The Bôcher Memorial Prize was founded by the
American Mathematical Society in 1923 in memory of
Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in
analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Coefficients of schlicht functions. I.Duke Math. J. 10 (1943), 611-635
Coefficients of schlicht functions. II. Duke Math. J. 12 (1945), 107-125
Coefficients of schlicht functions. III. Proc. Natl. Acad. Sci. U.S.A. 32 (!946), 111-116
Coefficients of schlicht functions. IV. Proc. Natl. Acad. Sci. U.S.A. 35 (1949), 143-150.
1953
Norman Levinson for "his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years"
1959
Louis Nirenberg for "his work in partial differential equations"
Bernoulli shifts with the same entropy are isomorphic.Adv. Math. 4 (1970), 337-352.
1979
Alberto Calderón for "his fundamental work on the theory of singular integrals and partial differential equations" and in particular
Cauchy integrals on Lipschitz curves and related operators. Proc. Natl. Acad. Sci. U.S.A. 74 (1977), 1324-1327.
1984
Luis Caffarelli for "his deep and fundamental work in nonlinear partial differential equations, in particular his work on free boundary problems, vortex theory and regularity theory"[1]
1984
Richard Melrose for "his solution of several outstanding problems in diffraction theory and scattering theory and for developing the analytical tools needed for their resolution"
1989
Richard Schoen for "his work on the application of partial differential equations to differential geometry," in particular
Conformal deformation of a Riemannian metric to constant scalar curvature.J. Diff. Geom. 20 (1984), 479-495.
The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp. [written with
Sergiu Klainerman
Examples of naked singularity formation in the gravitational collapse of a scalar field. Ann. of Math. (2) 140 (1994), no. 3, 607–653.
The instability of naked singularities in the gravitational collapse of a scalar field. Ann. of Math. (2) 149 (1999), no. 1, 183–217
The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp. [written with
Demetrios Christodoulou
Smoothing estimates for null forms and applications. Duke Math. J. 81 (1995), no. 1, 99–133 [with
Matei Machedon
1999
Thomas Wolff for "his work in harmonic analysis," "harmonic measure, and unique continuation," including
Counterexamples with harmonic gradients in ℝ3. Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), 321–384, Princeton Math. Ser., 42, Princeton Univ. Press, Princeton, NJ, 1995
An improved bound for Kakeya type maximal functions. Rev. Mat. Iberoamericana 11 (1995), no. 3, 651–674.
A Kakeya-type problem for circles. Amer. J. Math. 119 (1997), no. 5, 985–1026
On global existence and scattering for the wave maps equations. Amer. J. Math. 123 (2001) no. 1, 37-77
in addition to his "important work on Strichartz estimates for wave equations with rough coefficients and applications to quasilinear wave equations, as well as his many deep contributions to unique continuation problems"
Global regularity of wave maps I. Small critical Sobolev norm in high dimensions. Internat. Math. Res. Notices (2001), no. 6, 299-328
Global regularity of wave maps II. Small energy in two dimensions. Comm. Math. Phys. 2244 (2001), no. 2, 443-544.
in addition to "his remarkable series of papers, written in collaboration with J. Colliander, M. Keel, G. Staffilani, and H. Takaoka, on global regularity in optimal Sobolev spaces for KdV and other equations, as well as his many deep contributions to Strichartz and bilinear estimates."
Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math. 49 (1996), no. 4, 323–359.
Gradient estimates and blow-up analysis for stationary harmonic maps. Ann. of Math. (2) 149 (1999), no. 3, 785–829.
in addition to other "fundamental contributions to our understanding of the Ginzburg-Landau (GL) equations with a small parameter" and "many deep contributions to harmonic maps and liquid crystals."
2005
Frank Merle for "his fundamental work in the analysis of nonlinear dispersive equations" including:
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Ann. of Math. (2) 155 (2002), no. 1, 235–280 [written with
Yvan Martel
Blow up in finite time and dynamics of blow up solutions for the L2-critical generalized KdV equation.J. Amer. Math. Soc. 15 (2002), no. 3, 617–664 [written with
Yvan Martel
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation.Invent. Math. 156 (2004), no. 3, 565–672 [with
Pierre Raphael
Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem. Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford, 2000. xii+250 pp.
Vanishing viscosity solutions of nonlinear hyperbolic systems. Ann. of Math. (2) 161 (2005), no. 1, 223–342 [written with
Stefano Bianchini
2008
Charles Fefferman for "his many fundamental contributions to different areas of analysis" including
A sharp form of Whitney's extension theorem. Ann. of Math. (2) 161 (2005), no. 1, 509–577
Whitney's extension problem for Cm. Ann. of Math. (2) 164 (2006), no. 1, 313–359.
