The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Improving cold chain technologies through the use of phase change material

Gemstone Team FRESH

Fabrication of Poly (D,L-Lactic-Co-Glycolic Acid) Microparticles for Improved Human Papillomavirus Vaccine Delivery

Human papillomavirus (HPV) is the leading cause of cervical cancer and the most prevalent sexually transmitted disease worldwide. HPV vaccines require a multi-dose regimen to provide immunity, contributing to low patient compliance. We addressed this problem by formulating biodegradable poly(D,L-lactic-co-glycolic acid) (PLGA) microparticles and assessing their viability for use in controlled-release vaccines. We hypothesized that we could alter fabrication parameters to produce 1-10 μm microparticles in order to encapsulate ovalbumin (OVA) and HPV virus-like particles (VLPs). Microparticles were fabricated using a double emulsion method and used to elicit an immune response in JAWSII cells. Our results contribute to knowledge of vaccine delivery mechanisms and controlled-release technology, and could contribute to the creation of a viable controlled-release HPV vaccine.