About

Prudence Carter is the Sarah and Joseph Jr. Dowling Professor of Sociology and the Peltz Ruttenberg Family Director of the Center for the Study of Race and Ethnicity in America (CSREA) at Brown University. Her research explores the enduring inequalities in education and society, focusing on their root causes and potential solutions. She examines how race, ethnicity, class, and gender influence academic achievement and mobility disparities both in the United States and globally. Prior to her appointment at Brown, Carter served as the E.H. and Mary E. Pardee Professor and Dean of the Graduate School of Education at the University of California, Berkeley, from 2016 to 2021. She is an accomplished scholar whose award-winning book, Keepin’ It Real: School Success beyond Black and White (2005), critically analyzes cultural explanations for academic achievement and racial identity among low-income Black and Latino youth in the United States. Her work has received notable recognition, including the Oliver Cromwell Cox Book Award from the American Sociological Association’s Section on Race and Ethnic Minorities and being a finalist for the C. Wright Mills Book Award. Carter's scholarship also includes Stubborn Roots: Race, Culture, and Inequality in U.S. & South African Schools and Closing the Opportunity Gap: What America Must Do to Give Every Child an Even Chance, both published by Oxford University Press. Her research employs multi-year, mixed-methods studies to shed light on racial dynamics and barriers to school integration in diverse settings. Her work has been published in leading academic journals and featured on national media programs. Carter is a distinguished member of the academic community, having received multiple awards from the American Sociological Association and the American Educational Research Association. She is a past president of the ASA and an elected member of the American Academy of Arts and Sciences, the National Academy of Education, and the Sociological Research Association.

Research topics

• Mathematics
• Computer science
• Mathematical analysis
• Physics
• Geography

Selected publications

• Selection of pushed pattern-forming fronts in the FitzHugh-Nagumo system

  ArXiv.org · 2026-03-25

  articleOpen access

  We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the front interface. We prove that these pushed pattern-forming fronts attract initial data supported on a half-line, and therefore determine both propagation speeds and selected wave numbers for invasion from localized initial conditions. This provides to our knowledge the first proof of the marginal stability conjecture for pattern-forming fronts, thereby confirming universal wave number selection laws widely used in the physics literature. We present our analysis in the specific setting of the FitzHugh-Nagumo system, but our methods can be applied to general dissipative PDE models which exhibit pattern formation. The main technical challenge is to control the interaction between the localized mode driving the propagation and outgoing diffusive modes in the wake of the front. Through a subtle far-field/core decomposition of the linearized evolution, we resolve this interaction and describe the nonlinear response of the front to perturbations as a dynamically driven phase mixing problem for the pattern in the wake. The methods we develop are generally useful in any setting involving the interaction of localized modes and outward diffusive transport, such as in the nonlinear stability of undercompressive viscous shock waves or source defects.

  PublisherOA PDF

• Diffusive synchronization of phase waves in the FitzHugh-Nagumo system

  ArXiv.org · 2026-01-08

  articleOpen access

  We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-train solutions, we resolve for the first time the case of phase waves. These waves are nearly phase-synchronized relaxation oscillations, featuring quasistationary plateaus of length $\varepsilon^{-1}$ separated by fast transition layers, where $\varepsilon\ll1$ is the timescale separation parameter. Tracking the decay of modulations via a Bloch-wave eigenfunction analysis, we find a remarkably weak interaction strength of order $\varepsilon^{8/3}$. This weak layer interaction and many of the technical difficulties arise from repeated scattering of eigenfunctions through fold points at the ends of the quasistationary plateaus. We capture this by combining a novel geometric desingularization approach with Lin's method, exponential trichotomies, and the Riccati transform. While our spectral stability analysis yields diffusive synchronization of all phase waves in the FitzHugh-Nagumo system, it also identifies potential finite-wavelength instabilities, which we realize in a system variant.

