Dynamical Systems Seminars

Spring 2026

The Dynamical Systems seminar is held on Monday afternoons at 4:00 PM in CCDS 365 . There will be a brief tea in CCDS 365 at 3:45PM.

• January 26th Greg Handy (U of Minnesota - Twin Cities) - TALK CANCELLED DUE TO BU SNOW DAY, we plan to reschedule later in the semester.
  Title: Glial ensheathment of inhibitory synapses drives hyperactivity and increases correlations
  Abstract: Recent evidence shows that glial cells actively modulate neuronal dynamics. A recent study notably found that during and after anesthesia, microglia ensheath inhibitory synapses, disrupting neurotransmitter flow. In this talk, I will develop computational models that explore how this ensheathment affects neuronal dynamics. Extending a microscale synaptic cleft model, I show that ensheathment accelerates synaptic transmission but reduces its strength. I will then integrate this microscale model into a large network of exponential integrate-and-fire neurons, which introduces heterogeneous synaptic parameters determined by glial proximity, and extend linear response theory to analyze firing rates and noise correlations. I will show that this model reproduces the experimental finding that increased glial ensheathment of inhibitory synapses leads to hyperactivity and predicts significant increases in power spectrum magnitude across task-relevant frequencies, suggesting glial-driven synaptic plasticity is an underappreciated mechanism for modulating cortical dynamics.
  

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• February 2nd Petur Bryde (MIT)
  Title: Orientational dynamics and control of topological defects in 2D nematics
  > Abstract: Topological defects play a distinguished role in the dynamics of ordered media and present promising candidates for robust information storage and computation in soft matter systems. In particular, half-integer defects in nematic films carry orientational degrees of freedom whose long-range interactions can be used to realize nematic analogs of classical logic gates as well as generalized continuous logic functions. Designing such “nematic circuits” with prescribed input-output behavior requires a reduced-order model for the orientational dynamics of a system of defects which is amenable to control-theoretic methods. Here we introduce a framework in which the nematic director angle, which satisfies a linear diffusion equation, is coupled to the defect orientations via appropriate boundary conditions around the defect cores. This approach yields an analogy to heat conduction and enables the design of control protocols that can be implemented in liquid crystals using existing experimental techniques.
  

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• February 9th Richard Birkett (Brown U)
  Title: Rational Maps of Elliptic Surfaces
  Abstract: The algebraic or geometric form of rational self-maps is quite well-understood on curves. However, we know less on higher dimensional varieties. Other than $\mathbb P^n$, perhaps the only well-studied situation is on a rational or elliptic fibration where the rational map fixes the position of every fibre. In this case, we can view the map as a morphism of curves over a function field, as seen in families of rational maps. What if the rational map preserves but does \emph{not fix} the fibration? Skew products on ruled surfaces have garnered some attention; these can be expressed as $f(x, y) = (f_1(x), f_2(x, y))$. However, in the classification of algebraic surfaces, those with an elliptic fibration are more prevalent. In this talk, I will discuss \emph{elliptic skew products}: rational self-maps of elliptic surfaces that respect their fibration. This class of rational maps turns out to be surprisingly rigid. From a collaboration with G.\ Mezzedimi (University of Bonn), I will present a classification of elliptic skew products with key examples. The proofs involve algebraic geometry, dynamics, the arithmetic of elliptic curves, and some number theory.
  

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• February 16th No Seminar - President's day
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• February 23rd Jit Wu Yap (MIT) - SNOW DAY, talk will be rescheduled.
  Title: Common Preperiodic Points of Polynomials
  Abstract: Given two rational maps of degree at least two, Baker and DeMarco showed that either the maps share the same set of preperiodic points or they have only finitely many preperiodic points in common. DeMarco, Kreiger, and Ye conjectured that in the latter case, the number of common preperiodic points admits a uniform bound depending only on the degree. In this talk, we explain how to prove their conjecture for polynomials. The argument combines a non-archimedean rigidity theorem for equilibrium measures with a degeneration argument using ultrafilters. This is joint work with Chen Gong.
  

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• March 2nd Abigail Plummer (BU) -- NOTE!: This talk will be in a different room, CDS Room 1646
  Title: Rupture, instability, and phase transitions via constrained expansion
  Abstract: Consider an elastic material that increases in size due to growth or swelling. If the material is unable to expand freely, stresses develop. In this talk, I will present two systems in which stresses due to constrained expansion can generate complex and dramatic responses. First, I will discuss the mechanics of thin sheets that have been locally dilated at a periodic array of sites. When the dilations are sufficiently large, the affected sites buckle either above or below their surroundings. These bistable dilations form a programmable metamaterial, and their behavior can be understood through an analogy to the Ising model. Second, I will describe how hydrogels, polymer networks that imbibe large amounts of water, behave when forced to swell around rigid obstacles. We identify a regime in which stresses due to obstacles cause swelling hydrogels to rupture, tearing themselves apart as they expand.
  

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• March 9th No seminar - Spring Break ()
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• March 16th Karl Winsor (Stony Brook U)
  Title: Isoperiodic foliations of strata of abelian differentials
  Abstract: We will discuss the dynamics of isoperiodic foliations of strata of abelian differentials (or translation surfaces). Leaves of this foliation are navigated by varying an abelian differential without changing its integrals along closed loops. Roughly speaking, this is done by moving the zeros of the differential relative to each other. In the generic stratum, the dynamics of this foliation are well-understood due to a close connection with homogeneous dynamics. In this talk, I will discuss a classification of leaf closures for this foliation in all strata, outside of a high-codimension subvariety, in the spirit of Ratner's orbit closure theorem.
  

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• March 23rd David G. Clark (Harvard)
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• March 30th Emile Bukieda (Karlsruhe Institute of Technology)
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• April 6th Alanna Haslam-Hyde (BU)
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• April 13th Keith Promislow (Michigan State University)
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• April 20th No seminar - Patriot's Day ()
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• April 27th TBA ()
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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