Research Projects

• Categorified Sensor Networks: I model sensor networks that sense properties living in a vector space. In the scattered disk model of an ad-hoc sensor network this leads naturally to constructible sheaves. This provides a model for multi-modal sensing. In the continuum limit model a vector bundle is used.
• Pursuit-Evasion in Mobile Sensor Networks: In collaboration with Robert Ghrist, we use constructible (co)sheaves to study the intruder problem in mobile sensor networks.

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Papers

• "Euler Calculus with Applications to Signal Processing" with Robert Ghrist and Michael Robinson. Submitted to AMS Proceedings.
• "Soliton Solutions of Integrable Systems and Hirota's Method." Harvard College Mathematics Review. Issue 2.

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Talks

• Special Session on Applied and Computational Topology at MAA MathFest, Aug 2-4 2012.
• "Obstruction-Theoretic Sensing." AMS Special Session on Computational and Applied Topology, Joint Meetings. Jan 5, 2012.
• "Sensor Networks and Constructible (Co)Sheaves." Bob MacPherson's Sheaf Theory Seminar. IAS. December 15, 2011.
• "Cellular Sheaves, Cohomology and Applications." Bob MacPherson's Sheaf Theory Seminar. IAS. December 5, 2011.
• "Sheaves Incarnate." Graduate Student Pizza Seminar. University of Pennsylvania. December 2, 2011.
• "Physical Instantiations of Mathematics." PACM Graduate Student Seminar. Princeton University. November 8, 2011.
• "Constructible Sheaves." MIT-RTG Geometry Workshop with David Nadler: Fukaya Categories via Microlocal Sheaf Theory. June 15, 2011
• "Physical Instantiations of Mathematics." Graduate Student Pizza Seminar. University of Pennsylvania. March 18, 2011.
• Three talks: "Microlocal/Singular Supports of Sheaves and Morse Theory I,II,III." Jonathan Block's Research Group Seminar. University of Pennsylvania. February 2-11, 2011.
• "Intro to Morse/Conley/Floer Theory." Geometry Topology Reading Seminar. University of Pennsylvania. October 27, 2009.
• "Morse Theory and Classifying Spaces." Graduate Student Pizza Seminar. University of Pennsylvania. November 6, 2009.
• "Soliton Solutions of Integrable Systems and Hirota's Method." Graduate Student Pizza Seminar. University of Pennsylvania. February 18, 2009

Demos

• Experimental Verification of Signals Embedding Theorem via wireless and acoustic data. AMS MRC on Applied and Computational Topology. Snowbird, UT June 21-28 2011.

Conferences/Workshops Attended

• Joint Mathematics Meetings. Boston, MA. 2012.
• Workshop on Topology: Identifying Order in Complex Systems. University of Pennsylvania. November 2, 2011.
• Workshop on Topology: Identifying Order in Complex Systems. Rutgers University. October 5, 2011.
• Applied and Computational Topology. IMA Summer School. University of Pennsylvania. July 25 - August 12, 2011.
• AMS MRC on Applied and Computational Topology. Snowbird, UT. June 21-28, 2011.
• MIT-RTG Geometry Workshop: Fukaya Categories via Microlocal Sheaf Theory. Breckenridge, CO. June 13-20, 2011.
• Workshop on Topology: Identifying Order in Complex Systems. University of Pennsylvania. April 6, 2011.
• Workshop on Topology: Identifying Order in Complex Systems. IAS. March 2, 2011.
• Workshop on Topology: Identifying Order in Complex Systems. Rutgers University. February 2, 2011.
• Joint Mathematics Meetings. New Orleans, LA. 2011.
• Workshop on Topology: Identifying Order in Complex Systems. IAS. December 1, 2010.
• Workshop on Topology: Identifying Order in Complex Systems. University of Pennsylvania. November 3, 2010.
• Workshop on Topology: Identifying Order in Complex Systems. Rutgers University. October 6, 2010.
• Algebra and Topology: Methods, Computation, and Science (ATMCS IV). Meunster, Germany. June 21-26, 2010.
• Young Topologists Conference. New Orleans, LA. November 13-15, 2009.