From May 20 to 24, 2024, at the NSF-CBMS Regional Research Conference in Mathematical Sciences at Drake University in Des Moines, Iowa, Professor Jack Lutz from Iowa State University's Computer Science department will deliver a series of ten lectures on Algorithmic Fractal Dimensions. He will be giving two lectures each day.
Lutz's lectures will reflect his writing and research, while also incorporating insights from his esteemed colleagues. When asked about what he wants people to take away from the lectures, Lutz emphasized the influence of Algorithmic Fractal Dimensions as formidable instruments driving captivating revelations across diverse domains within computer science and mathematics.
Hosting this lecture series is Christopher Porter, an Associate Professor of Computer Science, Director of the Artificial Intelligence Program, and Co-Chair of Drake University's Mathematics & Computer Science Departments. This event is made possible through a partnership between the National Science Foundation and the Conference Board of Mathematical Sciences dedicated to funding conferences focused on important current research topics in mathematical sciences.
Exploring Algorithmic Fractal Dimensions
Algorithmic fractal dimensions, emerging at the beginning of the twenty-first century, have significantly developed in the past two decades. These dimensions represent inventive adaptations of traditional fractal dimensions, carrying profound implications across various domains, including computability theory, computational complexity, information theory, and number theory.
Each Algorithmic Fractal Dimension functions as a computational tool deeply rooted in theoretical computer science. These dimensions, rooted in rigorous mathematical foundations, are robust methodologies for quantifying information density hidden within diverse datasets. Their extensive applications span realms such as data compression, predictive analytics, artificial intelligence, and various aspects of society's intricate computational infrastructure.
The conference's lecture series begins with an introductory session that explores classical Hausdorff and packing dimensions, providing the essential backdrop for the ensuing in-depth discussions.
The lectures venture into the concept of effectivization, illustrating how it can be employed to define algorithmic versions of classical Hausdorff and packing dimensions. The speakers highlight the pragmatic utility of these dimensions and illuminate their role in amalgamating the Hausdorff dimension with subsequent information theories developed by Shannon and Kolmogorov.
Algorithmic dimensions will be employed to formulate fresh perspectives on the dimensions of individual points within Euclidean space. Special attention will be devoted to the Point-to-Set Principle, renowned for its unexpected applications in the domain of geometric measure theory.
Extending beyond the confines of pure mathematical theory, the lectures chart a course toward broader horizons. They delve into the expansive landscape of applications, encompassing computational complexity, information theory, and the intricate examination of Borel normal numbers. The conference fosters an interactive platform featuring open problem sessions and engaging discussions, facilitating the exploration of additional insights and collaborative opportunities.
“I’m excited about all the extra time that the conference will allow for spontaneous research discussions among participants,” added Lutz.
After the conclusion of the conference, Lutz plans to write a book on Algorithmic Fractal Dimensions, which the NSF-CBMS conference will publish. This forthcoming book will provide a structured and in-depth exploration of Algorithmic Fractal Dimensions, underling their profound significance in contemporary mathematics and computer science.
“The lectures and the book will highlight the unity and the beauty of this rapidly sprawling field,” says Lutz, emphasizing his commitment to celebrating the coherence and elegance that define Algorithmic Fractal Dimensions.
Fostering Diversity and Collaboration in Mathematical Sciences
Conference participants will represent diverse research communities, focusing on extending invitations to early-career researchers, individuals from historically underrepresented backgrounds, and institutions within the Midwest region. The primary audience comprises individuals involved in, or aspiring to be part of, research endeavors in the field and its practical applications, spanning from students to seasoned researchers.
This prioritization of early-career researchers and underrepresented groups underscores the conference's commitment to fostering inclusivity and diversity within the research community. Recognizing the significance of diverse perspectives, this approach aims to promote equity and broaden access to research benefits.
Moreover, the presence of attendees hailing from various research communities enriches the intellectual landscape of the conference. This cross-disciplinary exchange of ideas catalyzes the potential for innovative methodologies and fresh collaborations.