Georgia Institute of Technology College of Sciences

Degeneracy loci of morphisms between vector bundles have been used in a wide range of situations, including classical approaches to the Brill--Noether theory of special divisors on curves. I will describe recent developments in Schubert calculus, including K-theoretic formulas for degeneracy loci and their applications to K-classes of Brill--Noether loci. These recover the formulas of Eisenbud--Harris, Pirola, and Chan--López--Pflueger--Teixidor for Brill--Noether curves. This is joint work with Dave Anderson and Nicola Tarasca.

We will present a rigorous proof of non-existence of homotopically non-trivial invariant circles for standard map:x_{n+1}=x_n+y_{n+1}; y_{n+1}=y_n+\frac{k}{2\pi}\sin(2\pi x_n).This a work by J. Mather in 1984.

We use a stochastic dynamic programming approach to address the following question: Can a homogenous resource extraction model (one without extraction costs, without new discoveries, and without technical progress) generate non-increasing resource prices? The traditional answer to that question contends that prices should exhibit an increasing trend as the exhaustible resource is being depleted over time (The Hotelling rule). In contrast, we will show that injecting concerns for temporal resolution of uncertainty in a resource extraction problem can generate a non-increasing trend in the resource price. Indeed, the expected rate of change of the price can become negative if the premium for temporal resolution of uncertainty is negative and outweighs both the positive discount rate and the short-run risk premium. Numerical examples are provided for illustration.

TBA