Noémie Combe, mathematician and the first ESILV faculty member based at the Montpellier campus, recently presented her latest research at the Massachusetts Institute of Technology (MIT). Her talk was part of VaNTAGe, an international online seminar dedicated to major open questions in number theory and arithmetic geometry.
This invitation highlights both the academic reach of ESILV and the scientific ambition driving the school’s new campus in Montpellier.
VaNTAGe: A major platform for mathematics
Created in 2020, VaNTAGe (Virtual math seminar on open conjectures in number theory and arithmetic geometry) brings together leading mathematicians from around the world.
Its goal is to make advanced mathematics more accessible while connecting researchers without the need for travel.
The topics discussed are among the most abstract and fascinating in modern mathematics, addressing deep questions about numbers, symmetry, and geometry.
Understanding the heart of Noémie Combe’s research
During her presentation, Noémie Combe tackled one of the most mysterious objects in mathematics: the absolute Galois group.
In simple terms, this group encodes the hidden symmetries of all algebraic equations involving rational numbers—essentially, it describes how numbers relate to one another through these symmetries.
To study it, she draws inspiration from Alexander Grothendieck, a French mathematician whose work transformed algebraic geometry. Grothendieck had proposed a new way to view mathematics as a network of interrelated structures rather than isolated problems.
Noémie Combe revisits these ideas with fresh mathematical tools and a surprising source of inspiration: physics.
Her work uses concepts similar to path integrals, an approach introduced by physicist Richard Feynman to study how particles move in quantum mechanics. By translating these ideas into mathematics, she proposes a new way of describing the behavior of these numerical symmetries.
Connecting mathematics and physics
The originality of her approach lies in bringing together two worlds that rarely meet: arithmetic geometry (the study of numbers through geometric shapes) and theoretical physics (which uses mathematical models to describe natural phenomena).
In her talk, she suggested that some of the tools used in physics—particularly those for understanding motion and probability—could also help mathematicians describe how number systems behave.
Her approach also uses Cantor sets, structures composed of infinitely many points that illustrate how something can be continuous and discrete at the same time. These sets provide a geometric way to represent complex mathematical objects, such as the Galois group.
A global recognition for ESILV Montpellier
Being invited to speak at MIT represents a significant milestone for both Noémie Combe and the ESILV Montpellier campus. It places the school within a global research network and strengthens its academic identity.
At Montpellier, ESILV is building a learning environment that integrates advanced mathematics, engineering sciences, and digital technologies.
The arrival of faculty members like Noémie Combe contributes to developing a strong research culture from the very first year of the new site’s activity.
A new academic chapter in Occitanie
ESILV’s Montpellier campus welcomed its first cohort in 2025, marking the arrival of De Vinci Higher Education in the Occitanie region.
Around one hundred students began the year in the temporary Pise and Sienne building, located in the Euromédecine district—a hub for health and technology.
The permanent campus, planned for Castelnau-le-Lez in 2026, is designed to be an environmentally responsible space dedicated to learning, innovation, and collaboration.
Looking ahead
By sharing her research on an international stage, Noémie Combe demonstrates how fundamental mathematics can intersect with other disciplines to open new perspectives.
Her work reflects the academic philosophy of ESILV: bridging theory and application, science and innovation, and local presence and global outreach.