Einstein’s equations are difficult to solve and if you want to compute something in holography knowing an explicit metric seems to be essential. Or is it? For some theories, observables, such as on-shell actions and free energies, are determined solely in terms of topological data, and an explicit metric is not needed. One of the key tools that has recently been used for this programme is equivariant localization, which gives a method of computing integrals on spaces with a symmetry. In this talk I will give a pedestrian introduction to equivariant localization before showing how it can be used to compute the on-shell action of 6d Romans Gauged supergravity. 
 

Petros will present recent advances of developing ML algorithms for applications in computational and experimental fluid dynamics. A particular point of this talk is that classical control and optimisation techniques can outperform machine learning algorithms. He will share lessons learned and suggest future directions.

Bio: Petros Koumoutsakos is Herbert S. Winokur, Jr. Professor of Computing in Science and Engineering at Harvard University.  He has served as the Chair of Computational Science at ETHZ Zurich (1997-2020) and has held visiting fellow positions at Caltech, the University of Tokyo, MIT and TU Berlin. Petros is elected Fellow of the American Society of Mechanical Engineers (ASME), the American Physical Society (APS), the Society of Industrial and Applied Mathematics (SIAM). He is recipient of the Advanced Investigator Award by the European Research Council and the ACM Gordon Bell prize in Supercomputing. He is elected International Member to the US National Academy of Engineering (NAE). His research interests are on the fundamentals and applications of computing and artificial intelligence to understand, predict and optimize fluid flows in engineering, nanotechnology, and medicine.

Lagrangian mean curvature flow (LMCF) is a way to deform Lagrangian submanifolds inside a Calabi-Yau manifold according to the negative gradient of the area functional. There are influential conjectures about LMCF due to Thomas-Yau and Joyce, describing the long-time behaviour of the flow, singularity formation, and how one may flow past singularities. In this talk, we will show how to flow past a conically singular Lagrangian by gluing in expanders asymptotic to the cone, generalizing an earlier result by Begley-Moore. We solve the problem by a direct P.D.E.-based approach, along the lines of recent work by Lira-Mazzeo-Pluda-Saez on the network flow. The main technical ingredient we use is the notion of manifolds with corners and a-corners, as introduced by Joyce following earlier work of Melrose.