2008
Carlos Kenig for "his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE" including:
Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. 46 (1993), no. 4, 527–620 [written with
Gustavo Ponce and
Luis Vega
Global well-posedness of the Benjamin-Ono equation in low-regularity spaces. J. Amer. Math. Soc. 20 (2007), no. 3, 753–798 [written with
Alexandru Ionescu
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation.Acta Math. 201 (2008), no. 2, 147–212 [written with
Frank Merle
2011
Assaf Naor for "introducing new invariants of metric spaces and for applying his new understanding of the distortion between various metric structures to theoretical computer science" and his "remarkable work [...] on a lower bound in the sparsest cut problem" including
Metric cotype. Ann. of Math. (2) 168 (2008), no. 1, 247–298 [written with
Manor Mendel
Euclidean distortion and the sparsest cut. J. Amer. Math. Soc. 21 (2008), no. 1, 1–21 [written with
Sanjeev Arora and
James R. Lee
Compression bounds for Lipschitz maps from the Heisenberg group to L1. Acta Math. 207 (2011), no. 2, 291–373 [written with
Jeff Cheeger and
Bruce Kleiner
2011
Gunther Uhlmann for "his fundamental work on inverse problems" including
The Calderón problem with partial data. Ann. of Math. (2) 165 (2007), no. 2, 567–591 [written with
Carlos Kenig and
Johannes Sjöstrand
The Calderón problem with partial data in two dimensions. J. Amer. Math. Soc. 23 (2010), no. 3, 655–691 [written with
Oleg Imanuvilov and
Masahiro Yamamoto
as well as "incisive work on boundary rigidity with L. Pestov and with P. Stepanov and on nonuniqueness (also known as cloaking) with A. Greenleaf, Y. Kurylev, and M. Lassas."
2014
Simon Brendle for "his outstanding solutions of long standing problems in geometric analysis", including
Manifolds with 1/4-pinched curvature are space forms. J. Amer. Math. Soc. 22 (2009), no. 1, 287–307. [written with
Richard Schoen
Embedded minimal tori in S3 and the Lawson conjecture. Acta Math. 211 (2013), no. 2, 177–190.
in addition to "his deep contributions to the study of the Yamabe equation."
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces. Invent. Math. 194 (2013), 381-513.
2020
Camillo De Lellis for "his innovative point of view on the construction of continuous dissipative solutions of the Euler equations, which ultimately led to Isett's full solution of the Onsager conjecture, and his spectacular work in the regularity theory of minimal surfaces, where he completed and improved Almgren's program" including:
Dissipative continuous Euler flows. Invent. Math. 193 (2013), no. 2, 377–407 [written with
László Székelyhidi
Regularity of area minimizing currents III: blow-up. Ann. of Math. (2) 183 (2016), no. 2, 577–617 [written with
Emanuele Spadaro
2020
Lawrence Guth for "his deep and influential development of algebraic and topological methods for partitioning the Euclidean space and multi-scale organization of data, and his powerful applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations" including:
A restriction estimate using polynomial partitioning. J. Amer. Math. Soc. 29 (2016), no. 2, 371–413
A sharp Schrödinger maximal estimate in ℝ2. Ann. of Math. (2) 186 (2017), no. 2, 607–640 [written with
Xiumin Du and
Xiaochun Li
2020
Laure Saint-Raymond for "her transformative contributions to kinetic theory, fluid dynamics, and Hilbert's sixth problem on 'developing mathematically the limiting processes...which lead from the atomistic view to the laws of motion of continua,'" including:
The Brownian motion as the limit of a deterministic system of hard-spheres. Invent. Math. 203 (2016), no. 2, 493–553 [written with
Thierry Bodineau and
Isabelle Gallagher
Mathematical study of degenerate boundary layers: a large scale ocean circulation problem. Mem. Amer. Math. Soc. 253 (2018), no. 1206, vi+105 pp. [written with
Anne-Laure Dalibard
2023
Frank Merle,
Pierre Raphaël,
Igor Rodnianski, and
Jérémie Szeftel for "their groundbreaking work establishing the existence of blow-up solutions to the defocusing NLS equation in some supercritical regimes and to the compressible Euler and Navier-Stokes equations" including
On the implosion of a compressible fluid I: smooth self-similar inviscid profiles. Annals of Mathematics 196 (2022);
On the implosion of a compressible fluid II: singularity formation. Annals of Mathematics 196 (2022); and
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Inventiones Mathematicae 227 (2022).
^Caffarelli, Luis A. (1977). "The regularity of free boundaries in higher dimensions". Acta Mathematica. 139 (0): 155–184.
doi:
10.1007/BF02392236.
ISSN0001-5962.
