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Frenet Frame in Action

Associate Professor of Mathematics

Department of Mathematics
Lafayette College
Easton, PA 18042


Ph.D. Mathematics. Stanford 2000.
Dissertation: Scalar Curvature Deformation and General Relativity.
Advisor: Richard M. Schoen.

M.S. Mathematics. Stanford 1996.

B.S. Mathematics (Minor in Physics). MIT 1994.
Awarded Jon A. Bucsela Prize in Mathematics.


Differential Geometry, General Relativity, Partial Differential Equations.


I am on sabbatical leave through the Summer of 2014. Even while on sabbatical, I supervised an honors thesis project (on the Min-Oo Conjecture) and an independent study course (on elliptic PDE). I was humbled to receive from Lafayette College the 2014 Carl R. and Ingeborg Beidleman Research Award recognizing excellence in applied research or scholarship.

Here are some of my activities for the year.

I served as the Undergraduate Faculty Program Lecturer at the Summer Program on Geometric Analysis June 30-July 20, 2013, at the IAS/Park City Math Institute .

I co-organized the Clay-INdAM-MSRI Summer Graduate Workshop on Mathematical General Relativity in Cortona, Italy, July 29-August 9, 2013. You can read about it in the MSRI Newsletter, and there is more information at the MSRI workshop page .

I also co-organized the Introductory Workshop on Mathematical Relativity with Greg Galloway (University of Miami) and Hans Ringstrom (KTH-Royal Institute of Technology) at the Mathematical Sciences Research Institute in Berkeley, CA, September 9-13. The workshop is associated to the Fall 2013 semester-long MSRI program Mathematical General Relativity. I am a member of MSRI for this semester-long program.

In December, I traveled to the 2013 Taiwan International Conference in Geometry, where I was invited to speak. Pengzi Miao (Miami) and I will together offered an invited a six-lecture mini-course Scalar Curvature and the Einstein Constraint Equations during the week preceding the conference. Here is the poster.

In the summer of 2014, I delivered an invited five-lecture course on the Einstein Constraint Equations at the ESI-EMP-IAMP Summer School on Mathematical Relativity at the Erwin Schrodinger Institute in Vienna, Austria, July 28-August 1, 2014. Check out the poster. Together with Co-PI Greg Galloway (University of Miami), we secured funding from the National Science Foundation (DMS-1406614) to provide support for U.S. graduate students and postdocs to attend the summer school.

I returned to teaching at Lafayette in the fall, but I did travel to Japan, where I was invited to deliver three one-hour lectures as part of the workshop “Geometric Analysis in Geometry and Topology 2014,” October 28-31, 2014, hosted at the Tokyo University of Science in the center of Tokyo.


In 2010 I was promoted to Associate Professor of Mathematics, after having been an Assistant Professor at Lafayette College since the fall of 2004. Prior to this, I was a Tamarkin Assistant Professor and an NSF Postdoctoral Research Fellow at Brown University in Providence, RI.

I was honored to be chosen as one of the two recipients of the 2010-2011 Thomas Roy and Lura Forest Jones Lecture Award from Lafayette College. A Geometer’s Apology: Confessions of a Wannabe Physicist was the title of my Jones lecture on March 29, 2011.

During the Fall of 2008, I visited the Mittag-Leffler Institute and the Royal Institute of Technology in Stockholm as a Fulbright Scholar. I also participated in the programme “Geometry, Analysis, and General Relativity” at the Mittag-Leffler Institute and the “Geometry and Analysis” conference at KTH. You can read a bit more about it here.

During Summer 2010, I participated in the PRIMA Conference on Geometric Analysis, at PIMS/UBC in Vancouver, along with Farhan Abedin ’11. Read more about it here .

In 2011 I headed to Akko, Israel, for the conference on Complex Analysis and Dynamical Systems V, and then to China for the Beijing Summer Workshop in Mathematical Relativity at Peking University. Former students Farhan Abedin ’11 and Haotian Wu ’07 attended as well.

I co-organized a Summer Graduate Workshop with Pengzi Miao (University of Miami) at the Mathematical Sciences Research Institute in Berkeley, CA, July 9-20, 2012. The workshop is associated to the Fall 2013 semester-long MSRI program Mathematical General Relativity.

The Mittag-Leffler Insitute and MSRI mentioned above are two wonderful places for mathematics. I have been fortunate to have had the opportunity to visit these places, in addition to other truly special institutes for mathematics. The mathematics institute in Oberwolfach, Germany, is yet another truly special place for mathematics. I have had the opportunity to participate in workshops on Mathematical Aspects of General Relativity in 2000, 2003, 2006, 2009 and 2012. In addition, I have been able to participate twice in workshops in Banff, Canada, at the Banff International Research Station (BIRS): at the 2010 workshop on Geometric Analysis and General Relativity, and at the 2007 workshop on Minimal submanifolds and related problems.

L^2 (Lafayette-Lehigh) Geometry-Topology Seminar

The L^2 Geometry-Topology Seminar is co-organized by Ethan Berkove, John Meier, and me, in conjunction with faculty from Lehigh. Since 2006, the seminar has been held annually on a Saturday in the winter/spring. The 2014 seminar marked the first time the event was co-sponsored by Lafayette College, Lehigh University, and LVAIC (Lehigh Valley Association of Independent Colleges).

The Spring 2015 Lafayette-Lehigh Geometry-Topology Seminar will be held Saturday March 21, in Pardee 217. The following speakers have been confirmed: Moon Duchin (Tufts), Fernando Schwartz (U. Tennessee, Knoxville) and Sam Taylor (Yale).

The Spring 2014 Lafayette-Lehigh Geometry-Topology Seminar was held Saturday March 15, in Pardee 217. A wonderful set of talks was given by the following speakers: Jason Behrstock (CUNY-Lehman), Christine Breiner (Fordham University) and Christina Tønnesen-Friedman (Union College).

The Spring 2013 Lafayette-Lehigh Geometry-Topology Seminar was held Saturday March 23, in Pardee 217. We were delighted to have had the following speakers: Vincent Bonini (Cal. Poly. State Univ.), Andrew Cooper (University of Pennsylvania) and Cynthia Curtis (The College of New Jersey).

The Spring 2012 Lafayette-Lehigh Geometry-Topology Seminar was held Saturday March 24, in Pardee 217. We were delighted to have had the following speakers: Adam Pigott (Bucknell), Radmila Sazdanovic (University of Pennsylvania) and Valentino Tosatti (Columbia).

The Spring 2011 Lafayette-Lehigh Geometry-Topology Seminar was held on Saturday, March 26, in Pardee 217. We were delighted to have had the following speakers: Bob Gilman (Stevens Institute of Technology), Lan-Hsuan Huang (Columbia University), and Jeff Jauregui (University of Pennsylvania).

Fliers for current and past seminars:
2015 . 2014 . 2013 . 2012 . 2011 . 2010 . 2009 . 2008 . 2007 . 2006


I have supervised REU students during the 2005, 2007 and 2009 summers at Lafayette. The general topic for my groups has been differential geometry, with an eye toward general relativity. Please see the link below for more information about the Lafayette program.

Lafayette REU

Last Updated: March 19, 2015.