Mike Henderson

Whoops it's actually NY/NJ/PA.

Anyway, a nice, smallish weekend conference with a road range of topics.

A very busy image. A blue sphere and a yellow ellipsoid-ish surface. Both have polygonal tilings with white edges. They also have short red normal vectors and the tile centers marked as white balls. The points on the yellow surface are well spaced, but those on the blue sphere cluster around a create circle, which shows up as a red blur because of the normals.

My first thought was "Wow". My second was "I really messed that up". But hey.

A New Pyramid-Like Shape Always Lands the Same Side Up | Quanta Magazine A tetrahedron is the simplest Platonic solid. Mathematicians have now made one that’s stable only on one side, confirming a decades-old conjecture.

www.quantamagazine.org/a-new-pyrami...

Not sure what kind of question/field this is. But apparently theres an answer. Don't say gravitation.

I've been getting warnings for at least a year that the version of the OS I've been using is going away. Couldn't move to the supported version because my CPU is "unsupported".

Yesterday I searched and found out how to force it. You define a variable called something like DoItAnyway=1. Sheesh.

This year's NY/NJ Siam meeting is at PSU in October.

siamnnp2025.sciencesconf.org

*Recently is relative.

Obituary: Harry Coonce | SIAM Harry Bernard Coonce, founder of the Mathematics Genealogy Project, passed away on February 14, 2025, at the age of 86.

Apparently the founder of the mathematical genealogy project passed recently.
www.siam.org/publications...
I wish I'd known him -- which is a common refrain for me.

I read a lor of 1920's to 1930's mysteries, and the German professor is quite a figure.

BTW mactutor
mathshistory.st-andrews.ac.uk
Has bios and if course there's the mathematical genealogy project
www.mathgenealogy.org
Great stuff!

Richard Courant is in there too.

A conference wants me on a panel discussing applied math careers in industry. I declined. What would I say? Hell no, don't do that? Don't even think about it?

Sadly, I'm not sure any place is any better. It's why I never left.

Doing my math genealogy, and it's very heavily 1800's Germany. David Hilbert! All those guys came over here either to escape or were poached after the war.

I wonder where the next country is going to be. I don't have any students-- will always regret that -- but what would I tell them?

Academics seemed to view us not as colleagues but as a source of "real" problems or funding.

Mgmt was either non-technical (i.e. clueless) or from manufacturing, application oriented with their field the only important one. Then they started to come from Comp Sci.

Applied Math in Industry came up the other day.

Is that still a thing? I meet very few people doing it outside academia.

While I was in "industry" I was always surprised by how little Math people knew. Calculus was to be avoided at all costs, projection, or any other kind of linear algebra same.

A black beetle with white spots.

Hello? What exactly are you?

Yep. That's me right there.

Oooo. I just discovered that those silly AC adapter things for my external disk drives (that take up more than one plug spot on my outlet strip) can be replaced by "USB-PD Trigger" cable. Of the correct voltage of course.

Boy am I going to be organized.

Why don't they have batteries on desktops? Seems like there's a lot of space, and it sure would be nice to have some time to close things and shutdown when the power goes out.

Not that that ever happens to us.

A whitewashed pub wall, with mortar standing proud of the stones.

When I found a pub with an inverted normal map. (If you understand what this means, you have to repost.)

Three equations. The first says that the vector from the fixed point to the first iterate is normal to the unstable eigenspace (n). The second that the distance to the first iterate is less than R, and to the second is greater than R. The last equation is repeated, and say that the i+1 st iterate is the image of the i th under the map F.

I forgot to add the equations.

A blue oval, tiled y irregular polygons. A circular region is cut out of the enter, tiled in red polygons. Then a blue oval, then a white oval. Looks like an eye.

An enlarged version of the previous image. The outer blue oval is almost enttrely off screen, and a smaller blue oval inside the red oval can be seen.

These are my first steps at computing invariant manifolds of maps. This is the stable manifold of the origin in discrete Lorenz. A "point" is five three-d pts, each the image of the other under the map, with the first in the stable eigenspace. The first pair straddles the small, thin red ellipse.

Brown wooden three step library steps, with books on them as extra shelf space

If I'm using my library steps as extra bookshelf space, do I have a problem?

A paddle board with a man and a dog. The dog is posed at the front of the board.

I'm guessing that this takes way more coordination than I possess. The dog trots back and forth on the board. Looks slippery.

Ooo. Cool the way the reflections show on the waves.

A set of points on five curves with red normal vectors at the points. One curve is in green and is the first curve. The rest are iterates of the green curve and are in blue and black. The black is the fifth iterate.

Four gray surfaces drawn using non-overlapping polygons. They begin on the left with a large sphere which is partially off the edge of the image. The surfaces are images of each other under a map, and get smaller and more sausage shaped from left to right.

The equations for consecutive points on a boundary map trajectory that originate on a circle or sphere. The equations for a two dimensional map on the left and three dimensional on the right.

I'm not going to try to explain these, but the gods of computation decided that they'd let my code work.

The curves/surfaces are points on all trajectories of a mapping (2d->2d and 3d->3d) starting on a manifold of initial conditions (a circle/sphere here).

Yes. Now I see it

phi' = (I-Phi Phi^T) F_u phi

A bold curve which is a trajectory of a flow. The letmost piece between points u_a and u_b is labeled u_ab, and an curve offset from it in a direction phi_a is drawn. A second trajectory u_bc begins at u_b+e phi_b and ends at u_c. Equations and boundary conditions are written for the trajectory segments.

Argh. I messed up the equations on the figure, and somehow managed to mess the alt text. I thought I'd got it set not to let me do that. Hmmm.

I we have asymp. or something and can find the unstable direction at every point on the initial section we can offest it by a little and get a section that's transverse. With that dir. at one point we can write an equation for how the dir evolves, and not have to actually find the offset section.

Here's what I'm thinking about.

Invariant manifolds defined by smooth transverse sections are "easy". Those associated with a trajectory (like a periodic orbit) are collections of trajectories that approach or diverge from a curve tangent to the flow.

I guess you just put all the superscript indices first in the subscripts and throw in a transpose to change the order? The product is the sum over last index in the first term and first in the second?