Anderson localization and local eigenvalue statistics.
Svetlana Jitomirskaya, University of California, Irvine.
Homological mirror symmetry predicts an equivalence of categories, between the Fukaya category of one space and the derived category of another. We can "decategorify" by taking the Grothendieck group of these categories, to get an isomorphism of abelian groups. The first of these abelian groups is related, by work of Biran-Cornea, to the Lagrangian cobordism group; the second is related, via the Chern character, to the Chow group. I will define the Lagrangian cobordism and Chow groups (which is much easier than defining the categories). Then I will describe joint work with Ivan Smith in which we try to compare them directly, and find some interesting analogies.
An invitation to Kähler-Einstein metrics and random point processes.
Robert Berman, Chalmers University of Technology.
Relative mapping class group representations via conformal nets.
André Henriques, University of Oxford.
Deformed Airy kernel determinants: from KPZ tails to initial data for KdV.
Tom Claeys, Université Catholique de Louvain.
Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in models of positive-temperature free fermions. I will explain how logarithmic derivatives of the Fredholm determinants can be expressed in terms of a $2\times 2$ Riemann-Hilbert problem.
This Riemann-Hilbert representation can be used to derive precise lower tail asymptotics for the solution of the KPZ equation with narrow wedge initial data, refining recent results by Corwin and Ghosal, and it reveals a remarkable connection with a family of unbounded solutions to the Korteweg-de Vries (KdV) equation and with an integro-differential version of the Painlevé II equation.
From high dimensional space to a random low dimensional space.
Conceição Amado, Instituto Superior Técnico and CEMAT.
A solution of the Riemann-Hilbert problem on the $A_2$ quiver.
Davide Masoero, Group of Mathematical Physics, University of Lisbon.
Inverse problems in imaging range from tomographic reconstruction (CT, MRI, etc) to image deconvolution, segmentation, and classification, just to name a few. In this talk I will discuss
approaches to inverse imaging problems which have both a mathematical modelling (knowledge driven) and a machine learning (data-driven) component. Mathematical modelling is crucial in the presence of ill-posedness, making use of information about the imaging data, for narrowing down the search space. Such an approach results in highly generalizable reconstruction and analysis methods which come with desirable solutions guarantees. Machine learning on the other hand is a powerful tool for customising methods to individual data sets. Highly parametrised models such as deep neural networks in particular, are powerful tools for accurately modelling prior information about solutions. The combination of these two paradigms, getting the best from both of these worlds, is the topic of this talk, furnished with examples for image classification under minimal supervision and for
tomographic image reconstruction.
Stability of the symplectomorphism group of rational surfaces.
Silvia Anjos, Instituto Superior Técnico and CAMGSD.
Dealing with Systematic Uncertainties in HEP Analysis with Machine Learning Methods.
Tommaso Dorigo, Italian Institute for Nuclear Physics.