Daniel Álvarez Receives the 2026 André Lichnerowicz Award

A mathematician with a Ph.D. from IMPA, Daniel Álvarez was awarded the 2026 André Lichnerowicz Award, An award given to young researchers for significant contributions to Poisson geometry. Álvarez completed his Ph.D. at IMPA in 2019, conducted postdoctoral research at the University of Toronto, and returned to the Institute in 2024.

“I accept the 2026 André Lichnerowicz Prize with deep joy and gratitude. My research investigates how infinitesimal structures in Poisson geometry, Lie theory, and generalized geometry integrate into global objects, allowing us to address problems inspired by mathematical physics. “For me, the Lichnerowicz Prize represents a very important incentive to continue developing this research program,” says Álvarez.

Awarded every two years during the International Conference on Poisson Geometry, the prize recognizes up to two mathematicians who have held a Ph.D. for no more than eight years and who have made significant contributions to the field. The award was established in 2008 during the conference held in Lausanne, Switzerland. This year, the conference is taking place through August 14 in Antwerp and Leuven, Belgium.

The award recognizes Álvarez’s contributions to Poisson geometry and related fields, particularly his use of quasi-Hamiltonian techniques and, more broadly, methods from shifted symplectic geometry (shifted symplectic geometry) and higher groupoids.

According to the award citation, the researcher’s work on generalized double Bruhat cells and their Morita equivalences “revealed new connections between symplectic double groupoids, cluster structures, and Boalch’s work on meromorphic connections and fission spaces.” In collaboration with Gualtieri and Jiang, Álvarez used techniques involving module spaces and higher Morita equivalences to resolve the conjecture on the existence of generalized Kähler potentials, achieving a fundamental result for generalized geometry (in the sense of Hitchin).”

Broadly speaking, Álvarez’s research investigates how infinitesimally defined structures can be integrated into global geometric objects. His work lies at the interface between Poisson geometry, Lie theory, symplectic geometry, and generalized geometry, with problems also motivated by mathematical physics.

A career linked to IMPA

Supervised by IMPA researcher Henrique Bursztyn, Álvarez defended his dissertation in 2019, titled “Integrability of Quotients in Poisson and Dirac Geometry”. He later completed a postdoctoral fellowship at the University of Toronto and, in 2024, returned to IMPA to continue his research in Poisson geometry and related fields.

“Poisson geometry plays an important role in various areas of mathematics and physics, and Daniel’s work makes contributions that significantly advance this field,” notes Bursztyn.

This achievement forges a special bond between the two researchers. Bursztyn was one of the winners of the André Lichnerowicz Award in 2008, the first year the award was presented, sharing the honor with Marius Crainic. The award was presented in the same year it was established.

The field studied by the two researchers has its roots in the mathematical formulation of classical mechanics. Poisson geometry gained momentum as a systematic field beginning in the second half of the 20th century, driven by the work of mathematicians such as André Lichnerowicz and Alan Weinstein. Today, its applications and connections span topics such as geometric mechanics, integrable systems, representation theory, quantum groups, noncommutative geometry, and mathematical physics.