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A dynamical approach to generalized Weil’s Riemann hypothesis

ALGEBRAIC DYNAMICS

October 14, 2021      4:00 pm
Speaker: Fei Hu - University of Oslo and Harvard University

Inspired by a result of Esnault and Srinivas on automorphisms of surfaces and recent advances in complex dynamics, Truong raised a question on the comparison of two dynamical degrees, which...
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Quantitative Logarithmic Equidistribution and S-Integrality

ALGEBRAIC DYNAMICS

September 23, 2021      4:00 pm
Speaker: Jit Wu Yap - Harvard University

Given a rational map defined over a number field, the Galois orbits of points with canonical height tending to zero will equidistribute to a measure supported on the Julia set....
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On the dynamical Bogomolov conjecture

ALGEBRAIC DYNAMICS

September 9, 2021      4:00 pm
Speaker: Myrto Mavraki - Harvard University

Motivated by the Manin-Mumford and the Bogomolov conjecture for abelian varieties, Zhang conjectured that an analogous statement holds in a more general dynamical setting. In this talk we discuss various...
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The pentagram map and the arithmetic of abelian varieties

ALGEBRAIC DYNAMICS

August 26, 2021      3:00 pm
Speaker: Max Weinreich - Brown University

The pentagram map was introduced by Schwartz as a dynamical system on polygons in the real projective plane. The map sends a polygon to the shape formed by intersecting certain...
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Canonical heights and vector heights in families

ALGEBRAIC DYNAMICS

April 9, 2021      10:00 am
Speaker: Alex Carney - University of Rochester

Canonical heights are a standard tool of arithmetic dynamics over global fields. When studying families of dynamical systems, or systems over larger fields, however, there are significant geometric obstacles to...
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Irreducibility of periodic curves of cubic polynomials

ALGEBRAIC DYNAMICS

March 5, 2021      10:00 am
Speaker: Jan Kiwi - Pontificia Universidad Catolica de Chile

In the moduli space of one variable complex cubic polynomials with a marked critical point, given any $p \ge 1$, we prove that the loci formed by polynomials with the...
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Some applications of Vojta’s conjecture to arithmetic dynamics

ALGEBRAIC DYNAMICS

February 5, 2021      10:00 am
Speaker: Yohsuke Matsuzawa - Brown University

I will discuss applications of Vojta's conjecture to some problems in arithmetic dynamics, concerning the growth of sizes of coordinates of orbits, greatest common divisors among coordinates, and prime factors of...
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