Slides from selected recent talks.
- An alternative ordering on real quadratic fields and a connection to complex equiangular lines. April 3, 2025. Asymptotic results about real quadratic fields and unit-generated real quadratic orders in the “unit ordering,” particularly results on class numbers, and related phenomenology of SICs.
- The Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios. February 28, 2025. Construction of Stark units as real multiplication values of a multiplicative quantum modular cocycle.
- SIC-POVMs from binary quadratic forms. June 4, 2024. Conjectural construction of SICs in all dimensions.
- Class field theory for nonmaximal orders (abstractly and explicitly). April 17, 2024. Generalized class groups and class fields for orders of number fields, and some known and conjectured explicit realizations.
- Gauss composition, polyharmonic Maass forms, and Hecke L-series. March 31, 2022. Gauss composition with level structure; certain rank 2 Stark regulators as twisted traces of biharmonic Maass forms.
Below are some notes from older talks and activities from graduate school or earlier. Informal papers may be found under the “Papers” tab. If you’ve seen a set of notes by me that you can’t find here, please don’t hesitate to contact me by email.
- Generating weights of modules of vector-valued modular forms for the Weil representation. Talk at the AMS Special Session on Representation Theory, Automorphic Forms and Related Topics at the AMS Fall Central Sectional Meeting, University of St. Thomas, October 2016.
- The Arithmetic Geometry of Resonant Rossby Wave Triads. Talk at the AMS Fall Central Sectional Meeting, University of St. Thomas, October 2016.
- The Timid Computer Scientist Algorithm, an introduction to secret-sharing via an algorithm for secure matchmaking.
Gene S. Kopp 