JONAH BLASIAK

Winter 2016: Math 221 Discrete Mathematics

Winter 2015: Math 201 Linear Algebra

Winter 2015: Math 533 Abstract Algebra I

Spring 2013: Math 217 Linear Algebra

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 did a three year postdoc at the University of Michigan under the mentorship of John Stembridge. I was a visiting professor for a year at University of Southern California. I am now an assistant professor at Drexel University.

I was on the job market 2012-2013. Here are my research statements: Research Statement Short Research Statement

In 2012 I received an NSF grant for the project quantizing Schur functors.

The Rule of Three for commutation relations, May 2016.

Noncommutative Schur functions, October 2015.

Kronecker coefficients for one hook shape, September 2012.

version with less background version with more background

*(with T. Church, H. Cohn, J. A. Grochow, E. Naslund, W. F. Sawin, C. Umans)* **On cap sets and the group-theoretic approach to matrix multiplication.**
Preprint, August 2016. arXiv

*(with S. Fomin)* **Rules of Three for commutation relations.**
To appear in *J. Algebra*. Revised December 2016.
PDF

*(with R. I. Liu)* **Kronecker coefficients and noncommutative super Schur functions.**
Preprint, October 2015. PDF

*(with S. Fomin)* **Noncommutative Schur functions, switchboards, and Schur positivity.**
*Sel. Math.*, (2016), 1--40.
PDF

**Haglund's conjecture on 3-column Macdonald polynomials.**
*Math. Z.* **283**, (2016), 601--628.
PDF

**What makes a D _{0} graph Schur positive?**

Data files: vertexset.txt involutions.txt involutionswithzeros.txt maplegraph.txt checkaxioms.txt

*(with R. I. Liu and K. Mészáros)* **Subalgebras of the Fomin-Kirillov algebra.**
*J. Algebraic Combin.* **44**, no. 3 (2016), 785--829. PDF

**Kronecker coefficients for one hook shape.**
To appear in *Sem. Lothar. Combin.* Revised December 2016. PDF

**Representation theory of the nonstandard Hecke algebra.**
*Algebras and Representation Theory* (2014), 1--27.
PDF

*(with K. Mulmuley and M. Sohoni)* **Geometric complexity theory IV: nonstandard quantum group for the Kronecker problem.**
*Mem. Amer. Math. Soc.* **235(1109)**, (2015), ix--160.
PDF

**Quantum Schur-Weyl duality and projected canonical bases.**
*J. Algebra.* **402**, (2014), 499--532.
PDF

**Nonstandard braid relations and Chebyshev polynomials.**
*J. Algebra* **423**, (2015), 375--404.
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 $A_3$.