Self-Avoiding Walks and Parafermionic Observables

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A strong Onsager conjecture on the Euler equations

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T-coercivity: a practical tool for the study of variational formulations

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In this talk, I will focus on an approach that is completely equivalent to the inf-sup condition for problems set in Hilbert spaces, the **T-coercivity approach**. This approach relies on the design of an *explicit* operator to realize the inf-sup condition. If the operator is carefully chosen, it can provide useful insight for a straightforward definition of the approximation of the exact problem. As a matter of fact, the derivation of the discrete inf-sup condition often becomes elementary, at least when one considers conforming methods, that is when the discrete spaces are subspaces of the exact Hilbert spaces. In this way, both the exact and the approximate problems are considered, analysed and solved at once.

In itself, T-coercivity is not a new theory, however it seems that some of its strengths have been overlooked, and that, if used properly, it can be a simple, yet powerful tool to analyse and solve linear PDEs. In particular, it provides guidelines such as, which abstract tools and which numerical methods are the most “natural” to analyse and solve the problem at hand. In other words, it allows one to select simply appropriate tools in the mathematical, or numerical, toolboxes. This claim will be illustrated on classical linear PDEs, and for some generalizations of those models.

For further information about the seminar, please visit this webpage.

]]>Introduction to real del Pezzo surfaces

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Non-reflecting boundary conditions and domain decomposition methods for industrial flow acoustics

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[1] Marchner, P., Antoine, X., Geuzaine, C., & Bériot, H. (2022). Construction and numerical assessment of local absorbing boundary conditions for heterogeneous time-harmonic acoustic problems. SIAM Journal on Applied Mathematics, 82(2), 476-501.

[2] Lieu, A., Marchner, P., Gabard, G., Beriot, H., Antoine, X., & Geuzaine, C. (2020). A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics. Computer Methods in Applied Mechanics and Engineering, 369, 113223.

For further information about the seminar, please visit this webpage.

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