Order and function in complex systems: coherent structures, selection and stability

Conference on order and function in complex systems: coherent structures, selection and stability
August 10 – 14, 2026
University of Minnesota Twin Cities

Overview

Many systems of interest in the natural sciences and engineering are complex, in that they possess a large number of degrees of freedom, which makes it a priori difficult to predict their behavior. Despite this, the behavior of many complex systems may be largely driven by a small number of coherent states, with a simpler description and a small number of free effective degrees of freedom. The focus of this conference is on methods from dynamical systems, PDE theory, and functional analysis for explaining and predicting the emergence of such coherent structures, as well as understanding their subsequent temporal dynamics. These coherent structures include fronts, waves, vortices or patterned states such as rolls or spots. Their existence and dynamics are essential to a range of applications spanning ecology, fluid dynamics, materials science, biology, and physics. There are nonetheless many mathematical commonalities in the study of coherent structures in these seemingly disparate areas of application. Recent years have seen many significant advances in both the theoretical and experimental understanding of different aspects of coherent structures. The conference will assemble international experts in the dynamics of coherent structures, together with a sizable group of early career researchers, for a week-long meeting covering the many facets of coherent structures research. It will facilitate the cross pollination of ideas key to recent advances in theory, computation, and experiment.

The first day of the conference will be dedicated to junior participants with two tutorials offered on dynamical systems and functional analytic tools for coherent structures research. The full conference will commence on August 11th. We have confirmed tentative interest of 23 experts in coherent structures spanning career stages and geographical location from the US to Canada, France, Japan, the Netherlands, the UK, and Germany.

Tutorial leaders

Paul Carter, University of California, Irvine
Gabriela Jaramillo, University of Houston

Organizers

Montie Avery, Emory University
Grégory Faye, CNRS, Institut de Mathématiques de Toulouse
Ryan Goh, Boston University
Matt Holzer, George Mason University
Gabriela Jaramillo, University of Houston
Merlin Pelz, University of Minnesota
Qiliang Wu, Ohio University

Schedule & Abstracts

Abstract Booklet

Monday, August 10 (pre-conference day)

9:30 – 10:00 a.m. Welcome and ice-breaker
10:00 a.m. – Noon Tutorial (Dynamical Systems – Paul Carter)
Noon – 1:30 p.m. Lunch Break
1:30 – 3:30 p.m. Tutorial (Functional Analysis – Gabriela Jaramillo)
3:30 – 4:00 p.m. Coffee Break
4:00 – 4:45 p.m. State of the field talk

Tuesday, August 11 (start of the conference)

9:15 – 9:30 a.m. Conference Welcome
9:30 – 10:00 a.m. Arjen Doelman: On the transition from homoclinic pulse to double heteroclinic front patterns
10:05 – 10:35 a.m. Angela Stevens: Mathematical Modeling and Analysis of the Notch-Delta Pathway
10:35 – 11:00 a.m. Coffee Break
11:00 – 11:30 a.m. Jens Rademacher: The curious occurence of runaway modes
11:35 a.m. – 12:05 p.m. Dave Lloyd: Towards a spatial dynamics bifurcation theory for fully localised 2D patterns in anisotropic systems
12:05 – 2:15 p.m. Lunch Break
2:15 – 3:20 p.m. Discussion: Alternative funding opportunities and maintaining international collaboration
3:20 – 3:40 p.m. Coffee Break
3:40 – 4:30 p.m.+ Poster session and informal happy hour

Wednesday, August 12

9:00 – 9:30 a.m. Patrick Shipman: Patterns, Motion, Color, and Geometry from Nucleation and Growth
9:35 – 10:05 a.m. Björn Sandstede: Localized patterned states on graphs with random or structured connectivity
10:05 – 10:30 a.m. Coffee Break
10:30 – 11:00 a.m. Merlin Pelz: Dynamical behavior of diffusively coupled scalar differential equations as Wentzell boundary conditions
11:05 – 11:35 a.m. Olivia Clifton: Reversible gap formation in a 2D swarming model
11:40 a.m. – 12:10 p.m. Jasper Weinburd: Data Assimilation and Model Selection for Collective Motion in Locust Swarms
12:10 – 2:15 p.m. Lunch Break
2:15 – 2:45 p.m. Yasumasu Nishiura: Toward a Dynamical Theory of Rugged Energy Landscapes: Saddle Networks and Trajectory Bundles
2:50 – 3:20 p.m. Tasso Kaper: Les canards de Turing
3:20 – 3:40 p.m. Coffee Break
3:40 – 4:30 p.m. Discussion: Impact of AI on research

Thursday, August 13

9:00 – 9:30 a.m. Dmitry Pelinovsky: NLS models with competing nonlinearities: kinks, solitons, and their stability problems
9:35 – 10:10 a.m. Keith Promislow: Onset of Correlation in Simple Particle Models
10:10 – 10:30 a.m. Coffee Break
10:30 – 11:00 a.m. Margaret Beck: Stability in the Swift-Hohenberg equation via conjugate points and computer assisted proof
11:05 – 11:35 a.m. Doug Wright: Radiating Solitary Waves
11:40 a.m. – 12:10 p.m. Raj Beekie: Asymptotic behavior of the 2D linearized Euler equation
12:10 – 2:15 p.m. Lunch Break
2:15 – 2:45 p.m. Hao Jia: Global well-posedness of the dynamical Prandtl equation
2:50 – 3:20 p.m. Dan Spirn: Anchored Filaments in Stokes Flow: The Peskin Problem in the Half-Plane.
3:20 – 3:40 p.m. Coffee Break
3:40 – 4:30 p.m. Discussion: Future directions for research in the field

