All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
All inquiries about our graduate program are warmly welcomed and answered daily:
grad@math.lsu.edu
The computer representation of curves and surfaces in Mathematica (STL "Standard Tesselation Language" files) will be covered as well as options for scanning and printing of surfaces.
The list of topics that will be covered include the following: quiver mutation, Laurent phenomenon, finite type classification and other examples, dependence on coefficients, additive categorifications, quivers with potentials, cluster algebras in Teichmüller theory and Poisson geometry, Zamolodchikov periodicity, and dilogarithm identities.
The RHP in its modern formulation is a boundary-value problem of the theory of analytic, automorphic, algebraic, and generalized analytic functions. First this course will give an introduction to the classical RHP of the theory of analytic functions. Then more advanced topics will be considered. They include the RHP of symmetric and automorphic functions (the cases of finite and infinite discontinuous groups) and the RHP on an algebraic Riemann surface. The elements of the theory of abelian integrals and differentials, analogues of the Cauchy integral, the Riemann theta function and the Jacobi problem will also be discussed. The course will give applications of the RHP to the theory of conformal mappings, fracture mechanics, materials science (the problem on multiple neutral inclusions), and diffraction theory.
More specific topics include:
In this course, we will discuss several examples of geometric methods in representation theory. In particular, we will study flag varieties and the nilpotent cone and how they can be used to study representations (of Weyl groups, simple algebraic groups, Hecke algebras, etc) from a geometric perspective. Time permitting, we will also examine affine flag manifolds and the Bruhat-Tits building of a simple algebraic group.
The focus of this course will be on homology and cohomology. To a topological space, we will associate sequences of abelian groups, the homology and cohomology groups. Topics (from chapters 2 and 3 of Hatcher's book) include simplicial, singular, and cellular homology, Mayer-Vietoris sequences, and universal coefficient theorems. Geometric examples, including surfaces and projective spaces, will be used to illustrate the techniques. Discussion of cohomology theory, including products and duality, will (presumably) continue in MATH 7520 Algebraic Topology.