Noticias en español
Domain Branching in Micromagnetism.
Abstract: Nonconvex variational problems regularized by higher order terms have been used to describe many physical systems, including, for example, martensitic phase transformation, micromagnetics, and the Ginzburg–Landau model of nucleation. These problems exhibit microstructure formation, as the coefficient of the higher order term tends to zero. They can be naturally embedded in a whole family of problems of the form: minimize E(u)= S(u)+N(u) over an admissible class of functions u taking only two values, say -1 and 1, with a nonlocal interaction N favoring small-scale phase...
Read MoreOptimization of accessibility and application to supports in additive manufacturing.
RESUMEN: In this talk I will discuss a geometric constraint, called accessibility constraint, for shape and topology optimization of structures built by additive manufacturing. The motivation comes from the use of sacrificial supports to maintain a structure, submitted to intense thermal residual stresses during its building process. Once the building stage is finished, the supports are of no more use and should be removed. However, such a removal can be very difficult or even impossible if the supports are hidden deep inside the complex geometry of the structure. A rule of thumb for...
Read MoreErd\H{o}s-Ko-Rado Problems for Graphs.
Abstract: In this talk, we introduce a new line of research exploring the size and structure of the largest intersecting family of paths in a graph. A family of sets is called intersecting if every pair of its members share an element; such an intersecting family is called a star if some element is in every member of the family. Erd\H{o}s-Ko-Rado famously proved (1938, 1962) that the maximum size intersecting families of r-subsets of {1,2,…,n} (with r<=n/2) are precisely the stars. Here, we consider families of sets where the sets are the vertex sets of paths in a fixed graph. We...
Read MoreMean field games with heterogeneity.
Abstract: Mean field games (MFGs) are an extension of interacting particle systems, where the particles are interpreted as rational agents, offering applications in economics, social sciences, or computer science. They can be seen as the limits of large-population stochastic differential games with symmetric agents. In this work, we propose a method to incorporate heterogeneity into MFGs, thus relaxing the symmetry assumptions. We will present the concept of heterogeneous Markovian equilibria and provide a proof of their existence under standard conditions. Our definition of Nash Mean Field...
Read MoreRecent Progress on the Fractional Yamabe Problem.
Abstract: Let $(M^n, [\hat{g}])$ be the conformal infinity of an asymptotically hyperbolic Einstein (AHE) manifold $(X^{n+1},g^+).$ We will take the scattering operator associated to the AHE filling in as the fractional conformal Laplacian. Equipped with fractional conformal Laplacians defined via the AHE manifold, we can define a fractional Yamabe problem, looking for a conformal metric of $(M^n,[\hat{g}])$ which has constant fractional scalar curvature. We will present some new developments on the fractional Yamabe problem assuming an AHE filling in.
Read MoreRainbow path separation systems (RPSS)
Abstract: A family of paths P in a graph G is (k,t)-rainbow separating if it can be coloured with k colours such that for every t-tuple of edges e_1, …, e_t there exist t paths P_1, …, P_t of distinct colours such that P_i contains the edge e_i and does not contain any other edge of the t-tuple. Much work has been done on (∞,2)-RPSS, also known as strong path separation systems. In this talk I will present some optimal results on (2,2)-RPSS, together with a more general treatise on (k,2)-RPSS for all values of k.
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