LLT polynomials were first introduced by Lascoux, Leclerc, and Thibon using the action of an affine Hecke algebra for S$_n$, and can be viewed as a $q$-generating function for both ribbon tableaux and tuples of semistandard Young tableaux. This definition has since been expanded to arbitrary Lie type, although with no combinatorial definition. We establish a combinatorial model for LLT polynomials in particular cases for Sp$_{2n}$ and further conjecture a similar model for the orthogonal Lie types. Our definition uses a new object we call an out-in tableau as well as a correspondence between oscillating tableaux and symplectic tableaux that we use to give a proof of a Cauchy identity for Sp$_{2n}$.

The adverse effects of grapevine diseases must be mitigated through innovative and improved cultural techniques that are cost-effective and environmentally friendly. In this thesis, I aim to assess the effect of pruning practices on pathobiome and mycobiome of asymptomatic grapevine using both culture-based and amplicon-based Illumina sequencing approaches. We hypothesized that the severe pruning of Guyot-Arcure increases esca disease severity and incidence and provides a gateway for higher pathogen load and microbial diversity compared to Guyot Poussard. We recorded over a 3-year period the number of symptomatic and asymptomatic vines for the two training systems, including the number of vines with esca foliar symptoms, partially unproductive, and dead vines. We also selected 6 asymptomatic vines from each pruning method and provided culturing and sequencing data from 27 samples per vine. Results showed that fungi in the Phaeomoniellaceae, Togniniaceae, and Botryosphaeriaceae were the most frequently identified. Our data supported the hypothesis that severe pruning increased the risks of esca-pathogen infections caused by Phaeomoniella chlamydospora and Phaeoacremonium spp. and shortened vine longevity. Results also indicated that severe pruning increased microbial diversity in vines and that the pruning methods influenced mycobiome community composition. This gain in knowledge will improve the recommendations to growers for practical ways to manage GTD in a cost-effective manner. Innovative approaches that maximize crop output and quality while minimizing pesticide use are also required to attain environmental sustainability. Instead of using pesticides indiscriminately, agriculture can be supported by better pesticide management, ensuring that we can feed a growing population. With limited approaches to address the inefficiency of pesticide delivery, it is of special interest to explore how engineered nanomaterials can be used to target delivery of pesticides. In this research, an alternative targeted nano-technology delivery approach is tested using the grapevine and Botrytis cinerea pathosystem. Using surface functionalization of nanoparticles with biorecognition molecules of sucrose that can be scalable and low cost, nanoparticles were delivered to fungi in culture (in vitro) and to grapevine on leaves (in vivo). Confocal images showed delivery of naked GDCD (gadolinium doped carbon dot) and fully functionalized, sucrose coated-β-cyclodextrin gadolinium doped carbon dots (suc-β-GDCD) to plant and fungal structures. One direct application of nanotechnology is the targeted delivery of agrochemicals to distant plant biocomparments which could offer alternative management strategies to certain diseases. We discuss the strengths and weaknesses of nanoparticle application in the context of our discoveries and provide a research plan on how to move forward.