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Geometry-Topology Seminar

Thursday, April 22, 2021 - 4:30pm

Antoine Song

UC Berkeley


University of Pennsylvania

via Zoom

The Zoom link is: This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (, Davi Maximo ( or Herman Gluck (

One way to measure the complexity of a smooth manifold is to consider its minimal volume, denoted by MinVol, introduced by Gromov, which is simply defined as the infimum of the volume among metrics with sectional curvature between -1 and 1. I will introduce a close variant of MinVol, called the essential minimal volume, which has most of the ``good'' properties of MinVol and has also some additional advantages: it is always achieved by Riemannian metrics, which in some sense generalize hyperbolic metrics, moreover it can be estimated for Einstein 4-manifolds and most complex surfaces in terms of topology.