Introduction to Renormalization

University of Melbourne via Complexity Explorer

Overview

Discover the fascinating world of renormalization in "Introduction to Renormalization," offered by the University of Melbourne and provided by Complexity Explorer. This course unravels the intersections between seemingly unrelated areas like JPEG compression, economics, quantum gravity, and how simplifying complex descriptions links them all. Through this course, learners will explore how different fields approach the concept of simplification and abstraction, from the compression of images to the creation of economic models that overlook intricate psychological details, to the challenges in physics of observing the universe's most fundamental particles.

Guided by Simon DeDeo, students will embark on a journey from the basics of information theory and image processing to complex systems' critical notions such as emergence, coarse-graining, and effective theories. This tutorial requires only a preliminary familiarity with probabilities, with more advanced sections delving into algebra and basic calculus – adaptable based on the learner's comfort level. Additionally, solution sets featuring Python and Mathematica code are provided, allowing more advanced learners to gain practical experience in applying mathematics and data analysis techniques.

Participants will be introduced to model-building through simple examples like Markov Chains and Cellular Automata, alongside innovative concepts in complex systems such as the Krohn-Rhodes theorem and State-Space Compression. Furthermore, the course will bridge classical physics problems, like the Ising model and plasma physics, with modern challenges in machine learning and artificial intelligence, showcasing the broad applicability and significance of renormalization across different scientific domains.

This course belongs to the categories of Mathematics Courses and Cellular Automata Courses, reflecting its comprehensive coverage and interdisciplinary approach to understanding complex systems through the lens of renormalization.