La semaine de l’IMB

 I will talk about harmonic maps with respect to non-local 

Dirichlet forms. In particular, I will focus on stochastic processes 

with jumps on manifolds associated with them.

Bilevel optimization is useful in machine learning to tackle problems such as hyperparameter tuning, metalearning or even optimal transport problems. However it presents theoretical and computational challenges, particularly in the nonconvex setting. This talk presents recent advances that may improve our understanding of the complexity, algorithmic strategies, and statistical properties of bilevel problems. We establish the hardness of smooth bilevel programs by showing their equivalence to general lower semicontinuous minimization and proving that polynomial bilevel problems are Σ_p^2-hard (harder than NP-hard). This a joint work with J. Bolte, Q. T. Le & E. Pauwels.

Radio Frequency Integrated Circuits (RFICs) have democratized communications, with ever-greater data exchanges. With each generation, we invent new technologies and systems that increase communication potential by a new order of magnitude: 2G and 3G are nearing their sunset, 4G is fading from our memory, 5G is already in everyone’s pocket, and 6G is rapidly approaching. The future will not only link devices but also bridge human and artificial intelligences. Tomorrow’s networks will rely on integrated circuits we design today, but sustaining the exponential progression demands more than engineering alone. It requires an alliance between technology and science to keep pushing the boundaries of connectivity, ensuring that innovation remains possible in this never-ending race for communication.

In this talk I will present a conjecture of Burnett, which characterizes weak limits of solutions to the Einstein vacuum equations from general relativity. After a brief review of the Cauchy problem for these equations, I will show how their seemingly messy nonlinear structure actually leads to some beautiful cancellations. I will conclude by discussing potential Riemannian versions of Burnett's conjecture, in connection with results by Gromov and Lohkamp.