the main goal of this talk is to show that geometric information captured by certain invariant cr tensors provides sufficient information to establish the closed range property for $\bar\partial$ on a domain in $\mathbb{c}^n$. a secondary goal of the talk is to provide a general construction method for establishing when a domain (or its boundary) satisfies weak z(q).

we present a synthesis of several papers written with co-authors and related to the construction of adaptive testing procedures in non parametric statistics. we consider the examples of goodness-of-fit tests in a density model, homogeneity test for poisson processes and the two sample testing problem. the first step in such a construction is to define a test statistic $t$ which behavior under the null hypothesis and under the alternative differs. we consider test statistics based on the estimation of the $\mathbb{l}^2$ distance of the distribution of the observations under the null hypothesis and under the alternative. the testing procedures that we propose are non asymptotic : the level is guarantied for all sample size. several cases can occur : the most simple case is the case where the distribution of the test statistic $t$ under the null hypothesis is known, one can then determine the quantiles of this distribution and define the testing procedure. when the null hypothesis is composite, this distribution is generally unknown. one can then consider conditional tests, if it is possible to determine a random variable $z$ such that the distribution of $t$ conditionally on $z$ under the null is known. for the two sample testing problem in density, in regression or for poisson processes, we use kernel procedures combined with bootstrap and permutation methods. concerning the power of the testing procedures, we will see that the aggregation of several tests allows to adapt to the unknown structure of the alternative.

generalized nash equilibrium problems (gnep) have become very important as a modeling tool during the last decades. this talk summarizes some recent advances in the research on computational methods for gnep. for example, newton method, penalty method, vi-based method etc. the algorithms and their convergence properties are also included. furthermore, some results on error bound are presented.

a countable group is called schmidt if it admits an ergodic free pmp action whose full group contains a non-trivial central sequence. we discuss several permanence properties and examples of schmidt groups.

most bacteria on our planet reside in densely packed communities, yet we have little understanding of bacterial behavior in such communities. my laboratory has uncovered ion channel-mediated long-range signaling within such bacterial communities. these action potentials give rise to unexpected emergent behaviors at the community-level that are organized in space and time. we are working to understand the underlying electrophysiology of bacterial communities that allows them to cope with stress (such as antibiotic exposure) as a collective. i will discuss our recent efforts to develop new devices, techniques and theoretical frameworks to understand and control the electrophysiology and behavior of bacterial communities.

using ibukiyama's conjecture on transfers from inner forms
of gsp(4) we compute paramodular forms with prime levels up to 400.
this is joint work with jeffery hein and gonzalo tornar\'\i a.

the incompressible euler equation of fluid mechanics has been derived in 1755. it is one of the central equations of applied analysis, yet due to its nonlinearity and non-locality many fundamental properties of its solutions remain poorly understood. in particular, global regularity vs finite time blow up question for 3d euler equation remains open.

in two dimensions, it has been known since 1930s that solutions to euler equation with smooth initial data are globally regular. the best available upper bound on the growth of derivatives of solutions has been double exponential in time. i will describe a construction (based on a work joint with vladimir sverak) that shows that such fast generation of small scales can actually happen, so that the double exponential upper bound is qualitatively sharp.

this work has been motivated by numerical experiments due to hou and luo who propose a new scenario for singularity formation in solutions to 3d euler equation. the scenario is axi-symmetric, and the geometry of the scenario involves hyperbolic points of the flow located at the boundary. if time permits, i will also discuss some models that attempt to gain insight into this scenario.