The main focus of my research is geometric representation theory relating to the Langlands program. Ultimately, my work aims to better understand and classify representations of algebraic groups. One of the main tools in my work is the geometric Satake correspondence, which allows the use of methods from algebraic geometry and combinatorics.
J. Hopper, "Paving of fibers of convolution morphisms for non-split groups" in progress, available on request.
J. Hopper, "Twining character formula for reductive groups," J. Ramanujan Mathematical Society, 38 (2023), 237–263, arXiv:2204.03600.
J. Hopper and P. Pollack, "Digitally delicate primes," J. Number Theory 168 (2016), 247-256, arXiv:1510.03401.
J. Hopper, "Weyl algebras and D-modules," (2018). Part III Master's Essay for the University of Cambridge, available on request.
J. Hopper, "On covering systems of integers," (2017). Undergraduate Honors Thesis for the University of Georgia, arXiv:1705.04372.