My research area is algebraic combinatorics. More specifically, I study actions on combinatorial structures, mostly permutations. On the one hand, I study spectral properties (eigenvalues, eigenvectors) of random walks corresponding to card shuffling which I explain, in French, for the mathematics magazine *Accromath*.

Recently, I also got interested into dynamical algebraic combinatorics, which is the study of combinatorial actions and their orbits from an enumerative perspective. I also worked in combinatorics on words in the past.

### Preprints

- Nadia Lafrenière, Rosa Orellana, Anna Pun, Sheila Sundaram, Stephanie van Willigenburg, Tamsen Whitehead McGinley.
*The skew immaculate Hecke poset and 0-Hecke modules*. - Ashleigh Adams, Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch.
*Cyclic sieving on permutations – an analysis of maps and statistics in the FindStat database.*

### Published papers

- Will Dowling, Nadia Lafrenière.
*Homomesy on permutations with toggling actions*. To appear in*Involve*. - Nadia Lafrenière, Yan Zhuang.
*On the rix statistic and valley-hopping.*Discrete Mathematics and Theoretical Computer Science, vol. 26:2, no. 3, 2024, 27 p. - Darij Grinberg, Nadia Lafrenière.
*The one-sided cycle shuffles in the symmetric group algebra*. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 275-326. This is a corresponding extended abstract for FPSAC. - Isabelle Baraquin, Nadia Lafrenière, Katharina Schuh.
*The cutoff phenomenon in finite Markov chains.*Snapshots of Modern Mathematics from Oberwolfach, no. 5, 2023. - Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch.
*Toggling, rowmotion, and homomesy on interval-closed sets.*Journal of Combinatorics, vol. 15, no. 4, 2024. - Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch.
*Homomesies on permutations – an analysis of maps and statistics in the FindStat database*, Mathematics of Computations, 2023, 56 p. - Nadia Lafrenière.
*Eigenvalues of symmetrized shuffling operators*. FPSAC 2019, 12 pp. - Damien Jamet, Nadia Lafrenière, Xavier Provençal.
*Generation of Digital Planes Using Generalized Continued-Fractions Algorithms*. DGCI 2016, pp. 45-56. - Srecko Brlek, Nadia Lafrenière, Xavier Provençal.
*Palindromic Complexity of Trees*. DLT 2015, pp. 155-166. - Srecko Brlek, Nadia Lafrenière.
*Reconstructing Words from a σ-palindromic Language*. Fundamenta Informaticae, Vol. 135 no. 1-2, 2014, pp. 59-72.

### Theses

My Ph.D. thesis, defended in November 2019, was about two families of shuffles, called the symmetrized shuffling operators. The focus was the eigenvalues. My advisor was Franco Saliola.

- Nadia Lafrenière.
*Valeurs propres des opérateurs de mélange symétrisés*, Ph.D. thesis, Université du Québec à Montréal, 2019. (In French).

My master’s thesis was on combinatorics on words, and more specifically about palindromes. My advisors were Srecko Brlek and Xavier Provençal.

- Nadia Lafrenière.
*Complexité palindromique des mots et des arbres*, M.Sc. thesis, Université du Québec à Montréal, 2016. (In French).

## Selected talks

*Tricher à l’aide des mathématiques*, Grandes conférences du Centre de recherches mathématiques, March 14, 2024. Video.*Rowmotion on Interval-closed sets*, Commutative Algebra meets Algebraic Combinatorics (CAAC), Januar 26, 2024. Slides.*How many times should you shuffle a deck or cards?*, Graduate Online Combinatorics Colloquium (invited as an expert; virtual), April 19, 2023. Notes*Homomesy on permutations*, given several times as seminar talks (Michigan State University, Dartmouth College, Université de Sherbrooke), and at the Joint Mathematics Meetings, January 6, 2023.*The spectrum of the random-to-below Markov chain*, given several times as seminar talks (University of Waterloo, University of Massachusetts Amherst, Drexel Universty, University of California San Diego, Brandeis University, Stony Brook University), and at the American Mathematical Society Sectional Meeting in Amherst (MA), October 2, 2022.*Eigenvalues of symmetrized shuffling operators*, Formal Power Series and Algebraic Combinatorics (FPSAC), Ljubljana, July 1st, 2019. Slides.*Palindromic complexity of trees*, Developments in Language Theory 2015, Liverpool, July 30th, 2015.