Friday, August 14

9:00 – 9:30 a.m. TBD
9:30 – 10:00 a.m. Alin Pogan: Eigenvalues, Resonances and solutions of the abstract wave equations
10:10 – 10:30 a.m. Coffee Break
10:30 – 11:00 a.m. Yoichiro Mori: Convergence Results on Physical Learning
11:05 – 11:35 a.m. Tim Roberts: Resilience of Vegetation on Undulating Sloped Terrain
11:40 a.m. – 12:10 p.m. Montie Avery: Selection of pushed pattern-forming fronts
12:10 – 12:40 p.m. Discussion & conclusion of conference

Location

Confirmed Participants

Johnathan Andres, University of Houston — Participant
Montie Avery, Emory University — Organizer
Margaret Beck, Boston University — Speaker
Rajendra Beekie, Imperial College London — Participant
Paul Carter, University of California, Irvine — Speaker
Angel Chavez, University of Minnesota, Twin Cities — Participant
Olivia Clifton, University of Illinois at Urbana-Champaign — Speaker
Anthony Cortez, University of Minnesota, Twin Cities — Participant
Jacob Daniels, University of Minnesota, Twin Cities — Participant
Arjen Doelman, Rijksuniversiteit te Leiden — Speaker
Cameron Edgar, Boston University — Participant
Lauren Forbes, Boston University — Participant
Punit Gandhi, Virginia Commonwealth University — Participant
Ryan Nolan Goh, Boston University — Organizer
Daniel Hobbs, Rochester Institute of Technology — Participant
Matt Holzer, George Mason University — Organizer
Salomea Jankovic, World Wide Technology — Speaker
Gabriela Jaramillo, University of Houston — Organizer
Hao Jia, University of Minnesota, Twin Cities — Participant
Tasso Kaper, Boston University — Speaker
Todd Kapitula, Calvin University — Participant
Nikitas Kotsakis, Michigan State University — Participant
Benjamin Krewson, Boston University — Participant
Yeuk Yin Lam, University of Minnesota, Twin Cities — Participant
Nan Li, University of Minnesota, Twin Cities — Participant
Xinlu Li, University of Alabama at Birmingham — Participant
Grayson Light, University of Minnesota, Twin Cities — Participant
David J.B. Lloyd, University of Surrey — Speaker
Yoichiro Mori, University of Pennsylvania — Speaker
Angel Naranjo Rubio, University of Nebraska — Participant
Hieu Thanh Nguyen, University of Wisconsin, Madison — Participant
Yasumasa Nishiura, Tohoku University — Speaker
Dimitry Pelinovsky, McMaster University — Speaker
Merlin Pelz, University of Minnesota, Twin Cities — Organizer
Alin Pogan, Miami University — Speaker
Peter Polacik, University of Minnesota, Twin Cities — Participant
Keith Promislow, Michigan State University — Speaker
Jens Rademacher, Universität Hamburg — Speaker
Sky Ratcliffe, George Mason University — Participant
Timothy Roberts, University of Chicago — Participant
Bjorn Sandstede, Brown University — Speaker
Julia Seay, George Mason University — Participant
Patrick Daniel Shipman, University of Arizona — Speaker
Daniel Spirn, University of Minnesota, Twin Cities — Speaker
Angela Stevens, Westfälische Wilhelms-Universität Münster — Speaker
Michael Storm, New Jersey Institute of Technology — Participant
Nghi Lam Ngoc Vo, University of Wisconsin, Madison — Participant
Jonathan Waldmann, George Mason University — Participant
Anne Marie Warren, New York University — Participant
Jasper Weinburd, University of St. Thomas — Speaker
Doug Wright, Drexel University — Speaker
Qiliang Wu, Ohio University — Organizer
Paige Yeung, University of Minnesota, Twin Cities — Participant
Xiaoxing Yu, University of Minnesota, Twin Cities — Participant
Oluwatosin Babasola, University of Georgia — Participant
Jeremy Bellay, Battelle — Speaker
Martin Biehl, Cross Compass — Participant
Awildo Gutierrez, University of Wisconsin, Madison — Participant
Michelle Mastrianni, Harrison.ai — Speaker
David Paul Morrissey, 3M — Speaker
Rivkah Moshe, Purdue University — Participant
Kayode Oshinubi, Northern Arizona University — Participant
Idan Sorin, Technion-Israel Institute of Technology — Participant
Madi Yerlanov, Duke University — Participant

Order and function in complex systems: coherent structures, selection and stability

Conference details

Monday, August 10 (pre-conference day)

Tuesday, August 11 (start of the conference)

Wednesday, August 12

Thursday, August 13

Friday, August 14

Getting to UMN

Child care

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