Marc Troyanov

Marc Troyanov is a Professor of Mathematics at the Ecole Polytechnique Fédérale de Lausanne (EPFL), leading the Geometric Analysis Unit (Troyanov Group) within the Department of Mathematics (SMA). He holds an Honorary Professor title and has been affiliated with EPFL since 1993, progressing from an assistant professor to full professor in 2005. His research focuses on differential geometry, geometric analysis, Finsler geometry, and Hilbert geometries, with contributions to Lq,p-cohomology and metric space analysis.

Education:

• PhD in Mathematics, University of Geneva (1987)
• Postdoctoral research at University of Paris and University of Utah (Salt Lake City)
• Assistant Professor at Université du Québec à Montréal (UQAM) prior to joining EPFL

Research Interests: Troyanov's work bridges global differential geometry and analysis on manifolds/metric spaces. Key areas include curvature studies on Riemannian manifolds, Finslerian geometry, Hilbert geometries, and cohomological analysis (e.g., Lq,p-cohomology). Recent trends in his publications address isoperimetric inequalities in groups, geometric foundations (e.g., Busemann's axioms), and surface singularities.

Teaching & Supervision: He teaches courses on differential varieties, Riemannian geometry, and linear algebra. Supervised doctoral students include Bruno Santos Correia, Adrien Marcone, and Zahra Sinaei, among others. His academic leadership roles include directing the Swiss Doctoral Program in Mathematics and serving on EPFL’s Doctoral School Commission.

Labs & Teams: The Troyanov Group collaborates on projects like global invariants of manifolds and Finslerian analysis. Former members include Daniele Valtorta and Hugo Parlier, while current researchers include Louis Merlin and Davide Parise.