Profesión: Matematica

 Área (s) de especialización: Analisis

Categoría en la Academia Colombiana de Ciencias Exactas, Físicas y Naturales

Miembro Correspondiente

Fecha de posesión, Miembro Correspondiente: Agosto 23, 2017.

Datos personales

Fecha de nacimiento: 5 de Julio de 1964

Lugar de nacimiento

Ciudad: Bogota

Departamento/Estado/Provincia: Cundinamarca

País: Colombia

Dirección particular: 7554 14th Ave NE, Seattle WA 98115 

Teléfonos Código país, código ciudad, numero 1-206-729-6606

Dirección institucional: Department of Mathematics, University of  Washington, Box 354350,  Seattle WA 98195-4350

Teléfonos. Código país, código ciudad, numero1-206-543-1173

Dirección electrónica (e-mail): 

Hoja de vida (Curriculum Vitae en línea): 

Página (sitio) web: 

Títulos académicos:

Sc. Matematicas, Universidad Nacional de Colombia, Bogot\’a, 1986

M Sc. Matematicas, Stanford University, 1989

Ph.D. Matematicas, Stanford University, 1992

Áreas de investigación: Analisis matematico: Teoria Geometrica de laMedida, Ecuciones Diferenciales Parciales y Analisis Armonico.

Reseña Biográfica (Extensa)

Premios y reconocimientos recibidos

2019-2020 Simons Foundation Fellowship

2016 Fellow of the American Mathematical Society

2016- Craig McKibben & Sarah Merner Professor in Mathematics

2015-2016 Guggenheim Foundation Fellowship

2012-2016 Robert R. & Elaine F. Phelps Professorship in Mathematics

2012-2013 Simons Foundation Fellowship

2010 Orador invitado al Congreso Internacional de Matematicas, seccion de Analisis, Hyderabad, India.

1996-2000 Alfred P. Sloan Research Fellowship

1994-1998 National Science Foundation Mathematical Sciences

Postdoctoral Research Fellowship

1991-1992 Alfred P. Sloan Doctoral Dissertation Fellowship

1987-1989 Graduate Study Fellowship, Universidad Nacional de


Publicaciones (lista completa)

