Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Drawing Planar Graphs Badly.
Abstract: We study how far one can deviate from optimal behavior when drawing a planar graph on a plane. For a planar graph $G$, we say that a plane subgraph $H\subseteq G$ is a \textit{plane-saturated subgraph} if adding any edge (possibly with a new vertex) to $H$ would either violate planarity or make the resulting graph no longer a subgraph of $G$. For a planar graph $G$, we define the \textit{plane-saturation ratio}, $\psr(G)$, as the minimum value of $\frac{e(H)}{e(G)}$ for a plane-saturated subgraph $H\subseteq G$ and investigate how...
Hopf’s lemmas and boundary point results for the fractional p-Laplacian.
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...
Cellular automata and percolation in groups.
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...
Separating the edges of a graph by a linear number of paths
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...
Completely mixed linear games and irreducibility concepts for Z-transformations over self-dual cones.
Abstract: In the setting of a self-dual cone in a finite-dimensional real inner product space (in particular, over a symmetric cone in an Euclidean Jordan algebra), we consider zero-sum linear games. Motivated by dynamical systems, we concentrate on $Z$-transformations (which are generalizations of $Z$-matrices). It is known that a $Z$-transformation with positive (game) value is completely mixed (thus yielding uniqueness of optimal strategies). The present talk deals with the case of value zero. Motivated by the matrix-game result...
Constructions of circuits for the majority function.
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...
Asymptotic behavior of Fermat distances in the presence of noise.
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...
The joint transitivity property.
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Second-order dynamical systems associated with a class of quasiconvex functions.
Abstract: In this talk, we examine second-order gradient dynamical systems for smooth strongly quasiconvex functions, without assuming the usual Lipschitz continuity of the gradient. We establish that these systems exhibit exponential convergence of the trajectories towards an optimal solution. Furthermore, we extend our analysis to the broader quasiconvex setting by incorporating Hessian-driven damping into the second-order dynamics. Finally, we demonstrate that explicit discretizations of these dynamical systems result in gradient-based...
Spread measures on perfect matchings in regular pairs.
Abstract: The notion of spread distributions on copies of a given graph (or family of graphs) has played a crucial role in recent developments in probabilistic combinatorics, particularly in studying thresholds in random graphs. In this talk, I will show how to construct a spread distribution on perfect matching in regular pairs, which can be used together with the regularity lemma to find well-behaved embeddings of sparse graphs.
