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Upcoming Summer Graduate Schools

  1. Harmonic Analysis and Elliptic Equations on real Euclidean Spaces and on Rough Sets

    Organizers: LEAD Steven Hofmann (University of Missouri), Jose Maria Martell (Instituto de Ciencias Matematicas)

    The goal of the workshop is to present harmonic analysis techniques in $R^n$ (the ``flat" setting), and then to show how those techniques extend to much rougher settings, with application to the theory of elliptic equations. Thus, the subject matter of the workshop will introduce the students to an active, current research area:  the interface between harmonic analysis, elliptic PDE, and geometric measure theory.

    Updated on Jul 31, 2015 09:00 PM PDT
  2. An Introduction to Character Theory and the McKay Conjecture

    Organizers: Robert Guralnick (University of Southern California), Pham Tiep (University of Arizona)

    Character Theory of Finite Groups provides one of the most powerful tools to study groups. In this course we will give a gentle introduction to basic results in the Character Theory, as well as some of the main conjectures in Group Representation Theory, with particular emphasis on the McKay Conjecture.

    Updated on Jan 13, 2015 12:51 PM PST
  3. Electronic Structure Theory

    Organizers: LEAD Lin Lin (University of California, Berkeley), Jianfeng Lu (Duke University), James Sethian (University of California, Berkeley)

    Ab initio or first principle electronic structure theories, particularly represented by Kohn-Sham density functional theory (KS-DFT), have been developed into workhorse tools with a wide range of scientific applications in chemistry, physics, materials science, biology etc. What is needed are new techniques that greatly extend the applicability and versatility of these approaches. At the core, many of the challenges that need to be addressed are essentially mathematical. The purpose of the workshop is to provide graduate students a self-contained introduction to electronic structure theory, with particular emphasis on frontier topics in aspects of applied analysis and numerical methods. 

    Updated on Jul 15, 2015 03:30 PM PDT
  4. Chip Firing and Tropical Curves

    Organizers: LEAD Matthew Baker (Georgia Institute of Technology), Melody Chan (Harvard University), Sam Payne (Yale University)

    Tropical geometry uses a combination of techniques from algebraic geometry, combinatorics, and convex polyhedral geometry to study degenerations of algebraic varieties; the simplest tropical objects are tropical curves, which one can think of as "shadows" of algebraic curves.  Linear equivalence of divisors on an abstract tropical curve is determined by a simple but rich combinatorial process called "chip firing", which was discovered independently in the discrete setting by physicists and graph theorists.  From a pedagogical point of view, one can view tropical curves as a combinatorial model for the highly analogous but more abstract theory of algebraic curves, but there is in fact much more to the story than this: one can use tropical curves and chip firing to prove theorems in algebraic geometry and number theory.  This field is relatively new, so participants will have the opportunity to start from scratch and still get a glimpse of the cutting edge in this active research area.

    Updated on Jan 13, 2015 12:40 PM PST