Denis Auroux

Denis Auroux
Name	Denis Auroux
Nationality	French
Fields	Mathematics
Workplaces	University of California, Berkeley; École normale supérieure (Paris); Université Pierre et Marie Curie (now Sorbonne University)
Alma mater	École normale supérieure (Paris); Université Paris-Diderot; École Polytechnique
Doctoral advisor	Yakov Eliashberg
Known for	symplectic geometry, mirror symmetry, Floer homology

Denis Auroux is a French mathematician known for contributions to symplectic topology, mirror symmetry, and low-dimensional topology. He has held faculty positions at University of California, Berkeley and in France at institutions including École normale supérieure (Paris) and Université Pierre et Marie Curie. His work connects techniques from complex geometry, algebraic geometry, and contact topology with applications in Gromov–Witten theory and categorical aspects of homological mirror symmetry.

Early life and education

Auroux completed his early studies in France, attending the École normale supérieure (Paris) and later obtaining doctoral training under the supervision of Yakov Eliashberg at a Paris institution associated with Université Paris-Diderot. During his doctoral period he engaged with problems situated at the intersection of symplectic geometry and contact topology, interacting with researchers at institutions such as Institut Henri Poincaré and research groups linked to Centre national de la recherche scientifique. His formative influences included figures from the French school like André Haefliger and international visitors connected to programs at Université Paris-Sud and Institute for Advanced Study.

Academic career

Auroux joined the faculty at University of California, Berkeley, where he contributed to the Department of Mathematics alongside faculty such as Paul Seidel and Kenji Fukaya. Prior appointments and visiting positions included stays at École normale supérieure (Paris), collaborations with groups at Stanford University and interactions with scholars from University of Cambridge and Princeton University. He has participated in program committees for conferences held by organizations including the American Mathematical Society, the European Mathematical Society, and research semesters at Mathematical Sciences Research Institute. In addition to research, Auroux has supervised graduate students and postdoctoral researchers who later held positions at universities like Columbia University, MIT, and Brown University.

Research contributions and fields

Auroux's research centers on symplectic geometry and its interfaces with algebraic geometry and topology. He developed techniques in the study of Lefschetz fibrations influenced by work of Simon Donaldson and Robert Friedman, building links to Picard–Lefschetz theory and the study of vanishing cycles. Auroux made significant advances in explicit constructions of mirrors in homological mirror symmetry, drawing on categorical frameworks introduced by Maxim Kontsevich and analytic tools related to Gromov–Witten invariants. His work on the topology of symplectic 4-manifolds connects to results of Clifford Taubes and Michael Freedman in low-dimensional topology and to constructions by Ronald Fintushel and Ronald Stern.

He introduced methods for computing Fukaya categories for explicit symplectic manifolds, creating bridges to derived categories of coherent sheaves studied by researchers such as Alexander Grothendieck and Pierre Deligne. Auroux contributed calculations of open Gromov–Witten invariants with implications for enumerative problems traced back to conjectures by Cumrun Vafa and techniques related to Seiberg–Witten theory. His collaborations and dialogues with mathematicians including Denis-Charles Cisinski, Mohammed Abouzaid, and Paul Seidel have influenced directions in categorical symplectic topology and the use of tropical methods pioneered by Grigory Mikhalkin.

Selected publications and results

Auroux's publications span foundational papers and survey articles. Notable works include papers analyzing genus-zero and higher-genus aspects of symplectic manifolds, explicit descriptions of mirror pairs for hypersurfaces and complete intersections inspired by the Batyrev construction, and expositions on Fukaya categories and Lefschetz pencils. Specific results feature constructions of symplectic Lefschetz pencils following techniques from Simon Donaldson, computations of Fukaya categories for symmetric products and surfaces related to work by Abouzaid and Seidel, and mirror constructions for toric varieties building on frameworks by Victor Ginzburg and Borisov.

He contributed a framework for relating Lagrangian submanifolds and sheaf-theoretic mirrors, connecting to the categorical ideas of Maxim Kontsevich and the microlocal sheaf theory developed by Masaki Kashiwara and Pierre Schapira. Auroux also produced expository articles and lecture notes used in advanced courses at venues such as MathOverflow-linked seminars, summer schools at ICTP, and workshop series at MSRI.

Awards and honors

Auroux has been recognized by the mathematical community through invitations to speak at leading venues such as the International Congress of Mathematicians satellite events and plenary or invited addresses at meetings of the Society for Industrial and Applied Mathematics and the European Mathematical Society. He received research support from agencies including National Science Foundation grants during his tenure in the United States and funding from French bodies such as the Agence nationale de la recherche. His work is cited across literature on symplectic topology, mirror symmetry, and homological algebra, reflecting influence alongside contemporaries like Paul Seidel, Kenji Fukaya, and Mohammed Abouzaid.

Category:French mathematicians Category:Symplectic geometers