Seminars

A limit law for the most favorite point of a simple random walk on a regular tree.

Event Date: Dec 07, 2022 in Seminario de Probabilidades de Chile, Seminars

We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. We prove that, for the walk started from a leaf vertex and stopped upon hitting the root, as the depth of the tree tends to infinity the maximal time spent at any leaf converges, under suitable scaling and centering, to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale-like object associated with the square-root local-time process on the tree.

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Existence of solutions on the critical hyperbola for a pure Lane-Emden system with Neumann boundary conditions.

Event Date: Dec 06, 2022 in Differential Equations, Seminars

Abstract: I will present some recent results obtained in collaboration with A. Pistoia and H. Tavares for a Lane-Emden system on a bounded regular domain with Neumann boundary conditions and critical nonlinearities. We show that, under suitable conditions on the exponents in the nonlinearities, least-energy (sign-changing) solutions exist. In the proof we exploit a dual variational formulation which allows to deal with the strong indefinite character of the problem, and we establish a compactness condition which is based on a new Cherrier type inequality. We then prove such condition by...

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Competition and Recall in Selection Problems.

Event Date: Dec 07, 2022 in ACGO, Seminars

Abstract: In this talk, I will present an extension of the prophet inequality problem to a competitive setting. At every period, a new sample from a known distribution arrives, which is publicly observed. Then, two players simultaneously decide whether to pick an available value or to pass and wait until the next period (ties are broken uniformly at random). As soon as a player gets one sample, he leaves the market, and his payoff is the value of the sample. In a first variant, namely no recall case, the agents can only bid in each period for the current value. In a second variant, the full...

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Non-existence results for an eigenvalue problem involving Lipschitzian nonlinearities with non-positive primitive and applications.

Event Date: Dec 01, 2022 in Differential Equations, Seminars

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Generalized formulations for the traveling salesman problem.

Event Date: Nov 30, 2022 in ACGO, Seminars

Abstract:  The traveling salesman problem is a widely studied classical combinatorial problem for which there are several integer linear formulations. In this work, we consider the Miller-Tucker-Zemlin (MTZ) formulation. First, we argue that the choice of some parameters of this formulation is arbitrary and, therefore, there is a family of formulations of which MTZ is a particular case. We analyze this family, noting that in general the formulations involved are not comparable to each other and there is no one that dominates the rest. Then, we study the intersection of this family, which we...

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Nonlocal Aggregation-Difusion Equations: entropies, gradient flows, phase transitions and applications.

Event Date: Nov 29, 2022 in Differential Equations, Seminars

Abstract: his talk will be devoted to an overview of recent results understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics and nancial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear difusion Keller-Segel type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under...

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