# A transcendental birational dynamical degree

ALGEBRAIC DYNAMICS

##### Speaker:

Holly Krieger *- University of Cambridge and Radcliffe Institute*

I will speak about recent joint work with Bell, Diller, and Jonsson in which we refute a conjecture of Bellon-Viallet by constructing (mostly) explicit examples of birational maps of projective 3-space with transcendental dynamical degree, also known as algebraic entropy. The set of possible dynamical degrees for birational maps of projective space is known to be a countable set, with nearly all examples given by eigenvalues of integer matrices (and thus algebraic), yet we demonstrate the existence of infinitely many transcendental values in this set. The proof builds on previous work of Bell-Diller-Jonsson, combining the study of monomial maps of toric varieties with classical techniques from Diophantine approximation.

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