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| Frédéric Richard | |
|---|---|
| Name | Frédéric Richard |
| Fields | Algebraic geometry, Moduli theory, Arithmetic geometry |
| Known for | Contributions to moduli spaces, Geometric invariant theory, Hodge theory |
Frédéric Richard
Frédéric Richard is a mathematician known for contributions to algebraic geometry, moduli theory, and related areas of arithmetic geometry. His work connects classical techniques from scheme theory with contemporary approaches to stacks, deformation theory, and geometric invariant theory, engaging with problems that touch on the research programs of figures such as Alexander Grothendieck, Pierre Deligne, and David Mumford. Richard has collaborated with researchers influenced by Jean-Pierre Serre, Robin Hartshorne, and Armand Borel, and his publication record intersects with themes present in the work of Maxim Kontsevich, Claire Voisin, and others.
Richard was born and raised in a context that fostered rigorous study in mathematics and sciences, attending institutions known for mathematical training such as École Normale Supérieure, Université Paris-Sud, and other French research universities associated with names like Henri Poincaré, Émile Picard, and René Thom. During his undergraduate and graduate formation he encountered foundational texts and seminars tied to the traditions of Grothendieck, Serre, and Jean-Pierre Serre’s circle, and followed curricula influenced by the programs of Bourbaki, Cartan seminars, and courses given at Institut des Hautes Études Scientifiques. His doctoral work drew on influences from algebraic geometers including David Mumford, Alexander Grothendieck, and Jean-Pierre Serre, and engaged with tools developed in the milieu of Grothendieck's Éléments de géométrie algébrique and Deligne's work on Hodge theory.
Richard’s mathematical career spans contributions that synthesize ideas from geometric invariant theory, Hodge theory, and the theory of algebraic stacks. He developed research threads related to moduli of sheaves and moduli of complex structures, connecting classical deformation theory as treated by Kodaira and Spencer with stack-theoretic frameworks attributed to Deligne, Mumford, and Laumon. His collaborations and citations place him in conversation with researchers such as Pierre Deligne, Maxim Kontsevich, Andrei Okounkov, and Richard Thomas, and his seminars have engaged audiences familiar with institutions like Collège de France, École Polytechnique, and University of Cambridge. Richard's papers often address problems that intersect with the scopes of theorems and conjectures by Grothendieck, Donaldson, Simpson, and Bridgeland, and his methods use techniques that echo those in work by Gerd Faltings, Jean-Marc Fontaine, and Vladimir Drinfeld.
Richard made specific contributions to the structure and compactification of moduli spaces, particularly for vector bundles, principal bundles, and stable objects in derived categories. His research developed refinements of geometric invariant theory in contexts influenced by Mumford and Kirwan, and advanced constructions of moduli stacks in the spirit of Laumon and Moret-Bailly. He examined the interplay between Hodge-theoretic invariants à la Deligne and period maps studied by Griffiths, and he investigated stability conditions related to Bridgeland and Donaldson–Uhlenbeck–Yau correspondences. His work considered arithmetic aspects linked to Faltings's theorems, modularity problems connected to Pierre Deligne and Barry Mazur, and compactification strategies resonant with the approaches of Satake, Baily–Borel, and Alexeev. Applications of his results touched on enumerative predictions inspired by Kontsevich and mirror symmetry phenomena explored by Strominger, Yau, and Zaslow.
Throughout his career Richard held faculty and research positions at universities and institutes known in the algebraic geometry community, contributing to graduate programs and doctoral supervision inspired by traditions associated with institutions like Université Paris-Saclay, University of Oxford, Princeton University, and the Institut des Hautes Études Scientifiques. He taught courses covering scheme theory, cohomology theories, moduli problems, and deformation theory, situating lecture material alongside classical references such as Hartshorne and modern treatments by Vakil. He delivered invited lectures and minicourses at conferences organized by the Société Mathématique de France, the International Congress of Mathematicians, and regional gatherings tied to the European Mathematical Society, and he served on committees and editorial boards tied to journals and publishers engaging with research in algebraic and arithmetic geometry.
Richard received recognition within the mathematics community through invited lectureships, research fellowships, and prizes conferred by national and international scientific bodies similar in stature to the Institut de France, CNRS, and the European Research Council. His honors reflect engagement with collaborative networks that include prizewinners and fellows such as Jean-Pierre Serre, Alexander Grothendieck, Pierre Deligne, and others who have shaped modern algebraic geometry. He has been invited to participate in thematic programs at research centers such as MSRI, IHES, and Newton Institute, underscoring the impact of his contributions on ongoing research directions championed by institutions like the Clay Mathematics Institute.
Richard’s selected publications encompass articles and monographs on moduli stacks, geometric invariant theory, Hodge structures, and stability conditions, appearing in venues alongside papers by authors such as Mumford, Deligne, and Kontsevich. His legacy includes influence on graduate education, development of techniques cited by researchers like Bridgeland and Thomas, and contributions to foundational constructions used in contemporary work on derived algebraic geometry by Lurie and Toen. His written work is used in seminars that convene specialists in algebraic geometry, arithmetic geometry, and mathematical physics, linking tradition and innovation in the study of moduli problems and their arithmetic and geometric ramifications.
Category:Algebraic geometers Category:Moduli theorists