My research area is algebraic combinatorics. More specifically, I study spectral properties (eigenvalues, eigenvectors) of random walks corresponding to card shuffling. I explain this in the following excerpts from national media (in French):
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In a video for the show Électrons Libres, on Télé-Québec (the video might not be available anymore)
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.
My master’s thesis was in combinatorics on words, and more specifically about palindromes. My advisors were Srecko Brlek and Xavier Provençal.
Recently, I also got interested into dynamical algebraic combinatorics, the study of combinatorial actions and their orbits.
Published papers
- Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. Toggling, rowmotion, and homomesy on interval-closed sets. Accepted for publication in Journal of Combinatorics.
- 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.
Preprints
- Nadia Lafrenière, Yan Zhuang. On the rix statistic and valley-hopping.
- Darij Grinberg, Nadia Lafrenière. The one-sided cycle shuffles in the symmetric group algebra.
- Isabelle Baraquin, Nadia Lafrenière, Katharina Schuh. The cutoff phenomenon in finite Markov chains.
Research talks
- 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, AMS Fall Eastern Sectional Meeting, Amherst (MA), October 2, 2022; Michigan State University’s Combinatorics and Graph Theory Seminar (virtual), October 25, 2022; Dartmouth College Combinatorics Seminar, Hanover (NH), November 15, 2022; Séminaire SAG+Statistiques, Université de Sherbrooke, Sherbrooke (Qc), March 8, 2023.
- The spectrum of the random-to-below Markov chain, given several times: University of Waterloo Combinatorics Seminar (virtual), July 22, 2021; SIAM Conference on Applied Algebraic Geometry (virtual), August 16, 2021; UMass Discrete Math seminar, Amherst (MA), October 22, 2021; Philadelphia Area Combinatorics, Algebra and Geometry Seminar, Philadelphia, November 18, 2021; University of California San Diego’s Graduate Combinatorics Seminar (virtual), January 25, 2022; Brandeis Combinatorics Seminar (virtual), January 25, 2022; AMS Fall Eastern Sectional Meeting, Amherst (MA), October 2, 2022; Stony Brook University Probability and Combinatorics Seminar, Stony Brook (NY), December 5, 2022.
- Properties of Random Walks through standard Young Tableaux (and through other objects), Summer School in Algebraic Combinatorics (virtual), June 23, 2021.
- Do you know how to shuffle cards? A combinatorial study of the convergence towards a well-mixed deck of cards, Connecting Women in Mathematics Across Canada (virtual), June 1, 2021.
- Ordre et désordre: Comment y arriver rapidement, Association mathématique du Québec colloquium (virtual), March 11, 2021.
- Derangements: Solving Problems by Counting (Certain Types Of) Permutations, University of Connecticut Undergraduate Research Seminar (virtual), June 12, 2020. Slides
- Eigenvalues of symmetrized shuffling operators, University of Vermont Combinatorics Seminar, Burlington, February 10, 2020.
- Do you know how to shuffle cards?, Postdoc Research Day, Dartmouth College, Hanover (NH), January 16, 2020.
- Eigenvalues of symmetrized shuffling operators, Formal Power Series and Algebraic Combinatorics (FPSAC), Ljublijana, July 1st, 2019. Slides.
- Random walks on the faces of a hyperplane arrangement, Graduate Students Combinatorics Conference 2019, Philadelphia, April 6th, 2019.
- Eigenvalues of symmetrized shuffling operators, Dartmouth College’s Combinatorics Seminar, Hanover (NH), April 2nd, 2019.
- Valeurs propres des opérateurs de mélange symétrisés, Séminaire de combinatoire du LaCIM, Montréal, November 23rd, 2018.
- Propriétés spectrales des opérateurs de mélange symétrisés, Séminaire du groupe de travail Combinatoire énumérative et algébrique du LaBRI, Bordeaux, May 18th, 2018.
- Spectral properties of shuffling operators in symmetric group algebras, American Mathematical Society, Sectional Meeting, Boston, April 21st, 2018.
- Eigenvalues of shuffling operators and mixing time, Graduate Student Combinatorics Conference, Dallas, April 7th, 2018.
- Compter les palindromes dans les arbres, Séminaire de combinatoire du LaCIM, Université du Québec à Montréal, October 23rd, 2015.
- Palindromic complexity of trees, Developments in Language Theory 2015, Liverpool, July 30th, 2015.
- Diverses approches pour les marches aléatoires sur les permutations, Séminaire de logique, informatique et mathématiques discrètes du LAMA, Université de Savoie-Mont-Blanc, April 23rd, 2015.
- Extending the Brlek-Reutenauer conjecture, American Mathematical Society, Sectional Meeting, Halifax, October 18th, 2014.
- On f-palindromes and their applications, Analysis of algorithms 2014, Paris, June 16th, 2014.