Introduction to Aggregation-Diffusion Models On (non)Euclidean Spaces

Abstract

This lecture series introduces aggregation-diffusion models, starting from their basic background and historical development and continuing toward recent research directions. Aggregation-diffusion models are, as the name suggests, mathematical models that describe through PDEs how the density of particles evolves over time under the competition between aggregation, the tendency of particles to gather due to interactions among them, and diffusion, the tendency of particles to spread due to entropy. These models are deeply connected to the variational and optimal-transport framework developed through the works of Carrillo, McCann, Villani, Ambrosio, Gigli, Savaré, and others. From this point of view, the evolution equation can often be interpreted as the Wasserstein gradient flow of a free energy functional consisting of an interaction energy and an entropy. This variational structure plays an important role in understanding pattern formation, steady states, and the competition between aggregation and diffusion. In particular, this lecture series will not restrict aggregation-diffusion models to Euclidean space, but will also discuss them on spheres, hyperbolic spaces, and more general Riemannian manifolds. On compact manifolds such as spheres, we will examine how the compactness of the underlying space affects the structure of steady states and ground states. On the other hand, on hyperbolic spaces and more general Cartan–Hadamard manifolds, we will investigate how volume growth induced by negative curvature affects the existence of global minimizers.

Lectures

July 27(Mon)

1. Lecture 1. TBA, 10:00 – 11:30
2. Lecture 2. TBA, 14:00 – 15:30
3. Lecture 3. TBA, 16:00 – 17:30

July 28(Tue)

4. Lecture 4. TBA, 10:00 – 11:30
5. Lecture 5. TBA, 14:00 – 15:30
6. Lecture 6. TBA, 16:00 – 17:30

July 29(Wed)

7. Lecture 7. TBA, 10:00 – 11:30
8. Lecture 8. TBA, 14:00 – 15:30

July 30(Thu)

9. Lecture 9. TBA, 10:00 – 11:30
10. Lecture 10. TBA, 14:00 – 15:30

Venue

• #102, College of Natural Sciences, Kyungpook National University, Daegu, Korea

Accommodation Suggestion

• Hotel Inter-Burgo Exco (호텔 인터불고 엑스코)
• Standard double room rate is about KRW190,000 – KRW240,000 as of Jun. 2026.
• Breakfast is not included.
• Distance from Venue : 40min. by walk (map), 30min. by bus and walk

• Browndot-KNU (브라운도트-경북대점)
• Standard double room rate is about KRW70,000 – KRW90,000 as of Jun. 2026.
• Breakfast is not included.
• Distance from Venue : 15min. by walk (map)

Contact

• Byung Hee An (anbyhee_at_knu.ac.kr)
• Woojoo Shim (wjshim_at_knu.ac.kr)

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