Volume 34 (2026), Issue 2 (Special issue: "Latin American mathematics")

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1. A two-player zero-sum probabilistic game that approximates the mean curvature flow

Irene Gonzalvez ; Alfredo Miranda ; Julio D. Rossi ; Jorge Ruiz-Cases.

In this paper we introduce a new two-player zero-sum game whose value function approximates the level set formulation for the geometric evolution by mean curvature of a hypersurface. In our approach the game is played with symmetric rules for the two players and probability theory is involved (the game is not deterministic).

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2. Some arithmetic properties of Weil polynomials of the form $t^{2g}+at^g+q^g$

Alejandro J. Giangreco-Maidana.

An isogeny class $\mathcal{A}$ of abelian varieties defined over finite fields is said to be "cyclic" if every variety in $\mathcal{A}$ has a cyclic group of rational points. In this paper we study the local cyclicity of Weil-central isogeny classes of abelian varieties, i.e. those with Weil polynomials of the form $f_\mathcal{A}(t)=t^{2g}+at^g+q^g$, as well as the local growth of the groups of rational points of the varieties in $\mathcal{A}$ after finite field extensions. We exploit the criterion: an isogeny class $\mathcal{A}$ with Weil polynomial $f$ is cyclic if and only if $f'(1)$ is coprime with $f(1)$ divided by its radical.

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