From May 23 to May 27, dynamical systems researchers from around the world convened for the virtual edition of the SIAM DS21 conference. Co-chaired by Elizabeth Cherry (Georgia Tech) and Margaret Beck (Boston University), the meeting featured over 200 minisymposia and contributed speaker sessions and achieved record attendance with over 1300 registered participants. Although this edition of the SIAM DS conference was not held at the customary 8000 feet / 2.5 kilometer altitude, this virtual meeting provided a breathtaking array of theoretical and scientific developments across a range of dynamical systems topics.

The conference kicked off with a plenary talk by Chris Jones (UNC Chapel Hill), who spoke about tipping-point mechanism in models for models for climate dynamics, covering bifurcation tipping (“falling off a cliff”), noise-induced tipping (“pushing a boulder uphill), and rate-induced tipping (“moving the goalposts”). I particularly enjoyed the use of low-dimensional model problems for the climate, including ODE and SDE systems describing the intensity of hurricanes as a function of circular wind speed and moisture content, illustrating the tipping mechanisms that can result in the destruction or creation of North Atlantic hurricanes. The talk also featured a touching tribute to Charles Doering, remembering his role in the dynamical systems community and his love of the geophysical fluid dynamics summer program at Walsh Cottage at the Woods Hole Oceanographic Institute. 

To cap off the first day of the conference, two major awards were presented in a plenary session. The J.D. Crawford Prize for recent outstanding work in nonlinear science went to Igor Mezić (UCSB) for his paper titled “Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry”. The Jürgen Moser prize for outstanding contributions to nonlinear science was awarded to Lai-Sang Young (NYU) for her extensive theoretical work on non-uniformly hyperbolic dynamical systems. Professor Young then presented the associated Jürgen Moser lecture on “A Dynamical Model of the Visual Cortex”, explaining a realistic computational model of the monkey visual cortex designed to uncover the dynamical mechanisms underlying the processing of visual information. 

One major topic represented at the conference was infectious disease modeling, including plenary talks by Alex Arenas (Universitat Rovira i Virgili) on “A Mathematical Model for the Spatiotemporal Epidemic Spreading of COVID-19” and by Peko Hosi (MIT) on “Practical Math for Pandemics”. There was also a timely two-part minitutorial on mathematical modeling of infectious disease dynamics, organized by Jessica Conway (Penn State), Alun Lloyd (NC State), and Tim Reluga (Penn State). Starting from the history of infectious disease and the basics of compartmental ODE models for infectious disease, the organizers covered topics including contagion models on networks, game-theoretic models incorporating human behavior into epidemiological dynamics, and a case-study using real data from Vancouver to understand vaccination strategies for the 2009 H1N1 influenza pandemic. This tutorial was complemented by a session on infectious disease dynamics across scale, organized by Sara Capponi (IBM Research) and Jessica Conway, showcasing recent research on within-host and between-host factors in infectious disease modeling. 

As with previous SIAM DS meetings, the conference continued to highlight novel mathematical methodologies used to understand complex natural systems. This was evidenced by minisymposia on both topological systems processing and in the use of topological data analysis in biology, as well as three different minisymposium on the theory and applications of the Koopman operator approach. A plenary talk by Heather Harrington (Oxford) provided an exciting overview for the use of algebraic methods in systems biology and to understand the polynomial systems arising from dynamical models of chemical reaction networks. The interaction between machine learning and dynamical systems was illustrated by Weinan E (Princeton), whose plenary talk focused on the application of dynamical systems approaches to motivate machine learning algorithms and the application of deep learning to understand the behavior of dynamical systems. 

One topic I really enjoyed learning about at the conference was dynamical systems modeling of collective behavior in natural and engineered social systems. A minisymposium on human social systems organized by Vicky Chen (Santa Fe Institute) and Sara Clifton (St. Olaf College) featured a range of emergent phenomena in complex social systems. Topics in the session included bipartite networks characterizing diversity and shared identity (Chad Topaz, Williams College), models for the dynamics of continuous opinions on networks (Heather Zinn Brooks, Harvey Mudd College), a bifurcation analysis of a PDE model for the spatial distribution of wealth in cities (Nancy Rodriguez, CU Boulder), and a dynamical economic model for the origin of generic and name consumer products (Daniel Abrams, Northwestern). 

The topic of opinion dynamics in social systems was further highlighted in a minisymposium organized by Joseph Johnson (Northwestern) and Alexandria Volkening (Northwestern). The talks featured surprising collective effects that arise through individuals’ perceptions of opinions, from how media strategies can impact the perception of factual information (Cailin O’Connor, UC Irvine) to how social norms and false beliefs of cooperative behavior and  can help to establish the supply of public goods (Erol Akcay, UPenn). A theme featured in several sessions was the emergence and impact of ideological echo chambers, including the role of perception of opinion distributions impacts evolving opinions (David Sabin-Miller, Northwestern), the impact of clustered opinions on candidate platforms and electoral outcomes (Feng Fu, Dartmouth), as well as the role that polarization can play on collective decision-making (Sarah Shugars, NYU) and in the evolution of cooperation (Mari Kawakatsu, Princeton). 

There were so many great sessions at the conference, resulting in difficult choices regarding which talks to attend live. Fortunately, recordings of all talks will be available throughout the summer for registered participants throughout the summer, and a subset of the conference talks will be made publicly available after that. Social media activity really helped to increase the feeling of community in the conference, providing highlights of sessions and advertising upcoming talks across the program. One standout Twitter thread was authored by Alice Schwarze (University of Washington), who amplified talks featuring women in network science.

For those interested in more coverage on the conference, one can search the conference hashtag #SIAMDS21 on Twitter or many recent articles highlighting conference talks in SIAM News. While I really missed the opportunity to meet with the dynamical systems community in person this year, the virtual meeting was still one of my favorite conferences so far, and I really look forward to seeing you all in Portland for the next SIAM DS conference in 2023.