Dynamical Systems Seminars

Spring 2025

The Dynamical Systems seminar is held on Monday afternoons at 4:00 PM in CCDS 548 . There will be a brief tea in CCDS 548 at 3:45PM.

• January 27th Björn de Rijk (KIT)
  Title: Orbital stability of spatially periodic waves in the Klein-Gordon equation against localized perturbations Abstract: Nonlinear stability for spatially periodic waves in dispersive systems has so far been obtained against co-periodic or subharmonic perturbations by leveraging the Hamiltonian structure or other conserved quantities. However, nonlinear stability against localized perturbations remains largely unexplored. Since the perturbed wave is neither periodic nor localized in this case, the usual conservation laws are unavailable, thus obstructing a standard nonlinear stability argument. In this talk, I present a nonlinear orbital stability result for spatially periodic waves in the Klein-Gordon equation against $L^2$-localized perturbations. This is joint work with Emile Bukieda and Louis Garénaux.
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• February 3rd Mara Freilich (Brown)
  Title: Mixing of biological tracers: beyond turbulent diffusion
  Abstract: Ocean currents shape the distribution and magnitude of microbial populations with cascading influences on the global carbon cycle. In this talk, I will derive a parameterization for the turbulent flux of biological tracers and highlight the role of biological timescales. This parameterization reveals a growth-transport feedback that can generate diversity in phytoplankton community structure at fine scales (1-10 km) and higher net productivity in the presence of community diversity. I will then compare the theoretical results with ship-board observations to examine the interaction between ocean eddy processes and microbial communities revealing how frontal dynamics shape the upper ocean distribution of carbon and microbial communities.

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• February 10th Max Weinreich (Harvard)
  Title: Chaos and periodic orbits in complex billiards
  Abstract: Billiards is a mathematical model for anything that bounces: light, molecules, or the cue ball in the game of pool. In this talk, we will learn how to play billiards over the complex numbers. We prove two results on complex billiards in generic algebraic curves: first, the dynamical degree, or algebraic entropy, has an explicit lower bound; second, the set of periodic points has measure 0, confirming a classical conjecture of Ivrii and Weyl for generic algebraic plane domains.

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• February 17th No Seminar - President's Day (TBD)
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• February 24th Michelle Bartolo (Harvard)
  Title: Patient-Specific Mathematical Modeling of Pulmonary Hypertension
  Abstract: Patient-specific computational modeling provides an efficient, non-invasive method to study complex, multiscale pathologies such as pulmonary hypertension. By integrating medical imaging and hemodynamic data with computational fluid dynamics, we can uncover physiological mechanisms driving disease progression and quantify relationships not directly observable in vivo. In this study, we present a framework for generating patient-specific vascular models from segmentations of pulmonary arterial networks and examine the impact of uncertainty in medical image analysis. Using the one-dimensional cylindrical Navier-Stokes equations, we predict spatial and temporal variations in blood pressure, flow, and vessel deformation. Our model finds that network geometry significantly impacts pulmonary arterial pressure and flow dynamics, and that pulmonary hypertension is associated with decreased shear stress and increased cyclic stretch in the smallest blood vessels.

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• March 3rd Rebecca Winarski (College of the Holy Cross)
  Title: Thurston theory: unifying dynamical and topological
  Abstract: Thurston proved that a non-Lattés branched cover of the sphere to itself is either equivalent to a rational map (that is: conjugate via a mapping class), or has a topological obstruction. The Nielsen–Thurston classification of mapping classes is an analogous theorem in low-dimensional topology. We unify these two theorems with a single proof, further connecting techniques from surface topology and complex dynamics. Moreover, our proof gives a new framework for classifying self-covering spaces of the torus and Lattés maps. This is joint work with Jim Belk and Dan Margalit.

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• March 10th No Seminar - Spring Break (TBD)
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• March 17th Vanessa Matus de la Parra (SUNY-Stony Brook)
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• March 24th TBD (TBD)
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• March 31st Nicole Buczkowski (WPI)
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• April 7th TBD (TBD)
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• April 14th Jia Shi (MIT)
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• April 23rd (BU Monday Schedule) Roland Welter (Hamburg University)
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• April 28th TBD (TBD)
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  Directions to BU Math Dept.

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  Speakers from previous years

  

  BU Dynamical Systems Home Page
  

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  BU Mathematics Department Home Page