Welcome to my web page! My name is Jake Kettinger and I am an algebraic geometer and postdoc at Colorado State University at Fort Collins working with Chris Peterson. I earned my Ph.D. in math from the University of Nebraska - Lincoln in May 2023 under the supervision of Brian Harbourne. My research interests include the geproci property, (quasi-)elliptic fibrations, unexpected hypersurfaces, and the containment problem. You can read more about my research here.
My dissertation is titled On the Superabundance of Singular Varieties in Positive Characteristic. It is also related to my paper The geproci property in positive characteristic, published in the Proceedings of the AMS journal. There is also a link to an arXiv version here.
My latest paper The dynamics of the Hesse derivative on the j-invariant is also now up on arXiv! It is also referenced on the page for sequence A027376 in the OEIS!
My wife Laila Kettinger also has a Ph.D. in math from UNL. She offers private math tutoring! We are also organizing a math in Spanish seminar called Seminario de las matemáticas en español!
Here is the CARS Website, which I managed Fall 2021-Spring 2022.
Here are the classes I've
taken.
I also LOVE making gadgets in Desmos and Geogebra. Here, look! You can also see my GALLERY of gadgets here!
Above is a demonstration of the unique (up to isomorphism) unexpected quartic in characteristic 0. Points 1, 2, 3, 4, and 10 are click-and-draggable, and point 10 will always be a triple point no matter where you drag it! (Although it may not always appear that way because non-real slopes don't render in Desmos.) You can read about its construction and uniqueness in the 2019 paper by Farnik, Galuppi, Sodomaco, and Trok.
(Try refreshing if it doesn't work.)