Note. This page lists ISQGD Distinguished Lecture Series Records. Click “Abstract” to expand or collapse the abstract.
-
February 6, 2026 — ISQGD–DL07 — Distinguished Lecture by Dr. William O'Regan (The University of British Columbia, Canada)Title: Approximate incidence geometry in the plane
Abstract
Given a finite collection of points and a finite collection of lines in the plane, the theorem of Szemeredi and Trotter gives a sharp upper bound for the number of incidences between the points and lines. What if we instead consider infinite collections of points and lines and consider some form of fractal dimension(s)? Is it possible to gain a similar shaped looking bounds? In this talk we survey the rapidly developing literature on this class of problems. Some of the talk will be based on joint with with Ciprian Demeter.
-
January 30, 2026 — ISQGD–DL06 — Distinguished Lecture by Professor Patrick D. Shipman (The University of Arizona, USA)Title: Geometry, Fractals, and Dynamics from Nucleation and Growth
Abstract
We begin by observing patterns, motion, fractals, and a variety of geometric structures in a series of chemical experiments ranging from plant pigments under the influence of atmospheric pollutants to microtornados. A common theme of these experiments is nucleation from the vapor or liquid phase of solid nanoparticles, followed by their subsequent growth. Applications of size-controlled, uniform nanoparticles are vast. Yet the chemical mechanisms governing particle formation—and how to control particle size distributions—have long remained an unsolved problem in materials chemistry. We introduce Bayesian-enabled mechanism-enabled population balance modeling (BE-MEPBM), which allows us to determine previously inaccessible chemical mechanisms directly from measured particle size distributions. Mathematically, BE-MEPBM is based on coupled integro–partial differential equations describing nucleation, growth, and transport, and can be viewed as an infinite-dimensional dynamical system evolving in time (and, in many cases, space). Determining these parameters from experimental data leads naturally to a PDE-constrained inverse problem. By embedding the model within a Bayesian framework, we obtain uncertainty-aware reconstructions of kinetic mechanisms, posterior distributions over parameters, and quantitative assessments of identifiability and predictive reliability. Many of these experiments originated in discussions on developing engaging activities for applied mathematics courses, where chemical pattern formation serves as a concrete setting for dynamical systems, inverse problems, and uncertainty quantification. We close with reflections on this pedagogical endeavor and its role in connecting mathematical structure to visually compelling physical phenomena.
-
January 23, 2026 — ISQGD–DL05 — Distinguished Lecture by Professor Jonathan Fraser (University of St Andrews, UK)Title: Dimension interpolation and the geometry of fractals
Abstract
Dimension theory is an important sub-field of fractal geometry where one attempts to classify and describe fractal objects by assigning to them a “dimension”, that is, a quantity which reflects some geometric or analytic features of the object. It turns out there are many interesting and equally natural ways to define the “dimension” of a fractal, and one of the joys of the subject is in understanding how these different notions connect. Dimension interpolation is a relatively new programme where one tries to define “dimension functions” which live in-between classical notions of dimension, with the broad aim of gleaning more nuanced information about the object and a more holistic view of the field in general. I will survey some recent developments in this area.
-
January 16, 2026 — ISQGD–DL04 — Distinguished Lecture by Professor Stefano Galatolo (Università di Pisa, Italy)Title: Extreme events, local dimension and hitting-time statistics in deterministic and random dynamical systems
Abstract
In dynamical systems theory, extreme events have been extensively studied and related to the statistical and asymptotical behavior of waiting (or hitting) times to small targets. In this talk, I will review some recent and less recent results in this direction, showing how power-law behavior of waiting times is linked to the local (fractal) dimension of the invariant measure, both in the autonomous and in the non-autonomous setting. Time permitting, we will move to more refined asymptotic estimates and also discuss the limiting distribution of the waiting time for extreme events. In particular, I will present recent results in this direction for stochastic differential equations.
-
December 19, 2025 — ISQGD–DL03 — Distinguished Lecture by Professor Balázs Bárány (Budapest University of Technology and Economics, Hungary)Title: Exponential separation of analytic self-conformal sets on the real line
Abstract
In a recent article, Rapaport showed that there is no dimension drop for exponentially separated analytic IFSs on the real line. We show that the set of exponentially separated IFSs in the space of analytic IFSs contains an open and dense set in the C2 topology. Moreover, we provide sufficient conditions for the IFS to be exponentially separated, thereby allowing us to construct explicit examples that are exponentially separated. The key technical tool is the introduction of the dual IFS, which we believe has significant interest in its own right. As an application, we also characterise when an analytic IFS can be conjugated to a self-similar IFS. This is joint work with István Kolossváry and Sascha Troscheit.
-
December 12, 2025 — ISQGD–DL02 — Distinguished Lecture by Professor Peter Massopust (Technical University of Munich, Germany)Title: Fractal Interpolation and Quaternions
Abstract
In recent years, quaternionic methodologies have found their way into many applications, one of which is digital signal processing. The main idea is to use the multidimensionality of the quaternions to model signals with multiple channels or images with multiple color values, and to use the underlying algebraic structure of quaternions to operate on these signals. On the other hand, fractal interpolation has been employed successfully in numerous applied settings over the last decades. This talk focuses on fractal interpolation in the quaternionic setting. Properties and main results are presented.
-
December 5, 2025 — ISQGD–DL01 — Inaugural Lecture by Professor Palle Jorgensen (University of Iowa, USA)Title: Harmonic analysis, frames, and algorithms for fractal IFS L2 spaces via infinite products of projections
Abstract
We present new results at the crossroads of spectral theory for operators in Hilbert space, optimization, large sparse systems, and the geometry of fractals arising from iterated function systems (IFS), together with new developments in fractal harmonic analysis. In particular, we introduce a new recursive iteration scheme that takes as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and associated error estimates.