In this dissertation we study the connections over principal bundles in dimension four with bounded Yang-Mills energy, and present a new result on the existence a global Coulomb gauge with estimate in optimal space. To be precise, let $A$ be a $W^{1,2}$-connection on a principal $\text{SU}(2)$-bundle $P$ over a smooth...
The cuprate superconductor HgBa$_2$CuO$_{4+\delta}$ (Hg1201) has one of the simplest physical structures of the cuprates making it an ideal candidate for nuclear magnetic resonance (NMR) measurements. Here we discuss our NMR experiments aimed at studying the mixed state of two under-doped single crystal Hg1201 samples at high magnetic fields.
The evolutionarily conserved COMPASS family of methyltransferases implements histone H3 lysine 4 (H3K4) methylation, an epigenetic mark associated with transcriptional activation. Given the high mutational prevalence of COMPASS subunits across cancers and neurodevelopmental disorders, understanding COMPASS function would lend important insights into disease pathogenesis to facilitate development of effective therapies....
Supported metal oxides are an important class of catalysts for chemical synthesis and manufacturing, particularly for selective oxidation reactions. This dissertation seeks to understand broad relationships among families of silica-supported Group 4 and 5 metal oxide catalysts for the synthesis of epoxides with hydrogen peroxide (H2O2) and to further extend...
