## Videos

**Math and OCD: My story with the Thue-Morse sequence**

In this video I show a particular sequence that I was obsessed with as a child, and one of its many interesting properties regarding sums of powers of integers.

**Geometric series and my Irish heritage**

In this video I show a very nice property of geometric sums, and how that makes me 1/3 Irish.

**Bayes theorem, false positives, and why I’m terrified to go to the doctor**

In this video I show an interesting and surprising application of Bayes theorem that calculates how effective a medical test is.

## Talks

**The down operator and expansions of near rectangular k-Schur functions**

At KAIST in South Korea. In here we present a pair of Fomin dual graded graphs for k-cores, and develop expansions of k-Schur functions from k-Grassmannian permutations.

## Research Articles

- Multiplicative structures of the immaculate basis of non-commutative symmetric functions (with C. Berg, N. Bergeron, F. Saliola, M. Zabrocki) –
**Journal of Combinatorial Theory, Series A**, 2017 - Indecomposable modules for the dual immaculate basis of quasi-symmetric functions (with C. Berg, N. Bergeron, F. Saliola, M. Zabrocki) –
**Proceedings of the American Mathematical Society**, 2015 - The immaculate basis of the non-commutative symmetric functions (with C. Berg, N. Bergeron, F. Saliola, M. Zabrocki) –
**FPSAC 2013, France (extended abstract)**, 2013 - A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions (with C. Berg, N. Bergeron, F. Saliola, M. Zabrocki)-
**Canadian Journal of Mathematics**, 2014 - Combinatorial expansions for families of non-commutative k-Schur functions (with C. Berg, F. Saliola) –
**Siam Journal of Discrete Math**, 2014 - Quasi-symmetric and non-commutative affine Schur functions (with C. Berg) – 2014
- Pieri operators on the affine nilCoxeter algebra (with C. Berg, F. Saliola) –
**Transactions of the American Mathematical Society**, 2014 - Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials (With N. Loehr and G. Warrington) –
**Journal of Combinatorial Theory, Series A**, 2013 - The down operator and expansions of near rectangular k-Schur functions (With C. Berg, F. Saliola) –
**Journal of Combinatorial Theory Series A,**2013 - Staircase skew Schur functions are Schur P-positive (With F. Ardila) –
**Journal of Algebraic Combinatorics**, 2012 - Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials –
**Electronic Journal of Combinatorics**, 2011 - Generalized triangulations, pipe dreams, and simplicial spheres –
**FPSAC 2011, Austria (extended abstract)**, 2011 - Cyclic sieving for longest reduced words in the hyperoctahedral group (With K. Petersen) –
**Electronic Journal of Combinatorics**, 2010 - The shifted plactic monoid –
**Mathematische Zeitschrift**, 2009 - A simple recurrence for covers of the sphere with branch points of arbitrary ramification (With I. P. Goulden) –
**Annals of Combinatorics**, 2006 - Maintaining the spirit of the reflection principle when the boundary has arbitrary integer slope (With I. P. Goulden) –
**Journal of Combinatorial Theory, Series A**, 2003