The Bôcher Memorial Prize was founded by the
American Mathematical Society in 1923 in memory of
Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in
analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Coefficients of schlicht functions. I.Duke Math. J. 10 (1943), 611-635
Coefficients of schlicht functions. II. Duke Math. J. 12 (1945), 107-125
Coefficients of schlicht functions. III. Proc. Natl. Acad. Sci. U.S.A. 32 (!946), 111-116
Coefficients of schlicht functions. IV. Proc. Natl. Acad. Sci. U.S.A. 35 (1949), 143-150.
1953
Norman Levinson for "his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years"
1959
Louis Nirenberg for "his work in partial differential equations"
Bernoulli shifts with the same entropy are isomorphic.Adv. Math. 4 (1970), 337-352.
1979
Alberto Calderón for "his fundamental work on the theory of singular integrals and partial differential equations" and in particular
Cauchy integrals on Lipschitz curves and related operators. Proc. Natl. Acad. Sci. U.S.A. 74 (1977), 1324-1327.
1984
Luis Caffarelli for "his deep and fundamental work in nonlinear partial differential equations, in particular his work on free boundary problems, vortex theory and regularity theory"[1]
1984
Richard Melrose for "his solution of several outstanding problems in diffraction theory and scattering theory and for developing the analytical tools needed for their resolution"
1989
Richard Schoen for "his work on the application of partial differential equations to differential geometry," in particular
Conformal deformation of a Riemannian metric to constant scalar curvature.J. Diff. Geom. 20 (1984), 479-495.
The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp. [written with
Sergiu Klainerman
Examples of naked singularity formation in the gravitational collapse of a scalar field. Ann. of Math. (2) 140 (1994), no. 3, 607–653.
The instability of naked singularities in the gravitational collapse of a scalar field. Ann. of Math. (2) 149 (1999), no. 1, 183–217
The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp. [written with
Demetrios Christodoulou
Smoothing estimates for null forms and applications. Duke Math. J. 81 (1995), no. 1, 99–133 [with
Matei Machedon
1999
Thomas Wolff for "his work in harmonic analysis," "harmonic measure, and unique continuation," including
Counterexamples with harmonic gradients in ℝ3. Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), 321–384, Princeton Math. Ser., 42, Princeton Univ. Press, Princeton, NJ, 1995
An improved bound for Kakeya type maximal functions. Rev. Mat. Iberoamericana 11 (1995), no. 3, 651–674.
A Kakeya-type problem for circles. Amer. J. Math. 119 (1997), no. 5, 985–1026
On global existence and scattering for the wave maps equations. Amer. J. Math. 123 (2001) no. 1, 37-77
in addition to his "important work on Strichartz estimates for wave equations with rough coefficients and applications to quasilinear wave equations, as well as his many deep contributions to unique continuation problems"
Global regularity of wave maps I. Small critical Sobolev norm in high dimensions. Internat. Math. Res. Notices (2001), no. 6, 299-328
Global regularity of wave maps II. Small energy in two dimensions. Comm. Math. Phys. 2244 (2001), no. 2, 443-544.
in addition to "his remarkable series of papers, written in collaboration with J. Colliander, M. Keel, G. Staffilani, and H. Takaoka, on global regularity in optimal Sobolev spaces for KdV and other equations, as well as his many deep contributions to Strichartz and bilinear estimates."
Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math. 49 (1996), no. 4, 323–359.
Gradient estimates and blow-up analysis for stationary harmonic maps. Ann. of Math. (2) 149 (1999), no. 3, 785–829.
in addition to other "fundamental contributions to our understanding of the Ginzburg-Landau (GL) equations with a small parameter" and "many deep contributions to harmonic maps and liquid crystals."
2005
Frank Merle for "his fundamental work in the analysis of nonlinear dispersive equations" including:
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Ann. of Math. (2) 155 (2002), no. 1, 235–280 [written with
Yvan Martel
Blow up in finite time and dynamics of blow up solutions for the L2-critical generalized KdV equation.J. Amer. Math. Soc. 15 (2002), no. 3, 617–664 [written with
Yvan Martel
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation.Invent. Math. 156 (2004), no. 3, 565–672 [with
Pierre Raphael
Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem. Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford, 2000. xii+250 pp.
Vanishing viscosity solutions of nonlinear hyperbolic systems. Ann. of Math. (2) 161 (2005), no. 1, 223–342 [written with
Stefano Bianchini
2008
Charles Fefferman for "his many fundamental contributions to different areas of analysis" including
A sharp form of Whitney's extension theorem. Ann. of Math. (2) 161 (2005), no. 1, 509–577
Whitney's extension problem for Cm. Ann. of Math. (2) 164 (2006), no. 1, 313–359.
