I enjoy writing limericks, and to amuse myself I started composing some about my research and related mathematical topics. This doggerel is compiled below for entertainment purposes only. Enjoy!
RSK as a linear operator (with Alexander Yong).
Robinson, Schensted, and Knuth
Uncovered a beautiful truth
From a matrix they'd go
To pairs of tableaux
And back with scarcely an oof!
In theory, we know RSK
Is a linear map, and yet they
Seem not to have tried
From this frame of mind
To study it hard, 'til today!
To classify with ADE
Is common in fields close to Lie
Yet it also (we say)
Tells us when RSK
Can diagonalizable be!
Representations from matrix varieties, and filtered RSK (with Abigail Price and Alexander Yong).
Hilbert once had a beautiful vision
Of series expressed with precision
But fractional forms
Were taken as norms
And who'd bother to do long division?
To compute in a character ring
The crystal base method is king
Once careful inspectors
Count highest-weight vectors
The e's and f's solve the whole thing!
A good matrix Schubert variety
Has a basis of some notoriety
But fully reducing
Requires some juicing--
And remainders can lead to anxiety!
Combinatorial commutative algebra rules (with Alexander Yong).
Simplicial complexes are key
Computing each quotient's degree
When problems arise
You just polarize
To obtain an ideal squarefree!
Schubert determinantal ideals are Hilbertian (with Alexander Yong).
Once Hilbert described a large function
It grows (for large n) in conjunction
With a polynomial
Of use unparochial
Which we substitute sans compunction!
A hypergraph characterization of nearly complete intersections (with Chiara Bondi, Courtney Gibbons, Yuye Ke, Spencer Martin, and Shrunal Pothagoni).
A nearly complete intersection
Is only one step from perfection
With hypergraphs we
Find numbers Betti,
and splittings explain the connection!
Miscellany
Of skill, Hilbert surely had lots
His proofs slicing intricate knots
In finding a zero
He wound up a hero
Applying his Nullstellensatz!