Lecture 1: Introduction to TDA 1 (Harer)
In this first lecture we will introduce the basic concepts of
Topological Data Analysis including:  
1) Persistence for functions
2) Filtrations of simplicial complexes
3) Persistent homology  
4) Cech and Rips complexes
5) Persistence diagrams
6) Bottleneck and Wasserstein distance 
7) Interleaving distance 
8) Stability theorems

Lecture 2: Some TDA Methods
In the second lecture, we will cover some basic TDA approaches,
methods and algorithms.
1) Matrix reduction to compute persistence 
2) Matching to compute Bottleneck and Wasserstein distance
3) Delay Reconstruction/Sliding Windows for a Time Series 
4) Examples of Sliding window embeddings + TDA in multimedia data

Lecture 3:  TDA and Machine Learning 
In this lecture we will discuss the use of persistence diagrams as
features for Machine Learning and do some examples including:
1) Binning - Driving Behavior
2) Sort and Grab - Brain Arteries
3) Persistence Landscapes - Financial Time Series, FMRI Motor Tasks
4) CDER - Bone data

Brief Bio

John Harer is Professor of Mathematics, Computer Science
and Electrical and Computer Engineering at Duke University
and Chief Scientist and CEO at Geometric Data Analytics
(GDA). He works on the application of methods of Geometric
and Topological Data Analysis to a wide variety of problems
in the academic, commercial and government sectors.

Professor Harer is an expert in the application of methods
from geometry and topology to data of various types. He was
one of the creators/founders of Topological Data Analysis,
a new field of applied mathematics. TDA has been applied to
problems in agent tracking, robust network design, gene
regulatory network discovery, cyber security, intelligence
analytics, and many others.