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Department of Mathematics
University of Kentucky
753 Patterson Office Tower
Lexington, Kentucky
40506-0027
Recent Research Papers:
My recent research has focussed on three areas: random Schrodinger operators, geometric analysis of real and complex hyperbolic manifolds, and resonance and eigenvalue estimates. You can also check the archives for most of my recent papers.
A more complete list of my publications may be found on MathSciNet.
with P. Perry, S.-H. Tang: CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary, Analysis & PDE volume 1 #2 (2008) 197--227
with T. Christiansen: Maximal Order of Growth for the Resonance Counting Functions for Generic Potentials in Even Dimensions, to appear in the Indiana University Mathematics Journal
with T. Christiansen: Resonances for Schrodinger operators with compactly supported potentials, to appear in the proceeding of GDR Analyse des equations aux derivees partielles, Evian, France 2008
with Ph. Briet, G. Raikov, E. Soccorsi: Mourre estimates for a 2D quantum Hamiltonian on strip-like domains
with Peter Muller: The spectral shift function for compactly suppoerted perturbations of Schrodinger operators on large bounded domains
Lectures on random Schrodinger operators, Contemporary Mathematics, volume 476, pages 41-131, 2008.
Upcoming Workshops:
Spectral and Dynamical Properties of Quantum Hamiltonians. Centre Interfacultaire Bernoulli, EPFL, Lausanne, janvier - juin 2010.
Special session at the AMS sectional meeting in Lexington KY, 27-28 March 2010: Spectral and transport properties of Schrodinger operators, co-organized with Jeff Schenker, MSU. NEW: Abstract Deadline for the AMS changed to 26 January 2010!!
Local information about the March 2010 AMS meeting in Lexington: Hotels, sites, parking, venu, etc.
Five-day workshop at the Banff International Research Stations: Geometric scattering theory and applications, co-organized with R. Mazzeo, P. A. Perry, and A. Sa Barreto, 14-19 March 2010.
Five-day mini-workshop at the Mathematisches Forschungsinstitut Oberwolfach: Correlations and interactions for random quantum systems, co-organized with W. Kirsch, P. Mueller, and S. Warzel, 23-29 October 2011.
Course Material for Fall 2009:
MA 677 Real Analysis II:
This course is a continuation of Reals I taught in the spring of 2009. We will continue with the book of Stein and Shakarchi. You should be reading Chapter 6 on abstract measure theory. You should also be focussing on your paper and projects. Please see me to discuss them! A draft of you paper is due in class on 18 November 2009.
MA 214 Section 003 Ordinary Differential Equations:
We are finishing chapter 3 and we will begin chapter 6 on the Laplace transform method for solving initial value problems. Test #2 on Friday, 20 November. Review on Wednesday, 18 November. Test #2 will cover chapter 3 and section 6.1. You should be able to compute the Laplace transform of the solution to an initial value problem. Quiz #6 on Friday, 4 December, on sections 6.1-6.4.
This course will have a lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.
UPDATE: You may now download IODE from the main IODE web page. The program works on 2007, 2008 and 2009 versions of Matlab. The only feature that does not work is the Save feature. Save your work as described next: UPDATE on SAVING GRAPHS: If the usual save button does not work, you can save to a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the bottom on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc. Third project due date Friday, 4 December, in class. Please staple your pages together!
Open Lab Hours in CB313, Fall 2009 (Please note the change on T and R mornings!)
Instructions on how to start-up IODE using Matlab, Fall 2009
Course Material for Spring 2009:
MA 676 Real Analysis I:
The grades have been posted online and the solutions to the final are below. I will return the final exam and PS #7 to your mailboxes. Have a good summer!
MA 214 Section 003 Ordinary Differential Equations:
WEEKLY PROBLEM SESSION on Wednesdays at 4PM in CB 341. We are doing chapter 6 on Laplace transforms. Read sections 6.1-6.5. No problem session on Wednesday, 29 April. We will be reviewing all week. A final exam review is scheduled for Thursday, 7 May, at 5:30PM, room CB 333.
Course grades will be posted today, Monday, 11 May. The solutions to the final are posted below. You may stop by anytime to look at your final. Have a good summer!
Course Material for Fall 2008:
MA 214 Section 03 Ordinary Differential Equations:
NO WEEKLY PROBLEM SESSION this week, 10 December.
Final grades will be posted probably by tomorrow, Tuesday, 23 December. Have a nice holiday!
MA 575 Principles of Analysis:
WEEKLY PROBLEM SESSION: Wed. 3:30-4:30 PM CB 246
Final Exam on Friday, 19 December, 8AM-10AM in CB 347. Good Luck!
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