Computers have helped us prove many theorems, which like the four-color theorem are mostly combinatorial or discrete in nature. For domains like dynamical systems, however, computer-assisted proofs ...

Introduces undergraduate students to chaotic dynamical systems. Topics include smooth and discrete dynamical systems, bifurcation theory, chaotic attractors, fractals, Lyapunov exponents, ...

Researchers are using reaction networks and dynamical systems to study these hidden patterns in living systems: Reports ...

Iteration of a rational function R gives a complex dynamical system on the Riemann sphere. We introduce a C*-algebra 𝓞R associated with R as a Cuntz-Pimsner algebra of a Hilbert bimodule over the ...

The course will survey methods for characterizing time-series data by reading primary literature and implementing and testing methods on synthetic data. Students will simulate time-series from a ...

Mathematicians are finding inevitable structures in sufficiently large sets of integers. Despite that, Furstenberg’s paper left a lasting imprint on mathematics. His new argument contained a kernel of ...

Imagine a garden filled with every variety of flower in the world — delicate orchids, towering sunflowers, the waxy blossoms of the saguaro cactus and the corpse flower’s putrid eruptions. Now imagine ...