  1. Surfaces with generalized second fundamental form in L2 are Lipschitz manifolds, J. Differential Geometry, 39, 1994, 65-101.
  2. Geometric conditions and existence of bilipschitz parameterizations, Duke Mathematical Journal, 77, 1995, 193-227.
  3. Compactness Properties of Weakly p-Harmonic Maps into Homogeneous Spaces, (with C.Y. Wang), Indiana Univ. Math. J., 44, 1995, 87-113.
  4. Harmonic Measure on Locally Flat Domains, (with C. Kenig), Duke Mathematical Journal, 87, 1997, 509-551.
  5. Doubling and Flatness: Geometry of Measures, Notices of the AMS, 44, 1997, 1087-1094.
  6. Free Boundary Regularity for Harmonic Measures and Poisson Kernels (with C. Kenig), Annals of Math. 150, 1999, 369-454.
  7. Reifenberg Flat Metric Spaces, Snowballs and Embeddings, (with G. David), Math. Ann., 315, 1999, 641-720.
  8. Asympotically Optimally Doubling Measures and Reifenberg Flat Sets with Vanishing Constant, (with G. David and C. Kenig), Comm. Pure Appl. Math, 54, 2001, 385-449.
  1. A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations, (with C. Kenig, H. Koch and J. Pipher), Adv. Math. 153, 2000, no. 2, 231–298. 10. Free Boundary Regularity for the Poisson Kernel, Proceedings of the Eleventh Tokyo Conference in Nonlinear PDE 2001.
  2. Free Boundary Regularity for the Poisson Kernel below the Continuous Threshold, (joint C. Kenig), Math. Research Letters, 9, 2002, 247-254.
  3. Poisson Kernel Characterization of Reifenberg Flat Chord Arc Domains, (with C. Kenig), Ann. Scient. Ec. Norm. Sup. 36, 2003, 323-401.
  4. On the free boundary regularity theorem of Alt and Caffarelli, (with C. Kenig), Discrete and Continuous Dynamical Systems 10, 2004, 397-422.
  5. Regularidad por debajo del umbral de continuidad, Bolet ́in de Matem ́aticas, 8, 2001, 60-67.
  6. On the free boundary regularity theorem of Alt and Caffarelli, Errata, (with C. Kenig), Discrete and Continuous Dynamical Systems 14, 2006, 857-859.
  7. Free boundary regularity below the continuous threshold: 2-phase problems (with C. Kenig), J. Reine Angew. Math. 596, 2006, 1-44.
  8. When do good parameterizations exit?, (extended abstract) Proceedings of the AWM and MSRI workshop Women in mathematics: the legacy of Ladyzhenskaya and Oleinik , May 2006.
  9. Stability of Lewis and Vogel’s result (with D. Preiss), Revista Matem ́atica Iberoamericana 23, 2007, 17-55.
  10. Two phase free boundary regularity problem for Harmonic measure and Poisson kernel Report No 33/2005, Mathematisches Forschungsinstitut Oberwolfach, 1898-1900.
  11. Regularity of measures with H ̈older density ratio Report No 35/2007, Mathematisches Forschungsin- stitut Oberwolfach, 2046-2048.
  12. A generalization of Reifenberg’s theorem in R3 (with G. David and T. DePauw), GAFA 18 2008, 1168-1235.
  13. Geometry of Measures: Harmonic Analysis meets Geometric Measure Theory Handbook of geometric analysis. No. 1, 449465, Adv. Lect. Math. (ALM), 7, Int. Press, Somerville, MA, 2008
  14. Boundary Structure and size in terms of interior and exterior harmonic measures in higher dimensions (with C. Kenig and D. Preiss), J. Amer. Math. Soc. 22 (2009), 771-796.
  15. On the smoothness of H ̈older-doubling measures (with D. Preiss and X. Tolsa), Calculus of Variations and PDE’s 35 (2009), 339-363.
  16. Divergence form operators in Reifenberg flat domains (with E. Milakis), Mathematische Zeitschrift 264 (2010), 15-41.
  17. The Cauchy problem for Schr ̈odinger flows into K ̈ahler manifolds (joint Kenig, Lamm, Pollack, Staffilani) Discrete and Continuous Dynamical Systems 27, 2010, 389-439.
  18. Potential Analysis meets Geometric Measure Theory, Proceedings of ICM 2010, III.
    28. Reifenberg parameterizations for sets with holes (joint G. David), Memoirs of the AMS, 215 2012.
  19. Harmonic Analysis on Chord Arc Domains (joint with E. Milakis and J. Pipher), J. Geom. Anal. 23 (2013), 2091–2157.
  20. Quasisymmetry and rectifiability of quasispheres (joint with M. Badger, J. Gill and S. Rohde), Trans. Amer. Math. Soc.366, (2014), 1413-1431.
  21. Perturbations of elliptic operators in chord arc domains (joint with E. Milakis and J. Pipher), Contemporary Mathematics, 612 (2014) Amer. Math. Soc., 143-161.
  22. Rectifiability via a square function and Preiss’ theorem (joint with X. Tolsa), to appear in International Mathematics Research Notices 2014; (DOI) 10.1093/imrn/rnu082
  23. Regularity of Almost Minimizers with Free Boundary (joint with G. David), Calculus of Variations and PDEs, 54 (2015), 455-524.
  24. Square Functions and the A∞ Property of Elliptic Measures (joint C. Kenig, B. Kirchheim, and J. Pipher) The Journal of Geometric Analysis, 26 (2016), 2383-2410. (DOI) 10.1007/s12220- 015-9630-6
  25. Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps (joint with J. Azzam and M. Badger), Adv. Math., 275 (2015), 195-259.
  26. Wasserstein Distance and the Rectifiability of Doubling Measures: Part I (joint with J. Azzam and G. David), Mathematische Annalen, 364 (2016), 151-224.
  27. Wasserstein Distance and the Rectifiability of Doubling Measures: Part II (joint with J. Azzam and G. David) Mathematische Zeitschrift, 286 (2017), 861-891.
  28. Structure of sets which are well approximated by zero sets of harmonic polynomials (joint M. Badger and M. Engelstein) Analysis & PDE 10-6 (2017), 1455–1495. DOI 10.2140/apde.2017.10.1455 (arXiv:1509.03211)

Articles Acceptados

  1. A new characterization of chord-arc domains (joint J. Azzam, S. Hofmann, J.M. Martell, and K. Nystr ̈om) to appear in JEMS.
  2. A∞ implies NTA for a class of variable coefficient elliptic operators (joint S. Hofmann and J.M. Martell) (arXiv:1611.09561) to appear in Journal of Differential Equations.
  3. Boundary rectifiability and elliptic operators with W1,1 coefficients (joint with Z. Zhao) to appear in Advances in Calculus of Variations.
  4. Geometric measure theory – Some recent applications to appear in The Notices of the AMS in April 2019.

Manuscritos siendo considerados para publicacion:

  1. Free boundary regularity for almost-minimizers (joint G. David and M. Engelstein)(arXiv:1702.06580) 44. Uniform rectifiability and elliptic operators with small Carleson norm (joint S. Hofmann, J.M. Martell, S. Mayboroda, and Z. Zhao) arXiv:1710.06157
  2. Regularity of the singular set in a two-phase problem for harmonic measure with H ̈older data (joint M. Badger and M. Engelstein) arXiv:1807.08002
  3. Characterization of rectifiable measures in terms of α-numbers (joint J. Azzam and X. Tolsa) arXiv:1808.07661