Nemesis: An Exceptional ERC Synergy That Is Starting to Prove Its Worth
Two years after its official launch, the first scientific report from the Nemesis project1 (2024–2030) has just been approved by the European Research Council, with particularly positive feedback. Coordinated by the University of Montpellier and led by Daniele Di Pietro, a professor at Imag, this ERC Synergy project—funded to the tune of 7.8 million euros—paves the way for new numerical computation methods capable of solving complex mathematical equations.
No one is bound to do the impossible. Except, perhaps, the grantees of the European Research Council (ERC), a prestigious European funding body that supports exploratory research projects of the highest scientific caliber, aimed at “pushing the frontiers of knowledge.” Daniele Di Pietro is one of them.
In 2023, Daniele Di Pietro, a professor of numerical analysis at the Alexander Grothendieck Institute in Montpellier (Imag)—a CNRS-University of Montpellier research laboratory that he directed from 2021 to 2025—was awarded a €7.8 million ERC Synergy grant for the Nemesis project. This is a rare achievement for a mathematics project, reflecting both its scientific ambition and the many challenges it aims to tackle.
In addition to its substantial funding and the extremely competitive nature of the call for proposals, this project—like all ERC Synergy projects—is unique in that it brings together several world-class scientists to address a highly complex research topic. This requirement also explains the scale of its budget. Coordinated by the University of Montpellier, the Nemesis project thus brings together four principal investigators and their teams. Daniele Di Pietro serves as the project coordinator, alongside Jérôme Droniou of IMAG, Paola Antonietti of the Politecnico di Milano (Italy), and Lourenço Beirão da Veiga of the University of Milan-Bicocca (Italy).
When Equations Defy Computers
Launched in early 2024, Nemesis tackles a central challenge in numerical simulation: how to model physical phenomena that are too complex to be solved exactly using a computer. Its name, Nemesis, stands for “New Generation Methods for Numerical Simulations.” Daniele Di Pietro summarizes the challenge as follows: “Today, to model a physical system—such as a car or an airplane, but also the human heart or brain—we rely on computer simulations. To do this, we must first find the equations that describe the system. However, while we are often able to write these equations, it is generally impossible to solve them exactly. We must therefore find approximate versions of these equations that can be solved using a computer.” This is where Nemesis aims to break new ground: the project seeks to push beyond the current limits of numerical simulation as applied to complex physical problems.
A First Scientific Hurdle Cleared
How? By developing, at the heart of applied mathematics and numerical simulation, new methods for solving partial differential equations. The goal: to create a new generation of simulators capable of modeling highly complex physical phenomena in a more flexible, reliable, and computationally efficient manner. One of the project’s key drivers is a set of new methods known as “polytopic” methods, which rely on geometric subdivisions that are more flexible than traditional meshes.
This is what makes the validation of the first scientific report particularly important. The positive feedback received on this occasion reinforces the project’s scientific vision and highlights the first hurdle overcome by the Montpellier teams. “The major breakthrough recognized by this scientific report is the design of a common mathematical framework for polytopal methods, called Polytopal Exterior Calculus, ” explains Daniele Di Pietro. In other words, a common mathematical language for organizing these new methods and enabling them to interact. This framework paves the way for more precise, more robust, and less computationally intensive calculations.
Another significant advancement is the development of new methods for modeling incompressible flows—that is, fluids whose volume varies very little—particularly in regimes dominated by convection. While the project focuses on fundamental topics, its potential for application is broad. Possible applications include magnetohydrodynamics—which plays a role, for example, in aluminum melting—as well as flow in porous and fractured media, which is useful for studying CO₂ storage or assessing risks associated with nuclear waste storage.
The Strength of a Structured Group
The positive feedback received following the report’s evaluation also highlights the importance of the project’s roots in Montpellier. The University of Montpellier is home to two of the four principal investigators. This dual presence allows the project to draw on two teams from IMAG and a budget of more than 4.4 million euros allocated to the laboratory. As a result, several hires have been made, including non-tenured researchers as well as a project manager responsible for organizing fieldwork, working groups, and conferences. In total, nearly twenty people are working on numerical analysis at the Montpellier site, between the Nemesis project and other research in the field that directly contributes to this work.
An organization that illustrates the importance of collaboration in numerical analysis, in a discipline where this approach is not always the norm: “Very often in France—and particularly in mathematics—researchers are isolated from one another in terms of their research topics. Having a close-knit group significantly reduces this scientific isolation, which also fosters exchanges among non-tenured faculty and encourages more open discussions.” While, from a logistical standpoint, this organizational structure is not always straightforward—particularly due to a lack of available space—a working group has been established to address these challenges. It meets every two weeks in person for a half-day seminar. These meetings bring together Nemesis members, other students supervised by the two researchers from Montpellier, as well as external guests, depending on opportunities and needs. These guests are often internationally renowned scientists.
Exemplary progress to build upon
This first step confirms the scientific avenues identified by the project, but these advances must now be expanded upon and consolidated. For Daniele Di Pietro, this initial assessment confirms above all the value of taking scientific risks: “We’ve truly cleared a first hurdle that was ‘high risk, high gain’—in other words, risky, but well worth the effort. It took a lot of work to confirm that the initial vision held up; now, the goal is to build on these initial advances,” he emphasizes. By December 31, 2030, the next phase of the project will therefore need to both build on these scientific advances and undergo further monitoring, including an interim scientific report followed by a final report.
In other words, the research will likely have made significant progress by the timeERC representatives visit the University of Montpellier, as announced for January 26, 2027. This visit will also send a strong signal to Nemesis. The project already demonstrates strong scientific momentum: “This is an ERC Synergy project that is performing well and has yielded several publications by the principal investigators and their teams—nearly fifty scientific papers in top-tier journals in applied mathematics and computational science over the first two years,” confirms Daniele Di Pietro. He also hopes to share his experience in preparing and managing an ERC project with the entire local scientific community. This is one way for Nemesis to demonstrate its exemplary nature beyond its scientific results alone.
- ERC Synergie NEMESIS Contract Number 101115663 ↩︎