MIT PDE/Analysis Seminar
Tue Apr 30, 2024 4:00–5:30 PM
Location
Building 2, 2-136
Description
Speaker: Dubi Kelmer (Boston College)Title: Values of generic inhomogenous quadratic forms and the strong spectral gap.Abstract: Following Margulis’s proof of the Oppenheim conjecture we know that integer values of an irrational indefinite quadratic form, Q, in n ≥ 3 variables are dense. The same is true for an inhomogenous form Qα (v) = Q(v + α) if either Q or α is irrational. In this talk I will describe effective results that hold for a fixed rational form Q and almost all α. This turns out to be related to questions regarding the spectral gap of certain representations of the orthogonal group SOQ(R) that I will also discuss. This is based on joint work with Anish Ghosh and Shucheng Yu.
- MIT PDE/Analysis SeminarSpeaker: Dubi Kelmer (Boston College)Title: Values of generic inhomogenous quadratic forms and the strong spectral gap.Abstract: Following Margulis’s proof of the Oppenheim conjecture we know that integer values of an irrational indefinite quadratic form, Q, in n ≥ 3 variables are dense. The same is true for an inhomogenous form Qα (v) = Q(v + α) if either Q or α is irrational. In this talk I will describe effective results that hold for a fixed rational form Q and almost all α. This turns out to be related to questions regarding the spectral gap of certain representations of the orthogonal group SOQ(R) that I will also discuss. This is based on joint work with Anish Ghosh and Shucheng Yu.