Lightnews — Scholar-powered news

Ben Grimmer

@profgrimmer.bsky.social

510 followers 250 following 56 posts

Assistant Professor @JohnsHopkinsAMS, Works in Mathematical Optimization, Mostly here to share pretty maths/3D prints, sometimes sharing my research

Posts Media Videos Starter Packs

Ben Grimmer @profgrimmer.bsky.social · Aug 14

Enjoyed being part of the Brin Mathematical Research Center's summer school on Scientific Machine Learning last week. Many very good talks and always nice to visit UMD!

Ben Grimmer @profgrimmer.bsky.social · Aug 12

You'll have to read the paper if you want the maths defining these extremal smoothings for any sublinear function and convex cone. I now have a whole family of optimal smoothing Russian nesting dolls living in my office.

Enjoy: arxiv.org/abs/2508.06681

Ben Grimmer @profgrimmer.bsky.social · Aug 12

If instead, you wanted the optimal outer smoothings (ie, sets containing K), there is a similar spectrum of optimal smoothings being everything between the minimal and maximal sets shown below.

Ben Grimmer @profgrimmer.bsky.social · Aug 12

If we restrict to looking at inner smoothings (ie, subsets of K), it turns out there are infinitely many sets attaining the optimal level of smoothness. Our theory identifies that there is a minimal and maximal such smoothing, shown below (nesting dolls from before).

Ben Grimmer @profgrimmer.bsky.social · Aug 12

To do something more nontrivial, consider the exponential cone K={(x,y,z) | z >= y exp(x/y)}, which is foundational to geometric programming. The question: What is the smoothest set differing from this cone by at distance one anywhere?
My 3D print of this cone is below :)

Ben Grimmer @profgrimmer.bsky.social · Aug 12

For example, you could invent many smoothings of the two-norm (five given below). In this case, the Moreau envelope gives the optimal outer smoothing. If you wanted the best smoothing of the second-order cone (the epigraph of the two-norm) a different smoothing is optimal.

Ben Grimmer @profgrimmer.bsky.social · Aug 12

📢 Excited to share a new paper with PhD student Thabo Samakhoana. Nonsmooth optimization often uses smoothings, nearby smooth functions or sets. Often chosen in an ad hoc fashion.

We do away with ad hoc, characterizing optimal smoothings for convex cones and sublinear functions

Reposted by Ben Grimmer

Henrik A. Friberg @hafriberg.bsky.social · Aug 5

Oh, that’s so satisfying! I stopped at the 4-norm ball thinking I had the solution as it fits the hole like a pot lid (has a perfect circle as an intersection).

Ben Grimmer @profgrimmer.bsky.social · Aug 5

In honor of the fun I've had playing with this puzzle and property, a homemade, ocean-themed, ceramic p=4/3 norm ball. Enjoy!

Ben Grimmer @profgrimmer.bsky.social · Aug 5

As a cruel mathematician, I leave the task of verifying that the p=4/3 rotated appropriately fully and perfectly plugs a hole (equivalently has a perfect circle as a shadow) as an exercise to the reader.

The dual of this wonderful property is that the 4-norm hides a circle :)

Ben Grimmer @profgrimmer.bsky.social · Aug 5

For good measure, one extra round of this physical verification process, adding a purple ball fully blocks our view of the green ball, entirely plugging the hole and saving our lives yet again.

Ben Grimmer @profgrimmer.bsky.social · Aug 5

Don't believe me? We can put another green p=4/3-norm ball in the glass. Looking from above, you cannot see any of the blue ball past the green one. It entirely plugs the hole!

Ben Grimmer @profgrimmer.bsky.social · Aug 5

To demonstrate this, suppose my glass is the hole in our boat, we can plug it entirely by placing a blue 4/3-norm ball in the glass.

Ben Grimmer @profgrimmer.bsky.social · Aug 5

The solution to cork the hole is surprisingly, radically simple:
Just put the p=4/3 norm ball in the hole.
Appropriately rotated, sending the direction (1,1,1)/sqrt{3} to (0,0,1).

Ben Grimmer @profgrimmer.bsky.social · Aug 5

Yesterday I posted a maths puzzle that AIs all failed at (thanks for running the premium versions @xy-han.bsky.social and Ernest Ryu). The puzzle just needs elementary reasoning about p-norm balls (third row on my shelf below).

This thread gives the puzzle, solution, and a 3D printed demo :)

Ben Grimmer @profgrimmer.bsky.social · Aug 4

The answer is simple but hard to find, so I expect not too many humans will get it either. But I have greater faith in us :)

Ben Grimmer @profgrimmer.bsky.social · Aug 4

I've invented a simple, lovely math puzzle I expect every AI fails:

Suppose you're a mathematical sailor at sea on a boat that has a perfectly cylindrical hole in the floor. All you brought is a collection of every p norm ball except p=2 (drat!). What do you do to cork the hole and save yourself?

Reposted by Ben Grimmer

Sam Power @spmontecarlo.bsky.social · May 26

very cool talk:
youtu.be/K_dhTP2I2uo?...
"Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm"
- Jason Altschuler

Jason Altschuler - Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm

YouTube video by Institute for Pure & Applied Mathematics (IPAM)

Ben Grimmer @profgrimmer.bsky.social · Apr 30

Lots of great questions and engagement from Wisconsin folk! They were quick at turning around and getting it online. See below:
www.youtube.com/watch?v=QNfq...

Ben Grimmer @profgrimmer.bsky.social · Apr 30

Just landed in Madison! Tomorrow, I'll be sharing my work optimizing optimization methods, to and beyond minimax optimality in their SILO seminar.
Will share a link to the talk on YouTube after

Reposted by Ben Grimmer

Quanta Magazine @quantamagazine.bsky.social · Mar 29

The optimization technique of gradient descent is like feeling your way down a mountain in the dark. You may not be able to see the way, but you’ll eventually reach the lowest point in the area. (From the archive)
www.quantamagazine.org/risky-giant-...

Ben Grimmer @profgrimmer.bsky.social · Mar 15

My PhD students are awesome. They gave my fiancee(wife) and I this gorgeous cherry blossom card for our wedding and soon honeymoon in Japan <3

Ben Grimmer @profgrimmer.bsky.social · Mar 12

Yes! I'm slowly evolving my office into a Museum! Open for anyone mathematically inclined wandering through Baltimore

I would say come anytime, but I'm actually about to be gone til April for my honeymoon. So come anytime in April :)

Ben Grimmer @profgrimmer.bsky.social · Mar 12

Mathy details for the norms and embeddings are on my website's fun page: www.ams.jhu.edu/~grimmer/fun...

Benjamin Grimmer

www.ams.jhu.edu

Ben Grimmer @profgrimmer.bsky.social · Mar 12

From top row to bottom, Figure 0 above has Schatten p-norms, Vector p-norms, Function p-norms, CVAR norms, Their duals, OWL norms, Their duals.

Figure 1 on the other side of my office has induced p->q matrix norm balls. p goes 1 to inf left to right. q goes 1 to inf bottom to top.

A 7x7 Shelf full of plastic balls 3D printed, depicting induced matrix norm balls for varied values of p and q.