Recorded 08 May 2024. Evita Nestoridi of SUNY Stony Brook presents "Cutoff for biased transpositions" at IPAM's Statistical Mechanics Beyond 2D Workshop. Abstract: Diaconis and Shahshahani proved that shuffling a deck of n cards with random transpositions takes 1/2nlogn steps to mix. In this talk we will discuss the case where a card that is located in the top n/2 positions gets selected with probability b/n and otherwise it gets selected with probability (2−b)/n , where 0 b≤1 is fixed. We then swap the cards. In joint work in progress with A. Yan, we prove that this shuffle takes (2b)−1nlogn steps to mix. Our proof heavily relies on the results of Diaconis and Shahshahani for random transpositions. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-mechanics-beyond-2d/