## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Bounds for the Least Solution of Quadratic Inequalities

**Speaker:** Thomas Hille

**Speaker Info:** Northwestern U.

**Brief Description:** Part of Midwest Dynamics Conference

**Special Note**: **Part of Midwest Dynamics Conference**

**Abstract:**

Let Q be a non-degenerate indefinite quadratic form in d variables. In the mid 80's, Margulis proved the Oppenheim conjecture, which states that if d ≥ 3 and Q is not proportional to a rational form then Q takes values arbitrarily close to zero at integral points. In this talk we will discuss the problem of obtaining bounds for the least integral solution of the Diophantine inequality |Q[x]|< epsilon for any positive epsilon if d ≥5. We will show how to obtain explicit bounds that are polynomial in \epsilon^{-1}$, with exponents depending only on the signature of Q or if applicable, the Diophantine properties of Q. This talk is based on joint work with P. Buterus, F. Götze and G. Margulis.

**Date:** Saturday, November 13, 2021

**Time:** 2:30 PM

**Where:** Swift 107

**Contact Person:** Aaron Brown

**Contact email:** awb@northwestern.edu

**Contact Phone:**

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