The Global Attractor Conjecture (GAC) is one of the oldest and best studied problems within Reaction Network Theory, and is closely related to the Boltzmann equation. Indeed, the most general setting for the GAC can be traced back to Boltzmann's work on the H-theorem in the 1870s.
Since its formulation in the early 1970s, the GAC has resulted in a flurry of research activity, dozens of papers discussing various special cases, and a litany of false proofs. (The result is so intuitive that even Horn and Jackson, the authors of the groundbreaking 1972 paper "General Mass Action Kinetics", errantly believed they had already proved it!)
In his recent manuscript, "Toric Differential Inclusions and a Proof of the Global Attractor Conjecture", Professor Gheorghe Craciun proposed a proof of the conjecture in full generality. The manuscript represents the culmination of nearly a decade of work, and involves ideas from dynamical systems, differential inclusions, polyhedral geometry, and algebraic geometry.
A few years before Gheorghe's work, David Anderson used a different approach to prove an important special case of the conjecture.
A recent SIAM News article discusses Gheorghe's proof and a recent Workshop to examine it further at San Jose State University in March 2016.
Gheorghe will give a Colloquium talk on this work on September 23, 2016. https://www.math.wisc.edu/wiki/index.php/Colloquia