inspired by the rise on the interest for nonlocal models, mainly peridynamics, we decided to study a functional framework suitable for (variational) nonlocal models, such as that of nonlocal hyperelasticity. this has lead to a nonlocal framework based on truncated fractional gradients (i.e. nonlocal gradients with a fractional singularity defined over bounded domains), in which continuous and compact embeddings and, in particular, nonlocal poincaré inqualities has been obtained thanks to a nonlocal version of the fundamental theorem of calculus. as a consequence, the existence of minimizers of nonlocal polyconvex vectorial functionals is obtained, and more recently quasiconvex functionals. some of these last results have been obtained from a result that relates nonlocal gradients with classical ones and vice-versa. these results are accompanied by a study of the localization (recovering of the classical model) when s goes to 1 (actually, continuity on s with s being the fractional index of differentiability).

we will discuss quantum no-signaling correlations introduced by duan and winter with focus on its different subclasses (quantum commuting, quantum and local). they will appear as strategies of quantum-to-quantum non-local games. we will then discuss concurrent quantum non-local games, as quantum versions of synchronous/bisynchronous non-local games focusing on quantum graph homomorphism/isomorphism games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes; e.g. the perfect strategies for quantum graph isomorphism game are given by tracial states on the universal c∗-algebra of the projective free unitary quantum group. this is a joint work with michael brannan, sam harris and ivan todorov.

the animation of delicate vortical structures of gas and liquids has been of great interest in computer graphics. however, common velocity-based fluid solvers can damp the vortical flow, while vorticity-based fluid solvers suffer from performance drawbacks. we propose a new velocity-based fluid solver derived from a reformulated euler equation using covectors. our method generates rich vortex dynamics by an advection process that respects the kelvin circulation theorem. the numerical algorithm requires only a small local adjustment to existing advection-projection methods and can easily leverage recent advances therein. the resulting solver emulates a vortex method without the expensive conversion between vortical variables and velocities. we demonstrate that our method preserves vorticity in both vortex filament dynamics and turbulent flows significantly better than previous methods, while also improving preservation of energy.

among all nd euclidean shapes carrying a degree of shade function, only those black and white ones, defined by a single polynomial inequality are determined by finitely many moments. in the single variable situation, a landmark moment transform discovered by a. markov untangles the above uniqueness feature. the 2d case is not less interesting, touching some spectral inverse problem for pairs of non-commuting self-adjoint transforms. a super-resolution phenomenon will be described in some detail with optimization and asymptotic expansion techniques.

i will begin by defining the notion of the differential power of an ideal. focusing on polynomial rings in two or three variables over a field of characteristic zero, i will discuss when the differential power of an ideal becomes principal. i will use differential powers to define the differential closure of an ideal and discuss how it relates to the radical of an ideal.

 the possible asymptotic distributions of a random dynamical system are described by stationary measures, and in this talk, we will be interested in the properties of these measures — in particular, whether they are absolutely continuous. first, i will quickly describe the case of bernoulli convolutions, which can be seen as generalizations of the cantor middle third set, and then the case of random iterations of matrices in $\mathrm{sl}(2, \mathbb{r})$ acting on the real projective line, where the stationary measure is unique under certain conditions and is called the furstenberg measure. it had been conjectured that the furstenberg measure is always singular when the random walk has finite support. there have been several counter-examples, and the aim of the talk will be to describe that of bourgain, where the measure even has a very regular density. i will explain why the construction works for any simple lie group, using the work of boutonnet, ioana, and salehi golsefidy on local spectral gaps in simple lie groups.

 translators are known as candidates of type ii blow-up model for mean curvature flows. various examples of mean curvature flow translators have been constructed in the convex case and semi-graphical case, most of which have either infinite entropy or higher multiplicity asymptotics near infinity. in this talk, we shall present the construction of a new family of translators with prescribed end. this is based on the joint work with ao sun.

the central limit theorem (clt) plays an indispensable role in classical statistical inference for finite-dimensional parameters, including calibration of confidence sets and statistical tests. however, the validity of the clt in high dimensional problems where the dimension (p) of the observations diverges to infinity with the sample size (n) is no longer guaranteed. there is extensive recent work on the problem, following the seminal paper by chernozhukov, chetverikov, and kato (2013; annals of statistics), that attempts to establish the clt (or gaussian approximation) in high dimensions under various growth conditions on the dimension p. in this talk, we present some new results on gaussian approximation for different classes of sets, providing insights into specific distributional characteristics of the underlying high dimensional random vectors that determine the optimal growth rates.

the growth of an e. coli colony on hard agar exhibits robust expansion kinetics and morphology despite the complex interactions between millions of cells experiencing compact confinement under a spatiotemporally varying nutrient gradient. to probe the mechanistic origins of such robust colony characteristics, an agent-based model along with a set of reaction-diffusion equations to model the spatiotemporal dynamics of extracellular metabolites is employed. for colonies grown on glucose minimal medium plates, we find glucose depletion driven by anaerobiosis to be the primary factor contributing to the experimentally observed saturation in vertical expansion, while the excreted fermentation products play a crucial role for cell maintenance at the aerated colony surface. we also establish that the well-known linear expansion of the colony radius is not limited by nutrients. overall, our study emphasizes that in addition to mechanical interactions, the spatiotemporally varying metabolite gradients and the mode of metabolism of the individual cells determine the emergent morphology and expansion kinetics of the macroscopic colony.

i will talk about my recent joint work with aubert where we prove the local langlands conjecture for g_2 (explicitly). this  uses our earlier results on hecke algebras attached to bernstein components of reductive p-adic groups, as well as an expected property on cuspidal support, along with a list of characterizing properties. in particular, we obtain "mixed" l-packets containing f-singular supercuspidals and non-supercuspidals.

[pre-talk at 1:20pm]

i will talk about manolescu's work on the triangulation conjecture. using equivariant homology theory, it is proved that there exist non-triangulable manifolds in high dimensions. i will introduce the equivariant stable homotopy theory and some of its applications.