Bernard Teissier
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| Bernard Teissier | |
|---|---|
 Fischer, Gerd · CC BY-SA 2.0 de · source | |
| Name | Bernard Teissier |
| Birth date | 1945 |
| Birth place | Paris, France |
| Fields | Mathematics |
| Workplaces | Université Paris-Sud, Institut des Hautes Études Scientifiques |
| Alma mater | Université Paris-Sud |
| Doctoral advisor | Pierre Samuel |
| Known for | Research on singularity theory, valuation theory, resolution of singularities |
Bernard Teissier
Bernard Teissier is a French mathematician noted for contributions to singularity theory, valuation theory, and the interaction between algebraic geometry and commutative algebra. His work connects concepts introduced by figures such as Oscar Zariski, Heisuke Hironaka, and Jean-Pierre Serre, influencing contemporaries including Hiroaki Abhyankar, Janos Kollár, and Joseph Lipman. Teissier's research has informed developments in areas related to complex analytic geometry, real algebraic geometry, and tropical geometry.
Biography
Bernard Teissier was born in Paris and completed his studies at Université Paris-Sud under the supervision of Pierre Samuel. Early in his career he interacted with mathematicians at institutions such as the Institut des Hautes Études Scientifiques, the Centre National de la Recherche Scientifique, and the École Normale Supérieure. He collaborated with researchers including Heisuke Hironaka, Oscar Zariski, John Milnor, René Thom, and Laurent Lafforgue. Teissier participated in conferences organized by bodies like the International Congress of Mathematicians and contributed to seminars at places such as IHÉS and Institut Fourier.
Mathematical Contributions
Teissier made seminal contributions to the study of singularity theory of algebraic and analytic varieties, developing invariants and techniques that link multiplicity theory, equimultiplicity, and integral closure. He advanced the theory of valuations inspired by Abhyankar and Zariski, clarifying the role of valuation spaces in resolution problems studied by Hironaka and examined by Bernard Teissier's peers. His work on polar varieties and the concept of polar multiplicities built on ideas from John Nash's arcs and connected to the Milnor number of John Milnor and Hervé Moulin Ollagnier's research traditions. Teissier introduced and developed approaches to equisingularity, relating Whitney stratification and Thom's a_f condition with invariants studied by David Trotman and others. He influenced the application of Newton polygons and Puiseux series techniques to plane curve singularities, echoing methods of Santiago López de Medrano and Eduardo Casas-Alvero. Teissier's insights have been used in modern work by Janos Kollár, Markus Némethi, and António Araújo on links of singularities, mixed Hodge structures inspired by Pierre Deligne, and in the development of tropical geometry frameworks associated with Grigory Mikhalkin.
Selected Publications
- "Varieties polaires. II. Multiplicités polaires, sections planes, et conditions de Whitney" — influential paper developing polar multiplicities, cited alongside works by Heisuke Hironaka and Oscar Zariski; presented in venues connected to IHÉS and Séminaire Bourbaki. - "Monomial ideals, binomial ideals, and toric varieties" — contributions interacting with research by Gert-Martin Greuel and Herwig Hauser on toric methods. - Papers on valuation theory and integral closure that connect to classical texts by Emmy Noether and modern expositions by Hironaka and Zariski. - Expository and survey articles relating equisingularity to Whitney stratification and Thom conditions, often referenced with works of John Mather and David Trotman. - Collaborative articles and proceedings contributions appearing in collections alongside authors like Jean-Pierre Serre and Jean Giraud.
Awards and Honors
Teissier has been recognized by the French mathematical community and invited to prominent international gatherings such as the International Congress of Mathematicians. His influence is acknowledged through invited lectures at institutions including IHÉS, École Normale Supérieure, and Université Paris-Sud. He has been cited in festschrifts and collections honoring figures like Oscar Zariski and Heisuke Hironaka.
Academic Career and Positions
Bernard Teissier held positions at Université Paris-Sud and maintained affiliations with research institutes such as the Institut des Hautes Études Scientifiques and the Centre National de la Recherche Scientifique. He supervised doctoral students who continued work in algebraic geometry and commutative algebra and collaborated with mathematicians from institutions including Université Paris 13, Université Pierre et Marie Curie, University of Michigan, and international centers such as Mathematical Sciences Research Institute and Max Planck Institute for Mathematics.