Penn State - Göttingen

 Summer Schools in Mathematics


Topic in 2010:
Differential Equations


July 25 – August 14, 2010


Venue: Mathematics Department, University Park, State College, PA 16802

Prerequisites: Measure and integration theory, Lebesgue integral. A course on functional analysis and/or differential equations is helpful, though not strictly necessary.

We can participate with 10 math undergraduates. Each student will be subsidized with up to EUR 1,500. With more students interested than places available priority will be given to those relating to mathematical analysis and neighboring fields.

If you wish to participate, please contact Prof. Ingo Witt,
not later than April 20, 2010
.



Organizers

Juan Gil
Thomas Krainer
Victor Nistor
(Penn State)
Ingo Witt
(Göttingen)

Location: The Mathematics Department is housed in McAllister Building next to the Heztel Student Union (HUB) on the University Park Campus in State College, Pennsylvania.
Directions:
Directions via all types of transportation are available at the University Park map page
Maps:
Central Campus Map
Hub Vicinity Map


Organizational structure of the event:


The first two weeks will be seeing an educational part that will consist of lecture classes in the mornings and supervised theoretical and computer lab work in the afternoons. Penn State and Göttingen faculty will teach a total of 3–4 lecture courses (8–10 lectures per course, 50 min per lecture). This will be followed by an international research conference on the featured topic that will take place during the third week.

Students will be working in teams, each Germany based student will work with one student who is based in the U.S. Each team will be assigned several tasks that are to be accomplished during and after the Summer School. This includes theoretical work, work in a computer lab, and a research project for each team that is to result in a project paper due in December 2010 after their participation in the Summer School.
Mathematics Department
Penn State University
University Park
State College
PA 16802, USA

Mathematisches Institut

Georg-August-Universitaet
Bunsenstr. 3-5
D-37073 Göttingen



Supported by:
  • U.S. National Science Foundation
  • Göttingen International

    • List of topics for the lecture classes:
      Sturm–Liouville operators and eigenvalue problems: limit point and limit circle dichotomy, Weyl–Titchmarsh–Spencer–Kodaira formula, and applications; differential equations on quantum graphs and applications; methods based on separation of variables/special functions; singularities, asymptotic methods; introduction to spectral and scattering theory; differential equations and computer algebra systems (Maple or Mathematica), numerical methods.
    • Topics for project work:
      Develop diverse CAS applications for (regular-singular) second order differential equations on quantum graphs (laboratory and theoretical projects) such as tools to analyze the dependence of spectral data on the coupling conditions. Develop CAS applications for Sturm-Liouville operators: Numerical inclusion of eigenvalues, experimental verification of oscillation criteria, and the computation of the Weyl-Titchmarsh m-function. Use numerical methods to solve singular PDEs.
    • Topics featured at the conference:
      Quantum graph models in mathematical physics; elliptic equations on noncompact and rough domains – well-posedness, regularity, spectral theory; parabolic equations/maximal regularity; numerical methods for elliptic and parabolic PDEs.
    Upcoming Summer Schools:
    Topic in 2011: Dynamical Systems (Göttingen)
    Topic in 2012: Number Theory (Penn State)