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Mon Sep 09

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Emergent behavior in collective dynamics
Eitan Tadmor, University of Maryland

Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc.

I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different “rules of engagement”. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.

Mon Oct 07

Applied and Computational Math Colloquium

3:35pm - Vincent Hall 207
Nonuniqueness in Dynamical Systems
Richard McGehee, University of Minnesota

Discontinuous vector fields arise naturally in some applications. In this presentation, a simple classical model of ocean circulation is introduced as an example of how discontinuities give rise to nonunique solutions. Standard bifurcation techniques often fail when the vector field is not smooth, and certainly fail when the vector field is discontinuous. However, some topological techniques seem to carry over, and a crude birfurcation theory can be extended to a large class of discontinuous systems.

Mon Mar 16

Applied and Computational Math Colloquium

3:35pm - TBA
Applied and Computational Math Colloquium
Mauro Maggioni, Johns Hopkins