Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Stormwater Management Adaptation Pathways under Climate Change and Urbanization

Urban runoff volumes and flow peaks are likely to increase in the future owing to climate change-driven effects on rainfall and continued urbanization. Actionable planning estimates that anticipate these impacts are needed to assess stormwater management infrastructure requirements and to minimize impacts on ecosystem services. This study presents a planning-level simple flow simulation tool and quantifies benefits of green stormwater management practices in small watersheds. Flow simulation was performed using a curve number-based watershed model (CWM). A portfolio approach was used to assess cost-optimal stormwater adaptation pathways considering a suite of alternative practices including both gray and green infrastructure. The CWM provides actionable information for medium to highly urbanized watersheds with percent bias less than 30% for highly urbanized watersheds. Considering projected future stormwater needs, analysis of multiple stormwater management approaches showed that green stormwater management alternatives are less cost-optimal than gray infrastructure at small watershed scales. These results suggest the possible use of CWM for quick planning-level flow estimates and analysis of more green practices for cost-optimal alternatives

Young tableaux and crystal B(∞)B(\infty) for finite simple Lie algebras

We study the crystal base of the negative part of a quantum group. An explicit realization of the crystal is given in terms of Young tableaux for types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$. Connection between our realization and a previous realization of Cliff is also given