Seminars

Transición Secundaria-Universidad en Cálculo en la Formación Inicial Docente en Matemáticas: Reformando la Formación

Event Date: Oct 08, 2024 in Education, Seminars

Hopf’s lemmas and boundary point results for the fractional p-Laplacian.

Event Date: Sep 30, 2024 in Differential Equations, Seminars

Abstract: In this talk, we will discuss  different versions of the classical Hopf’s boundary lemma in the setting of the fractional $p-$Laplacian, for $p \geq 2$. We will start with a  Hopf’s lemma   based on comparison principles and for  constant-sign potentials. Afterwards, we will present a Hopf’s result for sign-changing potentials describing the behavior of the fractional normal derivative of solutions around boundary points. As we wiil see, the main contribution here is that we do not need to impose a global condition on the sign of the solution. Applications of the...

Cellular automata and percolation in groups.

Event Date: Sep 30, 2024 in Dynamical Systems, Seminars

RESUMEN: A famous theorem by Gilman shows that every cellular automaton over AZ satisfies an important dynamical dichotomy with respect to any Bernoulli measure: either almost every configuration is sensitive to initial conditions, or the system is equicontinuous. We show that there exists a fundamental relationship between the existence of a non-trivial percolation threshold on the Cayley graphs of a given group G and the failure of this dichotomy. We use this to give a characterization of the countable groups where Gilman’s dichotomy is satisfied, which correspond to the class of...

Separating the edges of a graph by a linear number of paths

Event Date: Sep 27, 2024 in Seminario de Grafos, Seminars

Abstract: A collection $\mathcal{P}$ of paths in a graph $G$ is called a \textit{strongly-separating path system} if, for any two edges $e$ and $f$ in $G$, there exist paths $P_e,P_f\in \mathcal{P}$ such that $e$ belongs to $P_e$ but not to $P_f$, and $f$ belongs to $P_f$ but not to $P_e$. If $\mathcal{P}$ contains a path that includes one edge but not the other, it is called a \textit{weakly-separating path system}. In 2014, Falgas-Ravry, Kittipassorn, Korándi, Letzter, and Narayanan conjectured that every graph on $n$ vertices admits a weakly-separating path system of size $O(n)$....

Asymptotic behavior of Fermat distances in the presence of noise.

Event Date: Sep 25, 2024 in Seminario de Probabilidades de Chile, Seminars

Resumen:  Fermat distances are metrics designed for datasets supported on a manifold. These distances are given by geodesics in the weighted graph determined by the points in which long jumps are penalized. When the points are given by a Poisson Point Process in Euclidean spaces, this model coincides with Euclidean First Passage Percolation (Howard-Newman 1997). In both contexts it is natural to consider perturbations of the model. We consider such perturbations and prove that if the noise converges to zero, then the noisy microscopic Fermat distance converges to the non-noisy macroscopic...

Constructions of circuits for the majority function.

Event Date: Sep 25, 2024 in ACGO, Seminars

Abstract:  We will consider a task of computing the majority function by Boolean circuits. This function has logarithmic-depth circuits. Moreover, this remains true when circuits consist of just binary AND and OR, no negations. However, in this regime, no simultaneously explicit and “simple” construction is known (with “simple” being an informal property, referencing a subjective expositional complexity of a construction). In the talk, I will present a small piece of progress towards getting such a construction, and I will probably explain some classical constructions...