19/10/2022

Shuffling cards is also mathematics, Diaconis showed.

“Who cares?”, asked Persi Diaconis, a researcher at Stanford University, to a packed auditorium of students and researchers on Wednesday morning (19). The question about shuffling cards, the topic of Diaconis’s lecture during the IMPA 70th Anniversary Conference, drew laughter from the audience. With comic relief like this, the researcher in the field of statistics and mathematics – who was a professional magician – led everyone to follow, with attention and curiosity, the reasoning about “randomness” in card games.

“People who shuffle the cards really care about how many times they should shuffle them. Basically, they changed the rules in Las Vegas because of a theorem that we proved! And, for sure, it will be written on my tombstone that seven shuffles are enough,” said the researcher.

In 1992, Diaconis and Bayer showed that after seven random shuffles of 52 cards, all configurations are almost equally likely. While shuffling more than that doesn't significantly increase "randomness," shuffling less makes the deck "far" from random. Awarded the Rollo Davidson Prize (1982), the Gibbs Lecture (1997), and the Levi L. Conant Prize (2012), the American began his lecture by explaining that the topic might interest those studying Markov Chains or performing simulations with algorithms.

Roberto Imbuzeiro, a researcher at IMPA, was a master's student at the institute when he met Diaconis. "Persi is a very inspiring mathematician! In 1999, he gave a lecture that was one of the main reasons I decided to study probability. Today's lecture did not disappoint; it was very interesting and mixed several mathematical topics, from probability, which is about chance, to group theory, which is the least random thing possible, talking about symmetries. And, of course, with a curious real-world application, which is shuffling cards, very mathematically rich," said Imbuzeiro.

Luna Lomonaco spoke about the Mandelbrot Modular Complex.

Continuing the conference, IMPA researcher Luna Lomonaco spoke to the audience about the Mandelbrot Modular Set, which classifies the behavior of quadratic polynomials and holomorphic correspondences of the same object, which "can be two different things at the same time, on the one hand maps and on the other hand groups," she highlighted.

Miguel Ratis Laude, a doctoral student supervised by Luna, watched with admiration. “I really enjoyed the lecture! I think it’s a difficult topic to introduce to people outside the field, because it’s something very specific to the complex dynamics, but it’s always a pleasure to follow the reasoning, and the beautiful drawings help,” he commented.

The researcher, who took a brief break from breastfeeding to present the results of her conjecture, also expressed her honor at participating in IMPA's 70th anniversary. "I'm very happy, honored, and rushed, because I've been spending most of my day on the couch breastfeeding," she said humorously.

In addition to being a mother and researcher, Luna was the first woman to receive the Brazilian Mathematical Society (SBM) Award, which recognizes the best original research work in the field. In 2020, she received the Umalca Recognition Award (Latin American and Caribbean Mathematical Union) for her work in dynamical systems. Another important achievement was the L'oreal-Unesco-ABC Award "For Women in Science" in 2018, created to promote gender equality in the field.