## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Dynamically canonical measures for birational transformations defined over number fields

**Speaker:** Paul Reschke

**Speaker Info:** University of Michigan

**Brief Description:**

**Special Note**:

**Abstract:**

Given a birational transformation $f$ of $\mathbb{P}^2$, one can generally (and in all known examples) construct a dynamically natural measure $\mu_f$ on some blow-up of $\mathbb{P}^2$. The construction comes from various results by Bedford, Diller, Dujardin, Favre, and Guedj. However, Buff showed recently that hypotheses on $f$ which guarantee nice properties of $\mu_f$ can fail to hold. We will explore this situation by looking at a concrete example due to Favre of a family of birational transformations. We will then discuss new results reflecting current progress towards showing that nice properties of $\mu_f$ are always guaranteed when $f$ is defined over a number field. This work is ongoing and joint with Mattias Jonsson.

**Date:** Tuesday, January 20, 2015

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Laura DeMarco

**Contact email:** demarco@math.northwestern.edu

**Contact Phone:**

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