21 January 2010
Quantum K-Theory of Grassmannians and the Geometry of Spaces of Curves
Leonardo Mihalcea
Department of Mathematics
Baylor University

The 3-point, genus 0, Gromov-Witten invariants of a Grassmannian count rational curves of degree d satisfying certain incidence conditions - if the number of curves is expected to be finite. Recently, Givental and Lee defined the K-theoretic Gromov-Witten invariants, which associate an integer to spaces of rational curves in question, regardless of whether it is finite or not. The resulting quantum cohomology theory - the quantum K-theory - encodes the associativity relations satisfied by the K-theoretic Gromov-Witten invariants. I will show how the Gromov-Witten invariants and quantum K-theory algebra can be computed explicitly. The key is a "quantum=classical" phenomenon: the K-theoretic Gromov-Witten invariants for Grassmannians are equal to structure constants of the ordinary K-theory of certain two-step flag manifolds.

11 February 2010
GasDay: Forecasting Customer Demand for Natural Gas
George F. Corliss
Electrical and Computer Engineering
Marquette University
Milwaukee, Wi

Natural gas for heating takes 2 - 3 days to get to Milwaukee from Louisiana. If our local utility does not order enough, they buy it on the spot market at premium prices. If they order too much, the pipeline companies charge them penalties. The GasDay lab at Marquette University licenses to local natural gas utilities software to forecast the gas demands of their customers hours, days, and months in the future. We license to 23 utilities across the US. Each day, software written by our students helps forecast 20% of the gas used by residential, commercial, and industrial customers in the US. Our customers tell us our forecasts save their customers tens of millions of dollars each winter. We also offer analysis consulting services including peak day studies and data cleaning. We will discuss some of the mathematical modeling challenges, as well as the entrepreneurial challenges of running a $500K business with students within the university.

18 February 2010
Max-Plus Algebra and the Computation of Nonlinear Controls
Ben G. Fitzpatrick
Loyola Marymount University

Mathematical methods for linear systems have had enormous impact on engineering applications, especially in control systems. Nonlinear approaches, however, suffer from many drawbacks, not the least of which are computational difficulties. The recent successes of max-plus and more general idempotent structures for attacking nonlinear control problems offer the potential for revolutionary improvements in our ability to design and implement nonlinear controls for real applications. In this talk, we describe the basic concepts behind max-plus methods. The key observation is that Bellman's dynamic programming principle yields a linear equation in the max-plus arithmetic. We will outline the max-plus approach to nonlinear control and provide some preliminary results in the extension from deterministic to stochastic problems. We will discuss numerical approximation schemes and examples problems in counterinsurgency and UAV sensing planning.