2008
Carlos Kenig for "his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE" including:
Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. 46 (1993), no. 4, 527–620 [written with
Gustavo Ponce and
Luis Vega
Global well-posedness of the Benjamin-Ono equation in low-regularity spaces. J. Amer. Math. Soc. 20 (2007), no. 3, 753–798 [written with
Alexandru Ionescu
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation.Acta Math. 201 (2008), no. 2, 147–212 [written with
Frank Merle
2011
Assaf Naor for "introducing new invariants of metric spaces and for applying his new understanding of the distortion between various metric structures to theoretical computer science" and his "remarkable work [...] on a lower bound in the sparsest cut problem" including
Metric cotype. Ann. of Math. (2) 168 (2008), no. 1, 247–298 [written with
Manor Mendel
Euclidean distortion and the sparsest cut. J. Amer. Math. Soc. 21 (2008), no. 1, 1–21 [written with
Sanjeev Arora and
James R. Lee
Compression bounds for Lipschitz maps from the Heisenberg group to L1. Acta Math. 207 (2011), no. 2, 291–373 [written with
Jeff Cheeger and
Bruce Kleiner
2011
Gunther Uhlmann for "his fundamental work on inverse problems" including
The Calderón problem with partial data. Ann. of Math. (2) 165 (2007), no. 2, 567–591 [written with
Carlos Kenig and
Johannes Sjöstrand
The Calderón problem with partial data in two dimensions. J. Amer. Math. Soc. 23 (2010), no. 3, 655–691 [written with
Oleg Imanuvilov and
Masahiro Yamamoto
as well as "incisive work on boundary rigidity with L. Pestov and with P. Stepanov and on nonuniqueness (also known as cloaking) with A. Greenleaf, Y. Kurylev, and M. Lassas."
2014
Simon Brendle for "his outstanding solutions of long standing problems in geometric analysis", including
Manifolds with 1/4-pinched curvature are space forms. J. Amer. Math. Soc. 22 (2009), no. 1, 287–307. [written with
Richard Schoen
Embedded minimal tori in S3 and the Lawson conjecture. Acta Math. 211 (2013), no. 2, 177–190.
in addition to "his deep contributions to the study of the Yamabe equation."
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces. Invent. Math. 194 (2013), 381-513.
2020
Camillo De Lellis for "his innovative point of view on the construction of continuous dissipative solutions of the Euler equations, which ultimately led to Isett's full solution of the Onsager conjecture, and his spectacular work in the regularity theory of minimal surfaces, where he completed and improved Almgren's program" including:
Dissipative continuous Euler flows. Invent. Math. 193 (2013), no. 2, 377–407 [written with
László Székelyhidi
Regularity of area minimizing currents III: blow-up. Ann. of Math. (2) 183 (2016), no. 2, 577–617 [written with
Emanuele Spadaro
2020
Lawrence Guth for "his deep and influential development of algebraic and topological methods for partitioning the Euclidean space and multi-scale organization of data, and his powerful applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations" including:
A restriction estimate using polynomial partitioning. J. Amer. Math. Soc. 29 (2016), no. 2, 371–413
A sharp Schrödinger maximal estimate in ℝ2. Ann. of Math. (2) 186 (2017), no. 2, 607–640 [written with
Xiumin Du and
Xiaochun Li
2020
Laure Saint-Raymond for "her transformative contributions to kinetic theory, fluid dynamics, and Hilbert's sixth problem on 'developing mathematically the limiting processes...which lead from the atomistic view to the laws of motion of continua,'" including:
The Brownian motion as the limit of a deterministic system of hard-spheres. Invent. Math. 203 (2016), no. 2, 493–553 [written with
Thierry Bodineau and
Isabelle Gallagher
Mathematical study of degenerate boundary layers: a large scale ocean circulation problem. Mem. Amer. Math. Soc. 253 (2018), no. 1206, vi+105 pp. [written with
Anne-Laure Dalibard
2023
Frank Merle,
Pierre Raphaël,
Igor Rodnianski, and
Jérémie Szeftel for "their groundbreaking work establishing the existence of blow-up solutions to the defocusing NLS equation in some supercritical regimes and to the compressible Euler and Navier-Stokes equations" including
On the implosion of a compressible fluid I: smooth self-similar inviscid profiles. Annals of Mathematics 196 (2022);
On the implosion of a compressible fluid II: singularity formation. Annals of Mathematics 196 (2022); and
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Inventiones Mathematicae 227 (2022).
^Caffarelli, Luis A. (1977). "The regularity of free boundaries in higher dimensions". Acta Mathematica. 139 (0): 155–184.
doi:
10.1007/BF02392236.
ISSN0001-5962.