Physical Sciences and Mathematics Commons^™

A Global Version Of A Classical Result Of Joachimstha, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we prove the following global analogue of this result. Suppose that two closed convex surfaces intersect with constant angle along a curve that is not umbilic in either surface. We prove that the principal foliations of the two surfaces along the curve are either both orientable, or both nonorientable. We prove this by characterizing the constant angle …

Weighted Composition Operators On Analytic Function Spaces: Some Recent Progress, Dip Acharyya

Publications

Theory of Composition Operators is a steady point of interest for almost 100 years. While studying these operators, our general goal is to describe their operator theoretic properties in terms of the associated function symbols. In this talk, I will discuss some recent results concerning linear combinations (sums, differences, etc.) of weighted composition operators in certain spaces of Analytic functions.

Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya

Publications

“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein. Pure mathematicians study abstract entities and structures that underlie mathematics. Although their general perspective is “math for math’s sake”, sometimes even the most abstract mathematics can have unexpected applications! Come learn some of these astonishing discoveries in the history of science and mathematics! They might make you thrilled but keep in mind real-world usage is rarely the goal behind developing a new mathematical theory.

Welcome to the world of pure mathematics! In this talk, we will focus on the theory of composition operators which is a …

A Mean-Risk Mixed Integer Nonlinear Program For Transportation Network Protection, Jie Lu, Akshay Gupte, Yongxi Huang

Publications

This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic programming model that allows for greater flexibility in handling risk preferences when allocating limited resources. In particular, the first stage minimizes the retrofitting cost by making strategic retrofit decisions whereas the second stage minimizes the travel cost. The conditional value-at-risk (CVaR) is included as the risk measure …