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Program

Monday, February 24 2025.

Day 1 - Monday, February 24

Basque Center for Applied Mathematics - BCAM

We will introduce the classical Brascamp–Lieb inequalities, providing motivations and displaying their connections to well known operators within the field of harmonic analysis.

Tuesday, February 25 2025.

Day 2 - Tuesday, February 25

Basque Center for Applied Mathematics - BCAM

We will exhibit heat flow argument by Bennett, Christ, Carbery, and Tao. We will show how this allows us to find the optimal constant and characterize the extremizers in the inequalities. 

Wednesday, February 26 2025.

Day 3 - Wednesday, February 26

Basque Center for Applied Mathematics - BCAM

We will survey the classification result about singular Brascamp-Lieb inequalities following the work of Durcik and Thiele, and we will discuss estimates in specific cases, e.g. for the bilinear Hilbert transform and twisted paraproducts. 

Thursday, February 27 2025.

Day 4 - Thursday, February 27

Basque Center for Applied Mathematics - BCAM

We will survey the local and global results about nonlinear Brascamp-Lieb inequalities following the work of Bennet, Bez, Buschenhenke, Cowling, and Flock, and Duncan. 

Friday, February 28 2025.

Day 5 - Friday, February 28

Basque Center for Applied Mathematics - BCAM

We will discuss further topics within the theory of Brascamp-Lieb inequalities, such as the proof of forward/reverse classical/ Gaussian Brascamp-Lieb inequalities via entropy and mass transport arguments, as well as different versions of the adjoint problem. 

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