B.A. Mathematics and Physics, Williams College,
May 1998
Graduated Phi Beta Kappa, Magna Cum Laude with Highest Honors.
Research Interests
Several Complex Variables
Partial Differential Equations
Harmonic Analysis
Grants
NSF Award DMS-1405100, ($133,318) 2014 - 2017. Principal Investigator. This was an individual research grant to support my research in Analysis and CR Geometry in Several Complex Variables.
NSF Award DMS-1157517, ($89,999) 2012 - 2015. Co-Principal Investigator. This grant supports the 2012, 2013, and 2014 Spring Lecture Series.
NSF Award DMS-0963810, ($85,762) 2010 - 2013. Principal Investigator. This grant supported the 2010, 2011, and 2012 Spring Lecture Series.
NSF Award DMS-0855822, ($95,602) 2009 - 2013. Principal Investigator. This was an individual research grant to support my research in Heat Equations, Boundary Operators and CR Geometry in Complex Analysis.
"You've Made a Difference", University of Arkansas, Fall 2011
Identified by a first-year student on the MAP-Works survey through University Housing as having helped the most in his/her college success during the first few weeks of school.
"Div-curl type inequalities for higher order operators", with Loredana Lanzani,
Advances in Analysis: The Legacy of Elias M. Stein (Princeton Mathematical Series). Princeton U. Press, (2013).
ISBN: 9780691159416.
Instructor: Osher Lifelong Learning Institute, March 2017
OLLI sponsored courses provide high quality, affordable educational, cultural, and engagement opportunities for seasoned adults. I taught a four hour class over two weeks about cardinality and the Cantor set.
Curriculum Committee Chair: U. Arkansas, Fall 2014-Spring 2015, Fall 2016-current
Hiring Committee: Dept. Math. Sci., U. Arkansas, Fall 2016-current
Third Year Review Committee: Dept. Math. Sci., U. Arkansas, Fall 2016-current
Faculty Mentor: Dept. Math. Sci., U. Arkansas, Fall 2014-current
Co-organizer, Celebration of the Mind, 2012, 2013.
Faculty Mentor, 2014 - current.
I am a co-organizer of a Math Fair for high school students and the community at large.
The Celebration of Mind is a math fair for K-12 students andand the community at large.
We enlisted graduate and undergraduate math students design interactive math games and projects for the fair.
We tie the projects directly to the Common Core Standards for Mathematics and provide handouts for the teachers that detail the activities and their tie-in to the standards.
Our goal is to increase the number of math and statistics majors at the University of Arkansas and anticipate that the fair will happen annually.
Instructor, M-SEA program, Summers 2011 - 2013
My colleague Janet Woodland and I organized a session for the
Mathematics, Science and Engineering Academy (M-SEA) run by the Cooperative Developmental Energy Program (CDEP) at Fort Valley State University. CDEP is a program whose
goal is to increase the number of women and minorities in the geosciences. Fort Valley offers a 3-2 program -- earn a B.S. at Fort Valley in three years and a second B.S. at a partner institution
in two years. The University of Arkansas is one of the partner institutions. The M-SEA is a program that identifies and prepares talented girls and minorities to enter CDEP.
The students enroll in eighth grade and their summers are spent at Fort Valley and the partner institutions receiving education and training. Dr. Woodland and I developed a class in which we had the students
derive a discrete version of Fick's Law of Diffusion and model lake pollution. We then pointed out that the mathematical underpinnings of Fick's Law of Diffusion are the same as Newton's Law
of Cooling, Fourier's Law of Heat Conduction, and Ohm's Law of Electrical Conduction.
Project Reviewer:
Universita degli Studi di Milano -- I served as a referee to comment on a project under review for research financing
Universita degli Studi di Padova -- I served as an external reviewer on a Ph.D. candidate's research achievements and also wrote a letter of recommendation for a post-doc applying for
an internal research award
Mathematical Sciences Graduate Committee, Fall 2010 - Spring 2013
Mathematical Sciences Library Representative, Fall 2009 - Spring 2013
Reviewer: Mathematical Reviews: (for the American Mathematical Society), Fall 2008 - current
Mathematical Sciences Hiring Committee, Fall 2008
Volunteer Instructor, Summer Educational Enrichment
in Math, June 2006, July 2007
Planned and led three 2.5 hour workshops titled "How Google Works" for incoming 6th, 7th, and 8th graders
"The $L^2$-theory of the d-bar equation on unbounded domains", Mathematics Colloquium, Fudan University, Shanghai, June 2016.