  PublisherOA PDF

• Selection of pushed pattern-forming fronts in the FitzHugh-Nagumo system

  arXiv (Cornell University) · 2026-03-25

  preprintOpen access

  We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the front interface. We prove that these pushed pattern-forming fronts attract initial data supported on a half-line, and therefore determine both propagation speeds and selected wave numbers for invasion from localized initial conditions. This provides to our knowledge the first proof of the marginal stability conjecture for pattern-forming fronts, thereby confirming universal wave number selection laws widely used in the physics literature. We present our analysis in the specific setting of the FitzHugh-Nagumo system, but our methods can be applied to general dissipative PDE models which exhibit pattern formation. The main technical challenge is to control the interaction between the localized mode driving the propagation and outgoing diffusive modes in the wake of the front. Through a subtle far-field/core decomposition of the linearized evolution, we resolve this interaction and describe the nonlinear response of the front to perturbations as a dynamically driven phase mixing problem for the pattern in the wake. The methods we develop are generally useful in any setting involving the interaction of localized modes and outward diffusive transport, such as in the nonlinear stability of undercompressive viscous shock waves or source defects.

  PublisherDOI

• Diffusive synchronization of phase waves in the FitzHugh–Nagumo system

  Repository KITopen (Karlsruhe Institute of Technology) · 2026-01-01

  articleOpen access

  We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-train solutions, we resolve for the first time the case of phase waves. These waves are nearly phase-synchronized relaxation oscillations, featuring quasistationary plateaus of length $\varepsilon^{-1}$ separated by fast transition layers, where $\varepsilon\ll1$. is the timescale separation parameter. Tracking the decay of modulations via a Bloch-wave eigenfunction analysis, we find a remarkably weak interaction strength of order $\varepsilon^{8/3}$. This weak layer interaction and many of the technical difficulties arise from repeated scattering of eigenfunctions through fold points at the ends of the quasistationary plateaus. We capture this by combining a novel geometric desingularization approach with Lin’s method, exponential trichotomies, and the Riccati transform. While our spectral stability analysis yields diffusive synchronization of all phase waves in the FitzHugh–Nagumo system, it also identifies potential finite-wavelength instabilities, which we realize in a system variant.

  PublisherOA PDFDOI

• Diffusive synchronization of phase waves in the FitzHugh-Nagumo system

  arXiv (Cornell University) · 2026-01-08

  preprintOpen access

  We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-train solutions, we resolve for the first time the case of phase waves. These waves are nearly phase-synchronized relaxation oscillations, featuring quasistationary plateaus of length $\varepsilon^{-1}$ separated by fast transition layers, where $\varepsilon\ll1$ is the timescale separation parameter. Tracking the decay of modulations via a Bloch-wave eigenfunction analysis, we find a remarkably weak interaction strength of order $\varepsilon^{8/3}$. This weak layer interaction and many of the technical difficulties arise from repeated scattering of eigenfunctions through fold points at the ends of the quasistationary plateaus. We capture this by combining a novel geometric desingularization approach with Lin's method, exponential trichotomies, and the Riccati transform. While our spectral stability analysis yields diffusive synchronization of all phase waves in the FitzHugh-Nagumo system, it also identifies potential finite-wavelength instabilities, which we realize in a system variant.

  PublisherDOI

• Seismic Stratigraphy and Geomorphology of Mass-Transport Complexes in Carbonate Depositional Environments: Insights from the Cenozoic Margin of the Exmouth Sub-Basin (North West Shelf, Australia)

  SEPM (Society for Sedimentary Geology) eBooks · 2025-01-01

  book-chapter

  Key Messages: (1) Mass-transport complexes (MTCs) developed in the Exmouth Sub-basin exhibit a continuum of downslope deformation along basal shear surfaces that coincide with third-order sequence boundaries. (2) Fault reactivation is a likely trigger for slope failure in several MTCs as suggested by the direct link observed between headscarps and underlying faults. (3) Variations in run-out distance (11–80 km), likely influenced by paleotopography and rheology, affect the architectural maturity of the MTCs, which are morphometrically comparable to other passive margin-attached systems in carbonate settings.

  PublisherDOI

• Deformations of acid-mediated invasive tumors in a model with Allee effect

  Journal of Mathematical Biology · 2025-05-05 · 1 citations

  articleOpen access1st authorCorresponding

  We consider a Gatenby-Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, an acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.

