ResearchI am interested in applied and computational topology. My advisor is Gunnar Carlsson, and I am a member of the CompTop research group. Here is a research statement.
"Morse Theory in Topological Data Analysis", with Atanas Atanasov and Gunnar Carlsson. Submitted Dec 2011.
[paper, data, software, javadoc]
- "On the Nonlinear Statistics of Range Image Patches", with Gunnar Carlsson. SIAM Journal on Imaging Sciences 2 (2009), 110-117. [paper, data]
- Applied Topology in Będlewo, Poland, July 21-27, 2013.
- Mini-symposium on Applied and Computational Topology at the SIAM Conference on Applied Algebraic Geometry, August 1-4, 2013.
"Evasion Paths in Mobile Sensor Networks."
- Stanford CompTop Seminar, May 2013.
- Special Session on Applied and Computational Topology at MAA MathFest, Aug 2012.
- Algebraic Topology: Applications and New Directions, July 2012.
- Minisymposium on Applied Algebraic Topology at SIAM Annual Meetings, July 2012. [video]
- Schloss Dagstuhl Seminar on Applications of Combinatorial Topology to Computer Science, March 2012.
- AMS Special Session on Computational and Applied Topology, Joint Meetings, Jan 2012.
- SIAM Conference on Applied Algebraic Geometry, Oct 2011.
- "Morse Theory in Topological Data Analysis."
- "Topological Data Analysis: Understanding Optical Flow." IMA Short Course on Applied Algebraic Topology, June 2009. [slides]
- "Topology Applied to Data Analysis." SUMaC Guest Lecture Series, July 2011. [slides]
- "Coverage Problems in Sensor Networks." SUMO Speaker Series, May 2010. [abstract]
- "JPlex Software Demonstration." AMS Short Course on Computational Topology, Joint Meetings, Jan 2011. [slides]
- "JPlex." CSRI Workshop on Combinatorial Algebraic Topology, Aug 2009. [slides]
- "Introduction to JPlex." IMA Short Course on Applied Algebraic Topology, June 2009. [notes]
- "Mobile Sensors and Pursuit-Evasion: Can Directed Algebraic Toplogy Help?" Aalborg GETCO Workshop, Jan 2010. [poster]
- Andrew Tausz and I maintain a javaPlex tutorial. All materials are available on the javaPlex site.
- I wrote a Matlab tutorial and a BeanShell tutorial for JPlex. All materials are available on the JPlex site.