"Global $L^q$-Gevrey Functions Spaces with Applications", Workshop on
Harmonic Analysis and Several Complex Variables, Vietnam Institute for the Advances Study in Mathematics, Hanoi, Vietnam,
June 2016.
"The Box_b-heat equation on quadric submanifolds", Analysis Seminar, Universit\`a degli Studi di Milano, Milan, Italy, June 2015.
"Regularity of the Bergman Projection", Analysis and Geometry in Several Complex Variables, Doha, Qatar, Janunary 2015.
"The $\Box_b$-heat equation for the Heisenberg group and quadric submanifolds", Analysis Seminar, Universit\`a degli Studi di Milano, Milan, Italy, June 2014.
"$L^p$-Sobolev and H\"older Estimates for the Bergman kernel", Analysis Seminar, Universit\`a degli Studi di Padova, Padua, Italy, June 2014.
"Box-b heat kernel decay and the Fourier transform", Analysis Seminar, University of British Columbia, Vancouver, Canada, November 2012.
"Closed range for d-bar on (0,q)-forms and a weak Z(q)-condition", Workshop: CR-Geometry and PDEs - V, Levico Terme, Trento, Italy, June 5-8, 2012.
"Compactness of the Complex Green Operator on CR Manifolds of Hypersurface Type",
First Joint International Meeting of the AMS with CMS, Special Session on Several Complex Variables and Applications,
Shanghai, China, Dec. 2008
"Pointwise heat kernel estimates with applications to complex analysis".
Complex Analysis, Operator Theory, and Applications to Mathematical Physics -- Followup Fall 2006,
International Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria, Nov. 15, 2006.
"The Kerzman-Stein operator for piecewise continuously differentiable regions", AMS 2012 Fall Central Sectional Meeting #1084, Special Session on Complex Analysis and
its Broader Impacts, Akron, OH Oct. 2012.
"Defining functions on unbounded domains in $\mathbb R^n$"
AMS 2012 Spring Central Section Meeting #1081, Special Session on Interplay between Geometry and Partial Differential Equations in Several Complex Variables,
Lexington, KY, Mar. 2012.
"Part 1: The Mathematics and Statistics Graduate Program at the
University of Arkansas. Part 2: Convergence of Power Series -- Think You're An Expert? Think
Again!", Colloquium, University of Arkansas-Fort Smith, Nov. 2011.
"An Aronsson type approach to extremal quasiconformal mappings", AMS 2011 Fall Eastern Sectional Meeting #1072, Special Session on Geometric Aspects of Analysis and Measure Theory,
Ithaca, NY, Sep. 2011.
"Heat kernels, Gaussian decay and the Fourier transform'', Several Complex Variables Seminar, Texas A&M University, Feb. 2011.
"How to study for graduate math classes and conduct research in mathematics",
Graduate Student Seminar, University of Arkansas, August 2010.
"Applying for academic jobs in the mathematical sciences", Graduate Student Seminar, University of Arkansas, March 2010.
"The Box_b-heat kernel on quadric manifolds", Mathematics Colloquium, Georgetown University, Oct. 2009.
"Compactness of the complex Green operator", Mathematics Colloquium, Notre Dame University, April 2009
"The weighted $\bar\partial$-heat equation with applications", Analysis and PDE Seminar,
Johns Hopkins University, Nov. 2008.
"On A Class of Integral Operators Related to the Weighted $\bar\partial$-equation in $C$",
AMS Southeastern Sectional Meeting #1037,
Special Session on Harmonic Analysis and Partial Differential Equations in Real and Complex Domains, Baton Rouge, LA,
Mar. 2008.
"Compactness of the complex Green operator II",
AMS Eastern Sectional Meeting #1031,
Special Session on Geometric Analysis of Complex Laplacians,
New Brunswick, NJ, Oct. 2007.
"Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, III",
Several Complex Variables Seminar, Texas A&M University, May 4, 2007.
"Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, II",
Several Complex Variables Seminar, Texas A&M University, Apr. 27, 2007.
"Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, I",
Several Complex Variables Seminar, Texas A&M University, Apr. 20, 2007.
"Scaling and PDEs -- how to solve a differential equation without doing any work", Pi Mu Epsilon
Undergraduate Math Club Talk, Texas A&M University, April 24, 2006.
"On limits of sequences of operators: a theorem of Stein". A series of three lectures
at the Graduate Student Analysis Seminar, University of Wisconsin-Madison, Feb. 2001
"Mixing drinks and kneading bread: an introduction to ergodic theory". Graduate
Student Analysis Seminar, University of Wisconsin-Madison, Nov. 1999.