Current contacts: Jaclyn Lang, Catherine Hsu, Ian Whitehead, and Djordje Milicevic
The Philadelphia Area Number Theory Seminar rotates between Bryn Mawr, Swarthmore, and Temple. In Fall 2022, we meet on Tuesday afternoons, usually with tea at 3pm and then the talk 3:30-5pm. Please pay careful attention to the times and locations of the talks as they change from week to week! If you would like to be added to our mailing list or if you are interested in being a speaker, please contact one of the organizers. In future semesters, we anticipate that the seminar will be on Wednesday afternoons.
Click on title for abstract.
Shira Gilat, UPenn
Abstract:The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras. Supernatural matrices are a minimal solution to the equation of unital algebras M_n(X) ∼= X, which we compare to several similar conditions involving cancellation of matrices. This algebra has appeared under various names before, and it generalizes both McCrimmon's deep matrices algebra and m-petal Leavitt path algebra.
Katy Woo, Princeton
Abstract: We resolve Manin's conjecture for all Châtelet surfaces over Q (surfaces given by equations of the form x^2 + ay^2 = f(z)) -- we establish asymptotics for the number of rational points of increasing height. The key analytic ingredient is estimating sums of Fourier coefficients of modular forms along polynomial values.
Ian Whitehead, Swarthmore College