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.
Uniform estimates for small volume asymptotics.
RESUMEN: We revisit the problem of studying the impact of a perturbation of the coefficients of an elliptic PDE on a set of small size. We show that the asymptotic structure of the perturbed solution can be described in terms of the spectrum of the Poincaré variational operators defined by the perturbations. This approach turns out to be useful in obtaining estimates which are uniform in the coefficient contrast.
Canonical colourings in random graphs.
Abstract: The canonical Ramsey theorem of Erdős and Rado impliesthat for a given graph H, if n is sufficiently large then any colouring of the edges of K_n gives rise to copies of H that exhibit certain colour patterns, namely monochromatic, rainbow or lexicographic. I will discuss recent results on the threshold at which the random graph G(n,p) inherits the canonical Ramsey properties of K_n.
Intrinsic ergodicity for a certain class of Derived from Anosov.
RESUMEN: We will talk briefly about some classic examples of Derived from Anosov (DA), that is, homotopic maps to an Anosov diffeomorphism, whose dynamics are partially hyperbolic. We will address some known results related to entropy invariance and the existence (and uniqueness) of measures of maximal entropy for this class of diffeomorphisms. Finally, we will present recent results in collaboration with L. Parra (PUCV) and C. Vásquez (PUCV) for a certain class of DA generated after a Hopf bifurcation, previously introduced by [M....
On the Asymptotic Stability of Solitary Wave Solutions to the Boussinesq Model in the Energy Space.
Abstract: The Good Boussinesq (GB) model is known to admit solitary wave solutions with speeds in the range −1<c<1. In this talk, we revisit existing results and present new findings on the asymptotic stability of solitary wave solutions to the GB equation with power-type nonlinearity and general initial data in the energy space H1xL2. These new result complete the orbital stability stability result established by Bona and Sachs (1988). The proof employs a novel set of virial estimates specifically tailored to the GB system in a moving...
Colour-bias perfect matchings in hypergraphs.
Abstract: We study conditions under which an r-edge-coloured k-uniform hypergraph has a perfect matching that contains substantially more than n/(kr) monochromatic edges. Our main result solves this problem for perfect matchings under minimum degree conditions, which answers recent questions of Gishboliner, Glock and Sgueglia. This is joint work with Hiêp Hàn, Richard Lang, João Pedro Marciano, Matías Pavez-Signé, Andrew Treglown, and Camila Zárate-Guerén.
A strongly polynomial algorithm for the minimum-cost generalized flow problem.
Abstract: We give a strongly polynomial algorithm for minimum cost generalized flow, and hence for optimizing any linear program with at most two non-zero entries per row, or at most two non-zero entries per column. Our result can be viewed as progress towards understanding whether all linear programs can be solved in strongly polynomial time, also referred to as Smale’s 9th problem. Our approach is based on the recent primal-dual interior point method (IPM) due to Allamigeon, Dadush, Loho, Natura and Végh (FOCS ’22). They show...
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...
Optimization 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...
Mean 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...
Differential-difference equations arising in number theory.
Abstract: In an attempt to find a more intuitive proof of the Prime Number Theorem, Lord Cherwell derived, through heuristic arguments, the equation: f'(x) = -(f(x) f(\sqrt{x})/(2x), where f(x) represents the “density of primes at x”. Through a simple change of variables, the differential equation can be rewritten as the following delay differential equation:h'(u) = -(ln 2)(h(u) + 1)h(u – 1) which marks the first appearance of this type of equation in number theory. In this talk, we present other families of differential...
