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

The history of Cinvestav's Department of Mathematics is marked by the quality of its founders. We can mention three results associated with the department that revolutionised their respective fields: Adem relations discovered by Professor José Ádem, founder of the department, the Brown-Gitler Spectrum introduced by Professors Edgar H. Brown Jr. and Samuel Gitler, the latter also founder of the department, and the Henkin-Ramírez kernel discovered almost simultaneously in 1969 by Professors Gennadi M. Henkin and Enrique Ramírez de Arellano, while they were PhD students aged 27 and 32, respectively.

It has passed a 52-year Calendar Round (i.e., a Mayan century or two generations) since the discovery of the Henkin-Ramírez kernel, so it is now up to us to celebrate Professor Enrique Ramírez de Arellano's academic career.

Monday, September 20th, 2021

• Welcoming remarks
  9:45am (GTM -5)
• R. Michael Range
  University at Albany, SUNY, USA
  10:00am (GTM -5)

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

  Abstract: 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-IPN, Mexico
  11:00am (GTM -5)

  A quaternionic version of the Mathieu functions

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

  Poly-analytic function spaces

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

  Removable Singularities and Devil Staircase Functions

  Abstract: 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.

Tuesday, September 21st, 2021

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

  Henkin-Ramirez kernels

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

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

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

• Araceli Medina-Bonifant
  The University of Rhode Island, USA
  12:00pm (GTM -5)

  Rational Quadratic Real Maps

  Abstract: 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).

Wednesday, September 22nd, 2021

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

  Intersection of quadrics in ℂⁿ, convex polytopes, complex manifolds and toric varieties Part 1

  Intersection of quadrics in ℂⁿ, convex polytopes, complex manifolds and toric varieties Part 2

• Josué Ramírez Ortega
  Universidad Veracruzana, Mexico
  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

Thursday, September 23rd, 2021

• Joseph J. Kohn
  Princeton University, USA
  10:00am (GTM -5)

  Solutions of PDE’s and resolution of singularities

  Abstract: 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, Mexico
  11:00am (GTM -5)

  Bicomplex Bergman Projection

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

  Bicomplex Cousin’s Problems I and II

  Abstract: 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-IPN, Mexico
  13:00pm (GTM -5)

  Memories of an academic life