Edmund R. Michalik Distinguished Lecture Series
On November 3, 2023, Dr. Mason Porter, who is a professor in the Department of Mathematics at UCLA and an External Professor at the Santa Fe Institute, gave the 2023 Edmund R. Michalik Distinguished Lecture in the Mathematical Sciences to a packed room full of students and faculty from Pitt and Carnegie Mellon. There has been a great deal of recent interest in applying the rigorous methods of the mathematical and physical sciences to questions in social sciences. People will sometimes change their opinions on issues if they discuss them with acquaintances or through other social interactions. Dr. Porter has been at the forefront of developing mathematical models for how opinions in a population of people change over time. Key to beginning this type of modeling is how to characterize social interactions between people. Dr. Porter modeled these interactions as a formal graph, where each person is a node and there are lines between nodes which indicate a social interaction between the two people. He then proposed that at a given time, t, each person has an opinion, x, which is characterized as a number between 0 and 1. Each person can change her opinion based on an interaction with her neighbors. If their opinions do not differ substantially from her own (her "confidence" in their opinion), she will adjust her opinions to be closer to the neighbors. Otherwise, she ignores them. People with small confidence with only adjust to very close opinions to theirs ("living inside the bubble") while more tolerant people will be more flexible. He then showed that depending on the nature of the network and the openness to change, this system will either tend toward consensus (one large group with close opinions), polarization (two distinct groups), or fragmentation (more than two groups). The audience was enthusiastic about the material and there were many questions afterward. The lecture highlighted the point that you can find interesting mathematical questions in any discipline.
Recent Workshops at the Pitt Mathematical Research Center
Analysis and PDE on Fractals: A Conference in Memory of Professor Ka-Sing Lau
During the weekend of October 27 to October 29, 2023, we hosted an international conference in memory of our beloved colleague Ka-Sing Lau on Analysis and PDE on Fractals, which were the primary areas of his expertise. Speakers from Norway, Canada, and the US delivered talks on the state of the art of analysis on fractal spaces. The conference was preceded by a week-long minicourse on Analysis and PDEs on Fractals: Themes and Applications taught by Palle Jorgensen, from the University of Iowa. During the evening of October 27, Eveline Young (Mrs. Lau), Ka-Sing's daughters Helen and Elaine, and others reminisced about Ka-Sing; and on October 28, Eveline donated Ka-Sing's extensive mathematical library to our department, with priority given to graduate students.
Ka-Sing Lau (December 16, 1948 - October 12, 2021) was a Professor of Mathematics at the University of Pittsburgh (1986 -1999), Professor of Mathematics at the Chinese University of Hong Kong (1996 - 2017) where he was chair from 1996 to 2012, Professor Emeritus at the Chinese University of Hong Kong (2017 - 2021), and Adjunct Professor at the University of Pittsburgh (2017 - 2021). Ka-Sing worked in Functional Analysis, Harmonic Analysis, Fractal Geometry, Wavelet Theory, and Applied Probability. These areas go from the very classical to the more avant-garde topics in Analysis. Ka-Sing’s view of the field was both deep and broad. He was the leader at our Analysis seminar, and he had a tremendous influence in the development of Analysis both in Pittsburgh and in Hong Kong. Ka-Sing advised at least 24 Ph.D. students, and many master's students and post-Docs and published 154 research articles. His last paper appeared on October 8, 2021. Ka-Sing is remembered by everyone who knew and loved him for his friendship, kindness, joy of life, gentleness, enthusiasm, curiosity, optimism, courage, wisdom, and profound intelligence.
Mini-Course: Analysis on Fractals, Themes, and Applications
A leading theme of the talks is the strong and surprising connections between topics from a list of otherwise disparate areas of mathematics, including multi-resolutions, fractal structures, wavelets, and harmonic analysis. The topics will be made concrete via such themes as: the harmonic analysis of Cantor spaces (and measures) arising as fractals (including fractal dust), and iterated function systems (IFSs), as well as the methods used to study their harmonic analyses and wavelets that span both classical and fractal domains.
With a breadth of topics, the talks aim at a broader audience, including both established researchers and students. The interconnectedness, and the sharply focused nature of the topics, will prove beneficial to audiences who are new to the field. Click here for more information on this mini course.