Abstract: 

Endperiodic surface maps is a family of proper mapping classes on infinite type surfaces that has been particularly well studied. By making use of infinite type translation surfaces, we proved that any weak Perron number (an algebraic integer no smaller than the absolute value of any of its Galois conjugates) can be the stretch factor of the Handel-Miller lamination of such a mapping class. In other words, the exponents of the minimal topological entropy of the one point compactification of a representative of such a mapping class can be any weak Perron number. This is a collaboration with Paige Hillen and Marissa Loving.