Wednesday, February 28, 2024

Spring 2024


29 March 024

Mohammad Sayeh

On Fourier and fractional Fourier transforms, and more.

Video of Part 1

Tuesday, February 20, 2024

Spring 2024

22 Feb 2024

Mathew Gluck

Introduction to Principal Component Analysis


Abstract: Principal component analysis (PCA) is a data dimensionality reduction technique whose goal is to throw away the least essential components of a data set. It is commonly used by data science practitioners whose data belongs to a vector space of large dimensions. It is well-known that the eigenpairs of a suitable covariance matrix “know” which components of data are most important and which are least important. However, in many expositions on PCA, the reason behind this well-known fact is rarely explained. I will offer an explanation and I will show a concrete application of PCA in image data.

Wednesday, October 11, 2023

Autumn 2023

Part 1:  12 Oct 2023   video
Part 2:  19 Oct 2023   video
Part 3:  26 Oct 2023   video
Part 4:    2 Nov 2023  Notes  (4 pages)
Part 5:    9 Nov 2023  videodiagram (NEW!)
Part 6:  16 Nov 2023   video
Part 7:  30 Nov 2023   video

Philip Feinsilver  

Symmetric functions: traces, determinants, the full story.

See references

Philip shares his notes here:

The links are to pdf files.  Added visualizations, namely Young diagrams. It should help clarify the definitions.  Suggestions welcome - - -

From JK:   This will be an opportunity to learn this topic in a novel and unique way.  The presentation is planned for a few meetings. Do not miss them!  You will be among the first few on the planet to get a new creative insight into the subject.  Matrices in use!

Wednesday, October 4, 2023

Autumn 2023


5 Oct (Thursday), 2pm

Duston Wetzel

Triply periodic and polyhedral helical weaves


Wednesday, September 27, 2023

Autumn 2023

P.P. Rubens: Bacchus 

28 September

K.V. Shajesh

Negative mass: A runaway solution


Sunday, September 10, 2023

Autumn 2023

A. Pasieka: Lorenz Attractor

Thursday, Sept 14, 21  (2pm, Nc 356)

Mike Sullivan

Geometric Lorenz Attractor

Video of Day 1
Video of Day 2

Here are links sent by Mike:

Plus, this is a series of well done videos on chaos theory. Number 7 covers some of the topics covered in my seminar talks.

Abstract of the talk:  The Lorenz equations, developed and studied by the meteorologist Edward Lorenz in the 1960s, were one of the first examples of a chaotic system. They are a set of three nonlinear ordinary differential equations in three variables. The trajectories move toward a bounded subset of $\mathbb R^3$ and then seem to oscillate about, but never truly repeat. Mathematicians began studying these equations using both quantitative and qualitative methods. The former proved very difficult. The latter yielded results. Guckenheimer and Williams developed a geometric model with behavior similar to the Lorenz equations. Then Birman and Williams used topological methods to analyze this Geometric Lorenz Attractor. Decades later it was proved that the two systems are equivalent.

Participants should have had basic undergraduate courses in differential equations and linear algebra. We will begin with a review of systems of ordinary differential equations. This should last about 20 minutes. Then we will cover the construction of the Geometric Lorenz Attractor. That should take about 30 minutes. Next week we will cover Birman and Williams' proofs of the knot types of periodic orbits in the Geometric Lorenz Attractor.

This material was originally covered last Fall in my MATH 405 course. For now, you may wish to amuse yourself with this video.  

Wednesday, April 26, 2023

Spring 2023

27 April (Thursday), 2pm

Duston Wetzel

Gyroid and the triply periodic helix linkages


Monday, April 3, 2023

Spring 2023

6 April (Thursday),
13 April, and 20 Apr.

Robert Owczarek   (University of New Mexico)

Proto-topological (Quantum) Field Theories of Kijowski and SÅ‚awianowski

Video of Part 1
Video of Part 2
Video of Part 3

Here are some links suggested by Robert:
1.  Seminar talk by Kijowskiego from the last year
2.  Related topic on variational principle.  

Abstract: Topological quantum field theories that are metric independent, like, e.g., Chern-Simons theory, give topological invariants of manifolds and knots. Classical field theories of Kijowski and SÅ‚awianowski are metric independent, and are defined on manifolds of a priori any dimension, and thus may give new topological invariants of manifolds.

In this talk, I will try to make a friendly introduction to these theories.   

Saturday, March 11, 2023

Spring 2023

From Treewewal
23 & 30 March (Thursdays)

John McSorley

Graphs with trees of certain types, and related topics

Video of Part 1
Video of Part 2

Wednesday, March 8, 2023

Spring 2023

9 March

Mohammad Sayeh

Neural networks and the global minimum problem

Video (there is a 20 min break in sound)

Sunday, February 19, 2023

Spring 2023

Thursday, 23 Feb

Annie Yojaira

Micropatterning with sugar
(on surfaces, curvatures, and nanoscales)

2pm, Neckers 356


Wednesday, February 1, 2023

Spring 2023

Thursday, 2 Feb -- part 1
Thursday, 9 Feb -- part 2
Thursday, 16 Feb -- part 3 

Mathew Gluck

From the isoperimetric inequality to scalar-flat Riemannian metrics

Neckers 356, 2pm

Abstract:  We shall discuss whether a given compact Riemannian manifold can be deformed in an angle-preserving way to achieve constant scalar curvature (so-called Yamabe's problem).

Part 2 -- video

Part 3 -- video