Tristan Rivière (born 26 November 1967,

Brest Brest may refer to: Places *Brest, Belarus **Brest Region **Brest Airport **Brest Fortress *Brest, Kyustendil Province, Bulgaria *Břest, Czech Republic *Brest, France **Arrondissement of Brest **Brest Bretagne Airport ** Château de Brest *Brest, ...

) is a French mathematician, working on

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

and the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

Biography

Rivière studied at the

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

and obtained his PhD in 1993 at the

Pierre and Marie Curie University Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public university, public research university in Paris, France, from 1971 to 2017. The university was located on the Jussi ...

, under the supervision of Fabrice Bethuel, with a thesis on harmonic maps between manifolds. In 1992 he was appointed chargé de recherche at

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...

. In 1997 he received his habilitation at the University of Paris-Sud in Orsay. From 1999 to 2000 he was a visiting associate professor at the Courant Institute of Mathematical Sciences (New York University). Since 2003 he is full professor at

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

and since 2009 he is the Director of the Institute for Mathematical Research at ETH.

Research activity

His research interests include

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

(

liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. T ...

s, Bose–Einstein condensates,

micromagnetics Micromagnetics is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored (the continuum approximat ...

, Ginzburg–Landau theory of superconductivity,

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...

) and

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

(

harmonic map In the mathematical field of differential geometry, a smooth map between Riemannian manifolds is called harmonic if its coordinate representatives satisfy a certain nonlinear partial differential equation. This partial differential equation for ...

s between manifolds,

geometric flow In the mathematical field of differential geometry, a geometric flow, also called a geometric evolution equation, is a type of partial differential equation for a geometric object such as a Riemannian metric or an embedding. It is not a term with ...

s, minimal surfaces, the Willmore functional and Yang–Mills fields). His work focuses in particular on non-linear phenomena, formation of vortices, energy quantization and regularity issues.

Awards and recognition

In 1996 he received the Bronze Medal of the

, while in 2003 he was awarded the first

Stampacchia Medal The Stampacchia Gold Medal is an international prize awarded every three years by the Italian Mathematical Union (''Unione Matematica Italiana'' - ''UMI'' ) together with the Ettore Majorana Foundation (Erice), in recognition of outstanding contrib ...

. In 2002 he was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Beijing } Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...

, where he gave a talk on bubbling, quantization and regularity issues in geometric non-linear analysis.

Selected publications

* "Everywhere discontinuous Harmonic Maps into Spheres." ''

Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

'', 175 (1995), 197-226 * with F. Pacard: ''Linear and Nonlinear Aspects of Vortices.'' Birkhäuser 2000 * "Conservation laws for conformally invariant variational problems". '' Inventiones Math.'', 168 (2007), 1-22 * with R. Hardt: "Connecting rational homotopy type singularities of maps between manifolds". ''Acta Mathematica'', 200 (2008), 15-83 * "Analysis Aspects of Willmore Surfaces". ''Inventiones Math.'', 174 (2008), no. 1, 1-45 * with G. Tian: "The singular set of 1-1 Integral currents". ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...

'', 169 (2009), no. 3, 741-794 * with Y. Bernard: "Energy Quantization for Willmore Surfaces and Applications". ''Annals of Mathematics'', 180 (2014), no. 1, 87-136 * "A viscosity method in the min-max theory of minimal surfaces". ''Publications mathématiques de l'IHÉS'', 126 (2017), no. 1, 177-246

External links

Homepage, ETH Zürich
* {{DEFAULTSORT:Rivière, Tristan 1967 births Living people French mathematicians Mathematical analysts Academic staff of ETH Zurich Pierre and Marie Curie University alumni Courant Institute of Mathematical Sciences faculty Academic staff of the University of Paris