Emerging symmetries in 2D percolation

Emerging symmetries in 2D percolation

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Hugo Duminil-Copin, IHES and University of Geneva

Online Talk

 *Please note the change in time*

Zoom link:  https://princeton.zoom.us/j/99136657600

Passcode required

(The colloquium password will be distributed to Princeton University and IAS members. We ask that you do not share this password. If you would like to be included in the colloquium and are not a member of either institution, please email the organizer Casey Kelleher (caseyk@princeton.edu) with an email requesting to participate which introduces yourself, your current affiliation and stage in your career.)

A great achievement of physics in the second half of the twentieth century has been the prediction of conformal symmetry of the scaling limit of critical statistical physics systems. Around the turn of the millennium, the mathematical understanding of this fact progressed tremendously in two dimensions with the introduction of the Schramm-Loewner Evolution and the proofs of conformal invariance of the Ising model and dimers. Nevertheless, the understanding is still restricted to very specific models. In this talk, we will gently introduce the notion of conformal invariance of lattice systems by taking the example of percolation models. We will also explain some recent proof of rotational invariance for a large class of such models. This represents a progress in the direction of proving full conformal invariance.