JONAH BLASIAK

Fall 2012: Math 565 Combinatorics and Graph Theory

Winter 2012: Math 566 Combinatorial Theory

Fall 2011: Math 565 Combinatorics and Graph Theory

I graduated from UC Berkeley under the direction of Mark Haiman. I did a one year postdoc at the University of Chicago with Ketan Mulmuley on complexity theory and the Kronecker problem. I am now in my third year of a three year postdoc at the University of Michigan.

I recently received an NSF grant for the project quantizing Schur functors.

I am now applying for tenure track positions.

CV

Research Statement

Short Research Statement

Kronecker coefficients for one hook shape, September 2012.

**Kronecker coefficients for one hook shape.**
Preprint, September 2012. PDF

**Representation theory of the nonstandard Hecke algebra.**
Preprint, January 2012. PDF

*(with K. Mulmuley and M. Sohoni)* **Geometric complexity theory IV: nonstandard quantum group for the Kronecker problem.**
Revised preprint, April 2013; accepted in Memoirs of the AMS. PDF

**Quantum Schur-Weyl duality and projected canonical bases.**
Preprint, February 2011; submitted to Journal of Algebra. PDF

**Nonstandard braid relations and Chebyshev polynomials.**
Preprint, October 2010; submitted to Journal of Algebra. PDF

**An insertion algorithm for catabolizability.**
*European J. Combin.* **33**, no. 2 (2012), 267--276. PDF

**Cyclage, catabolism, and the affine Hecke algebra.**
*Adv. Math.* **228**, no. 4 (2011), 2292--2351. PDF

**W-graph versions of tensoring with the S _{n} defining representation.**

**A factorization theorem for affine Kazhdan-Lusztig basis elements.**
Preprint (2009). PDF

**The toric ideal of a graphic matroid is generated by quadrics.**
*Combinatorica* **28**, no. 3 (2008), 283--297.
PDF

*(with A. Berglund and P. Hersh)* **Combinatorics of multigraded Poincaré series for monomial rings.**
*J. Algebra.* **308**, no. 1 (2007), 73--90.
PS

**A special case of Hadwiger's conjecture.**
*J. Combin. Theory Ser. B* **97**, no. 6 (2007), 1056--1073.
PDF

A longer version that was my senior thesis: PDF

*(with R. Durrett)* **Random Oxford graphs.**
*Stochastic Process. Appl.* **115**, no. 8 (2005), 1257--1278.
PDF

**Cyclage, catabolism, and the affine Hecke algebra.**
(2009), Advisor: Mark Haiman. PDF

**Cohomology of the complex Grassmannian.**
An expository paper for the final in Hutchings' algebraic topology class.
PDF

**Longest common subsequences and the Bernoulli matching model: numerical work and analyses of the R-reach simplification.**
For my spring semester undergraduate junior paper.
PDF

These files cbparabolic give certain canonical basis elements of $V^{\otimes r}$ in terms of the monomial basis. The file labeled by the partition $\nu$ contains all the canonical basis elements corresponding to the Yamanouchi words with content $\nu$. This data is in magma-readable format. All computations are done over the finite field $\mathbb{F}_{100003}$. The Kazhdan-Lusztig coefficients are given in several formats. See the end of the file for the most human-readable format.

combinatorics.txt Lots of functions from algebraic combinatorics including cyclage, catabolizability, and the standardization map of Lascoux and Schützenberger.

affineHecke.txt Some messy, slow, but quite general code to compute canonical bases for iterated restriction and inductions. Supports affine Weyl group computations in type A and was written to work for all types but it does not yet do so. Computes cells and the partial order on cells in terms of tableaux.

affineHeckeuserRes3H4.txt
An example using affineHecke.txt to compute the cells of

$\text{Res}_{H_K} \text{Ind}_{H_J}^H$ triv, where $K = \{s_1, s_2\}, J = \{s_2\}$, and $H$ is the Hecke algebra of type $A_3$.