  PublisherOA PDFDOI

• Rethinking Tipping Points in Spatial Ecosystems

  The American Naturalist · 2025-10-20 · 2 citations

  article

  AbstractTipping point theory has garnered substantial attention over recent decades. It predicts abrupt and often irreversible transitions from one ecosystem state to an alternative state. However, ecosystem models that predict tipping typically neglect spatial dynamics. Recent studies reveal that incorporating spatial dynamics may enable ecosystems to evade tipping predicted by nonspatial models. Here, we use a dryland and a savanna-forest model to synthesize mechanisms by which spatial processes can alter the theory of tipping. We further propose that the underlying drivers of positive feedback leading to alternative stable states may provide insight into the tipping evasion mechanisms most relevant to a specific ecosystem. For instance, while positive feedbacks may arise in drylands from direct self-facilitation, such as enhancing the uptake of a limiting resource, at the savanna-forest boundary, it may arise from mutual inhibition between two ecosystem components. In the former case ecosystems can evade tipping by forming self-organized patterns, whereas in the latter the presence of environmental heterogeneity may be required. Our study highlights that deepening our understanding of how ecological feedbacks connect to tipping evasion mechanisms is crucial to formulate better strategies to increase ecosystem resilience.

  PublisherDOI

• Stability of coherent pattern formation through invasion in the FitzHugh–Nagumo system

  Journal of the European Mathematical Society · 2025-07-27 · 3 citations

  articleOpen access

  We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate pattern selection from compactly supported or steep initial data. We focus on pulled fronts, that is, on fronts whose propagation speed is determined by the linearization about the unstable state in the leading edge, only. We present our analysis in the specific setting of the FitzHugh–Nagumo system, where pattern-forming uniformly translating fronts have recently been constructed rigorously [Carter and Scheel (2018)], but our methods can be used to establish nonlinear stability of pulled pattern-forming fronts in general reaction-diffusion systems. This is the first stability result for critical pattern-selecting fronts and provides a rigorous foundation for heuristic, universal wave number selection laws in growth processes based on a marginal stability conjecture. The main technical challenge is to describe the interaction between two separate modes of marginal stability, one associated with the spreading process in the leading edge, and one associated with the pattern in the wake. We develop tools based on far-field/core decompositions to characterize, and eventually control, the interaction between these two different types of diffusive modes. Linear decay rates are insufficient to close a nonlinear stability argument and we therefore need a sharper description of the relaxation in the wake of the front using a phase modulation ansatz. We control regularity in the resulting quasilinear equation for the modulated perturbation using nonlinear damping estimates.

  PublisherDOI

• A Stabilizing Effect of Advection on Planar Interfaces in Singularly Perturbed Reaction-Diffusion Equations

  SIAM Journal on Applied Mathematics · 2024-06-10 · 5 citations

  article1st authorCorresponding
  PublisherDOI

Recent grants

• Patterns and Bifurcations in Multiple Timescale Dynamical Systems

  NSF · $84k · 2018–2020

• Patterns and Bifurcations in Multiple Timescale Dynamical Systems

  NSF · $91k · 2019–2021

• Self-Organization, Stability, and Defects in Pattern-Forming Systems

  NSF · $238k · 2021–2025

• Patterns and Bifurcations in Multiple Timescale Dynamical Systems

  NSF · $14k · 2021–2023

Frequent coauthors

• Björn Sandstede

  21 shared

• Arjen Doelman

  9 shared

• Peter Baillie

  6 shared

• David Lowry-Duda

  5 shared

• Laura Slivinski

  Cooperative Institute for Research in Environmental Sciences

  4 shared

• Jenna Palmer

  John Brown University

  4 shared

• Björn de Rijk

  4 shared

• Melissa McGuirl

  Brown University

  4 shared

Education

• PhD, Department of Mathematics

  Brown University

  2016

• MASt, Department of Applied Mathematics and Theoretical Physics

  University of Cambridge

  2011

• BA, Mathematical Institute

  University of Oxford

  2010

Awards & honors

• Oliver Cromwell Cox Book Award from the American Sociologica…
• Finalist for the C. Wright Mills Book Award from the Society…
• Recipient of multiple distinguished career awards from secti…
• Elected member of the American Academy of Arts and Sciences
• Elected member of the National Academy of Education