Support l'X Clémence's work falls within the framework of random matrix theory and concerns the dynamic study of the spectrum of an initially Hermitian matrix with Gaussian entries, modified by a rank-1 anti-Hermitian perturbation. Far from being arbitrary, this model is motivated by questions of experimental physics, and in particular by the modeling of quantum dispersion phenomena. In a colorful presentation, she outlined her study and illustrated how all trajectories remain close to the real axis, with the exception of a single eigenvalue (called the “outlier”) whose imaginary part tends toward infinity. Using the latest techniques, Clémence was able to verify the estimated emergence time of this outlier and locate it precisely in the plane. This work was carried out at the CMLS under the supervision of Guillaume Dubach and was based on research conducted over the last fifteen years on random matrices
Three Bachelor's students honored with the 2025 Maryam Mirzakhani Junior Prize
De gauche à droite : Clémence Moullet, Ioana Popescu, Anca Sfia
Three students from École Polytechnique's Bachelor of Science program were honored at the 2025 Maryam Mirzakhani Junior Prize ceremony held by the Jacques Hadamard Mathematics Foundation, highlighting the excellence of teaching and encouragement of research in this program launched in 2017, whose success and appeal have continued to grow since its creation.
The Maryam Mirzakhani Junior Prize rewards a first research project in mathematics and honors three winners: one in a bachelor's degree program (L3) and two others in their first year of a master's degree program (M1).
Clémence Moullet is the winner for her L3 work entitled “Perturbation of a Random Hermitian Matrix.” In 2024, she won first prize in the Bachelor's program public speaking competition.
After a brilliant performance in the X Bachelor's program, Clémence has now joined the PhD program at Brown University.
Two other Bachelor's students, Ioana Popescu and Anca Sfia, received special mentions from the Maryam Mirzakhani Junior Prize jury for their work entitled “Energy of Preferential Attachment Trees” and “Upper bounds for two-color Ramsey numbers,” respectively.
The 2025 Maryam Mirzakhani Junior Prize award ceremony took place on September 2 at Paris-Saclay University.
Ioana studied the energy of “preferential attachment” (PA) trees, a random model of growing networks where new vertices connect to old ones with a probability depending on their degree. The energy of such a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. While two cases (called “linear” and ‘sublinear’) had already been studied, Ioana's work contributed to the analysis of a third case called “superlinear.” Ioana was thus able to characterize the growth of energy as a function of the number of vertices, and further verify these results through new computer simulations. This work was supervised by Igor Kortchemski at the Department of Mathematics and Applications (DMA) at ENS Paris.
Created in February 2011 by mathematics laboratories associated with the CNRS, including the Center for Applied Mathematics (CMAP*) and the Laurent Schwartz Mathematics Center (CMLS**), part of École Polytechnique, the Jacques Hadamard Foundation promotes research in mathematics through excellence scholarships, courses for young researchers, scientific events, and long-term grants for young researchers.
Anca studied recent advances in “Ramsey theory,” a field that deals with graph combinatorics and the different ways of coloring graphs. “How many people must be invited to a party to ensure that a subgroup of 100 people will either all know each other or none of them will know each other?”... Ramsey theory, introduced in the 1930s, attempts to answer precisely these kinds of questions! After decades of steady but modest progress, significant advances were made by various teams in 2024. For her bachelor's thesis, Anca took a close look at these recent developments and improved some of the proofs. Her work was supervised by Marius Tiba (King's College London), one of the world's leading experts in the field.
Maryam Mirzakhani, an Iranian mathematician and professor at Stanford University, who died in 2017 at the age of 40 and was known for her work in topology and geometry, was the first woman to win the Fields Medal, one of the two most prestigious awards for mathematical research alongside the Abel Prize.
Launched in 2017, École Polytechnique's Bachelor of Science program is a three-year post-baccalaureate program taught in English and designed for high-potential French and international students, with mathematics at the heart of its curriculum.
The first year is devoted to acquiring the fundamental knowledge essential for the rest of their studies, as well as experimenting with several disciplines in order to choose the right specialization later on.
In their second and third years, students must then choose between three double majors, or specializations: Mathematics and Physics; Mathematics and Computer Science; Mathematics and Economics.
In their third year, students have the opportunity to study abroad for the fall semester at one of our partner universities, such as the University of Toronto, UC Berkeley, EPFL, KAIST, King's College London, or the University of Melbourne. In the spring, students complete an eight-week research internship, at the end of which they must submit their Bachelor's thesis.
At the end of June 2025, around fifteen students in their second year of the Bachelor of Science program (class of BX26) gathered for two weeks under the guidance of Guillaume Dubach, Monge Professor at École Polytechnique and member of CMLS, for a summer camp introducing them to mathematical research through exploration and play.
*CMAP: a joint research unit CNRS, École Polytechnique – Institut Polytechnique de Paris
** CMLS: a joint research unit CNRS, École Polytechnique – Institut Polytechnique de Paris