Lectures

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.

--- Lecture 3 on Thursday, May 19 at 6 pm US ET

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

Background 2: Manifold Learning and Spectral Clustering

--- Mini-courses at the Fields Institute (May 19 - 20)

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!

Background 3: Persistent Laplacian

--- Lecture 1 on Wednesday May 11th at 2PM US ET

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).

Background 4: Persistent Cohomology and Dimensionality Reduction

--- Lecture 1 on Tuesday, May 10th at 12:30 PM ET

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.

--- Lecture 2 on Thursday, May 12th at 4:00 PM ET

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".)

--- Lecture 3 on Saturday, May 14th at 12pm ET

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

--- Lecture 4 on Sunday, May 15th at 12 ET

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

--- Lecture 5 (Recording: https://ins.sjtu.edu.cn/seminars/2052)

Soledad Villar gives a talk on equivariant machine learning.

--- Lecture 6 on Monday, May 16, 11:20 am ET

Soledad Villar will give another talk on equivariant machine learning.

Background 5: Adversarial Learning

--- Lecture 1: On Thursday, May 19 at 6 pm US ET

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

Background 6 Gerrymandering

TBA