52 years (a calendar round) of the Henkin-Ramirez kernel,
a tribute to Professor Ramírez de Arellano's career

La historia del Departamento de Matemáticas del Cinvestav está marcada por la calidad de sus fundadores. Así, podemos mencionar tres resultados asociados al departamento que en su tiempo cambiaron el área donde fueron publicados: Las Relaciones de Ádem descubiertas por el profesor José Ádem, fundador del departamento, el Espectro de Brown y Gitler construido por los profesores Edgar H. Brown Jr. y Samuel Gitler, el último también fundador del departamento, y los Núcleos de Henkin y Ramírez descubiertos casi simultáneamente en 1969 por los profesores Gennadi M. Henkin y Enrique Ramírez de Arellano, cuando eran estudiantes de doctorado con 27 y 32 años de edad, respectivamente.

Desde el descubrimiento de los Núcleos de Henkin y Ramírez, ha acaecido una Rueda Calendárica de 52 años (léase, un siglo maya o dos generaciones), por lo cual nos corresponde ahora celebrar la carrera académica del profesor Enrique Ramírez de Arellano.

Lunes 20 de septiembre de 2021

• Palabras de bienvenida
  9:45am (GTM -5)
• R. Michael Range
  Universidad de Albany, SUNY, EUA
  10:00am (GTM -5)

  From Cauchy, via Bochner-Martinelli and Leray, to the Henkin-Ramirez Kernel

  Resumen: We begin by recalling Enrique Ramirez's days at the University of Göttingen in the late 1960s, and the roots of my connection to him and his work. We then look back at some of the key results in the development of integral representations in multidimensional complex analysis up to the early 1960s. Next, we explain the impact that the Henkin-Ramirez kernel and its subsequent variations and generalizations had on the field in the 1970s and 1980s. We conclude by briefly discussing some unsolved problems that relate to this work, including some suggestions to encourage the next generation to attempt to make progress on them.

• R. Mike Porter
  Cinvestav del IPN, México
  11:00am (GTM -5)

  A quaternionic version of the Mathieu functions

• Nikolai Vasilevski
  Cinvestav del IPN, México
  12:00pm (GTM -5)

  Poly-analytic function spaces

• Eduardo S. Zeron
  Cinvestav del IPN, México
  13:00pm (GTM -5)

  Removable Singularities and Devil Staircase Functions

  Resumen: We generalise some ideas of Professor Chirka on removable singularities for pointwise ω-Hölder holomorphic functions. We consider in particular functions for which |f(z)−f(ξ)| is locally less than Λ_ξω(|z−ξ|) for some positive constant Λ_ξ>0 independent of the first variable z. Moreover, using the properties of removable singularities we deduce some results on the local growth of continuous devil’s staircase functions.

Martes 21 de septiembre de 2021

• John Erik Fornæss
  NTNU, Noruega
  10:00am (GTM -5)

  Henkin-Ramirez kernels

  Resumen: I will discuss Henkin-Ramirez reproducing kernels in the weakly pseudoconvex case.

• Xavier Gómez-Mont
  CIMAT, México
  11:00am (GTM -5)

  On the non-periodic part of the monodromy of plane curves singularities

• Araceli Medina-Bonifant
  Universidad de Rhode Island, EUA
  12:00pm (GTM -5)

  Rational Quadratic Real Maps

  Resumen: En esta plática discutiremos mapeos reales cuadráicos racionales, con ambos, coeficientes reales y puntos críticos reales. El espacio de moduli para estos mapeos es un anillo suave. En el caso críticamente finito, el “algorítmo de retroceso iterado de Thurston” puede llevarse acabo explícitamente y exhibirse visualmente para combinaciones arbitrarias. (Trabajo en progreso con John Milnor y Scott Sutherland).

Miércoles 22 de septiembre de 2021

• S. Alberto Verjovski
  UNAM, México
  10:00am (GTM -5)

  Intersection of quadrics in ℂⁿ, convex polytopes, complex manifolds and toric varieties 1^a parte

  Intersection of quadrics in ℂⁿ, convex polytopes, complex manifolds and toric varieties 2^a parte

• Josué Ramírez Ortega
  Universidad Veracruzana, México
  11:00am (GTM -5)

  Núcleos Reproductores, Espacios y Operadores de Toeplitz

• Fermín Acosta Magallanes
  IPN, México
  12:00pm (GTM -5)

  Estimates for the Cauchy-Riemann equations on singular complex spaces

Jueves 23 de septiembre de 2021

• Joseph J. Kohn
  Universidad de Princeton, EUA
  10:00am (GTM -5)

  Solutions of PDE’s and resolution of singularities

  Resumen: This lecture is concerned with the relationship between the operator ∂ and the study of the singularities of complex analytic varieties. [complete abstract].

• Lino F. Reséndis
  UAM, México
  11:00am (GTM -5)

  Bicomplex Bergman Projection

• Luis Manuel Tovar
  IPN, México
  12:00pm (GTM -5)

  Bicomplex Cousin’s Problems I and II

  Resumen: In this talk we present the bicomplex version of Cousin's problems I and II as well as its relationships with the bicomplex meromorphic version of Weierstrass and Mittag-Leffler's theorems. We establish relations between these theorems and the Cousin's problems, which reveal peculiarities of the bicomplex meromorphic function theory.

• Enrique Ramirez de Arellano
  Cinvestav del IPN, México
  13:00pm (GTM -5)

  Memorias de una vida académica