical theory of geometric analysis helps us to better understand these models. For example, on the one hand we use partial differential equations (analysis) to understand and hence predict the behavior of heat, light, and waves. More complicated pde's can also describe a variety of natural phenomena including turbulent water, mixing gases, and erosion. On the other hand, we use differential geometry to describe shapes. How does an object's shape affect its physical properties? This question motivates much of my work in geometric analysis.

My research in geometric analysis focuses on the following topics: geometric analysis on singular spaces, dynamics and mathematical physics, spectral theory, and interdisciplinary collaboration. Articles are organized below according to topic.


If you have trouble accessing any of these articles or would like further information regarding my research, please send me an email!

I also review articles for the American Mathematical Society and Zentralblatt Math. Check out MathSciNet for the AMS, or for Zentralblatt. You can find my reviews by searching for "Rowlett" in the "Reviewer" search-field. Lately I have been too busy for much reviewing, but I hope to get back to it soon!