In this note we list the bibliographic references for the Advanced Calculus 2 lectures given by Ricardo A. Sáenz at UNM, on Tuesday and Thursday, April 18 and 20.
Most of the material of the lectures can be found in the book Mathematics of Fractals, by Masaya Yamaguti, Masayoshi Hata and Jun Kigami, published by the AMS (1997). There you can find the proof of the existence and uniqueness of self-similar sets given a finite collection of contractions, and the proof of Hutchinson’s theorem.
The Hausdorff dimension was published by Felix Hausdorff in the paper “Dimension und äußeres Maß” (Dimension and Outer Measure) in Mathematische Annalen79 (1918), pp. 157-179. You can find the paper in the European Digital Mathematics Library: Dimension und äußeres Maß.
Ricardo A. Sáenz visited the University of New Mexico at Albuquerque from April 17 to April 21, and participated at several activities at the Department of Mathematics and Statistics. He taught the 3-hour minicourse Harmonic Analysis on Fractals to faculty and graduate students, gave talks at the Colloquium and the Analysis Seminar, and gave a pair of lectures at the course Advanced Calculus 2 to Junior and Senior undergraduates.
Together with Ma. Cristina Pereyra, they visited Taos Middle School, where they talk to approximately 160 8th-graders about Mathematics, the work of Mathematicians, and gave them activities on geometry.
He also talked to students about of Summer Research projects on fractals.
Ma. Cristina Pereyra visited the University of Colima from March 13 to March 17, and participated in several activities in the Facultad de Ciencias. She taught the 5-hour minicourse Dyadic Harmonic Analysis, gave lectures at both the Physics/Mathematics Colloquium and the CUICBAS Seminar, and attended the Fourier Seminar.
Moreover, she also attended an outreach visit at the Elementary School Liceo Llankay, where Ricardo A. Sáenz talk to 4-5 grade students about Mathematics and Mathematicians.
She also talked to Mathematics and Physics undergraduate mayors about UNM graduate programs.