Morse theory

A Youtuber's guide to discrete Morse theory [Nick Scoville]

Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Its applications are vast, including applications to topological data analysis, combinatorics, and computer science. In this lecture, we will develop the main ideas behind discrete Morse theory, i

From playlist Tutorial-a-thon 2021 Spring

Henry Adams and Enrique Alvarado: An introduction to Morse theory

We give an introduction to Morse theory. Given a space equipped with a real-valued function, one can use Morse theory to produce a compact cellular model for that space. Furthermore, the cellular model reflects important properties of the function. We describe CW cell complexes, the Morse

From playlist Tutorials

Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group

Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv

From playlist AATRN 2022

Neža Mramor (2/17/21): An application of discrete Morse theory to robot motion planning

Title: An application of discrete Morse theory to robot motion planning Abstract: We will shortly recollect the basics of discrete Morse theory and two of its variants, parametric and fiberwise discrete Morse theory. We will then describe how it can be used to construct a continuous motio

From playlist AATRN 2021

Towards Morse theory of dispersion relations - Gregory Berkolaiko

Mathematical Physics Seminar Topic: Towards Morse theory of dispersion relations Speaker: Gregory Berkolaiko Affiliation: Texas A&M University Date: April 20, 2022  The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises i

From playlist Mathematics

Morse-Bott cohomology from homological perturbation - Zhengyi Zhou

http://www.math.ias.edu/seminars/abstract?event=132696 More videos on http://video.ias.edu

From playlist Mathematics

Morse-Bott theory on singular analytic spaces and applications to the topology of… - Paul Feehan

Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds Speaker: Paul Feehan Affiliation: Rutgers University Date: November 29, 2021 We describe two extensions, called th

From playlist Mathematics

Pre-Calculus - The vocabulary of linear functions and equations

This video will introduce you to a few of the terms that are commonly used with linear functions and equations. Pay close attention to how you can tell the difference between linear and non-linear functions. For more videos please visit http://www.mysecretmathtutor.com

From playlist Pre-Calculus

Mechanics and curves | Math History | NJ Wildberger

The laws of motion as set out by Newton built upon work of Oresme, Galileo and others on dynamics, and the relations between distance, velocity and acceleration in trajectories. With Newton's laws and the calculus, a whole new arena of practical and theoretical investigations opened up to

From playlist MathHistory: A course in the History of Mathematics

Discrete Morse Theory -- math major seminar.

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.

From playlist MathMajor Seminar

The Morse Complex on Singular Spaces - Graeme Wilkin

Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: The Morse Complex on Singular Spaces Speaker: Graeme Wilkin Affiliation: University of York Date: September 17, 2022 Morse theory is a beautiful subject with a long history, which includes sign

From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday

Ulrich Bauer (4/6/22): Persistence in functional topology

I will illustrate the central role and the historical development of persistent homology beyond applied topology, connecting recent developments in persistence theory with classical results in critical point theory and the calculus of variations. Presenting recent joint work with M. Schmah

From playlist AATRN 2022

Ryan Budney, "Filtrations of smooth manifolds from maps to the plane"

The talk is part of the Workshop Topology of Data in Rome (15-16/09/2022) https://www.mat.uniroma2.it/Eventi/2022/Topoldata/topoldata.php The event was organized in partnership with the Romads Center for Data Science https://www.mat.uniroma2.it/~rds/about.php The Workshop was hosted and

From playlist Workshop: Topology of Data in Rome

Steve Zelditch - Critical Points of Random Super-potentials and Spin Glasses

In the early 2000s, one often heard that the vacuum counting problem in string theory was like a spin glass problem. My talk will review results of Douglas, Shiffman, and myself on probabilistic methods for counting vacua of certain string theories. I then review some more recent results b

From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday

The Thue-Morse Sequence (with visualizations)

In this video, we introduce the Prouhet-Thue-Morse sequence, which is a binary sequence. We discuss three methods to construct the sequence and then investigate some of the sequence's properties (including why it is the "fair sharing" sequence, the overlap-free property, its connection to

From playlist Fractals

Symplectic homology via Gromov-Witten theory - Luis Diogo

Luis Diogo Columbia University February 13, 2015 Symplectic homology is a very useful tool in symplectic topology, but it can be hard to compute explicitly. We will describe a procedure for computing symplectic homology using counts of pseudo-holomorphic spheres. These counts can sometime

From playlist Mathematics