Ariane Carrance

Ariane Carrance is a postdoctoral researcher at the Department of Mathematics, Faculty of Mathematics, University of Vienna, where she works with Professor Nathanaël Berestycki. Her research program bridges combinatorics, probability theory, and theoretical physics with applications to quantum gravity.

• PhD in Mathematics, Institut Camille Jordan, supervised by Grégory Miermont and Fabien Vignes-Tourneret
• Postdoctoral position at Laboratoire de Mathématiques d'Orsay with Nicolas Curien and Jean-François Le Gall
• Hadamard lecturer at Centre de Mathématiques Appliquées de l'École polytechnique

Dr. Carrance specializes in the combinatorial and probabilistic aspects of discrete metric spaces. Her work in dimension 2 focuses on specific families of maps, while in higher dimensions she investigates "colored trisps" and associated tensor models. She has made significant contributions to the understanding of random discrete structures and their continuum limits, with implications for quantum gravity theories. Her research combines deep theoretical insights with computational approaches, including development of mathematical software.

Dr. Carrance's publication record demonstrates a consistent progression from foundational work on planar maps and triangulations toward more complex higher-dimensional structures. Her recent work shows increasing sophistication in handling the interplay between combinatorial structures and probabilistic phenomena, with particular attention to asymptotic behaviors and scaling limits. The mathematical tools she employs span from classical combinatorics to advanced probability theory and computational mathematics.

Dr. Carrance has collaborated with leading researchers in probability theory including Nicolas Curien, Jean-François Le Gall, and Nathanaël Berestycki. She co-developed the SageMath package dynpuiseux for Puiseux series expansions, demonstrating her commitment to computational approaches in pure mathematics. Her research is supported through postdoctoral fellowships and academic positions at prestigious institutions across Europe.

As a member of the probability research group at the University of Vienna, Dr. Carrance contributes to a vibrant mathematical community focused on stochastic processes, random geometry, and their applications. Her work connects with broader efforts to understand the mathematical foundations of quantum gravity through discrete approaches.