Nicolás García Trillos will have our first of two sessions on OT through Zoom.
The topics that I aim to discuss in these 2 sessions are:
Definition of the OT problem (Kantorovic and Monge).
Existence of transport maps (Brenier's theorem)
Multimarginal optimal transport and Wasserstein barycenter problems
Definition of Gromov-Wasserstein distance
Entropic optimal transport
Geometry of OT (Benamou-Brenier formulation).
Partial optimal transport and distances in spaces of positive Radon measures.
Optimal transport on graphs
Samir Chowdhury and Tom Needham will give a joint lecture on "The Gromov-Wasserstein distance: properties, computation and applications" via zoom. This lecture will be based on the material about the GW distance that Nicolas will describe on May 10th. The lecture should last about 1hr and will be recorded.
Nicolás García Trillos will give the second of two sessions on OT through Zoom.
The topics that I aim to discuss in this second session are:
Entropic optimal transport
Geometry of OT (Benamou-Brenier formulation).
Partial optimal transport and distances in spaces of positive Radon measures.
Optimal transport on graphs
Spearker: Marina Meila
If you would like to get an introduction in the area of Manifold Learning and Non-linear dimension reduction, on May 19-20 I will be teaching a mini-course at the Fields Institute Focus Program for Data Science, Approximation Theory and Harmonic Analysis . The link of the course is here. Anyone can register and take the course online. The other courses and talks in the program will be very interesting as well!
we will host a talk about the Persistent Laplacian (definition, main properties, some open questions) along the lines of this paper https://arxiv.org/abs/2012.02808. The talk will be given by one of the authors, Zhengchao Wan (who is now a postdoc at UCSD).
Facundo Memoli will give a talk about "The math behind classical Multidimensional Scaling".
My presentation will be loosely based on one of the sections of this paper: https://arxiv.org/abs/2201.09385.
Luis Scoccola will give an introduction to some of the best known dimensionality reduction algorithms.
(My plan is to talk for about 45 min. If you can come, please ask all the questions you may have, as I want this to be as interactive as possible. The tutorial will be recorded, but I recommend attending, if possible.
If you want something to start reading, I recommend: "Dimensionality Reduction: A Comparative Review".)
Jose Perea will give a talk on persistent cohomology.
(I hope you can come and ask questions, as these topics will be central to the TDA projects. The recordings will be made available afterwards.)
Talk 1 – Persistent Cohomology:
Persistent vector spaces and their barcodes/diagrams
Topology of the space of persistence diagrams
Cohomology and persistence
Examples
Jose Perea will give a talk on circular coordinates.
(I hope you can come and ask questions, as these topics will be central to the TDA projects. The recordings will be made available afterwards.)
Talk 2 – Circular coordinates:
From circle-valued maps to cohomology classes and back
Computational details
Examples
Soledad Villar gives a talk on equivariant machine learning.
Soledad Villar will give another talk on equivariant machine learning.
Nicolás García Trillos will give the second of two sessions on OT through Zoom.
The topics that I aim to discuss in this second session are:
Entropic optimal transport
Geometry of OT (Benamou-Brenier formulation).
Partial optimal transport and distances in spaces of positive Radon measures.
Optimal transport on graphs
TBA