Events for 08/22/2023 from all calendars

P and T Talk- A general theory of coexistence for stochastic populations

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Alexandru Hening

Description: One of the longstanding, fundamental problems in population biology is understanding the coexistence of multiple interacting species. In order to accurately model real ecosystems one needs a theory that takes into account the interplay between species interactions (predation, competition, mutualism, etc) and environmental stochasticity. Modern coexistence theory (MCT) is the most successful theory which incorporates all these factors. However, MCT has some significant drawbacks and rigorous mathematical results are only available in special settings. I will present a general theory of coexistence and extinction for populations modelled by stochastic differential equations, explain how the theory resolves an important conjecture by Pallis, and showcase with an illuminating example that environmental fluctuations can facilitate coexistence.

P and T Talk- Universality of dynamic processes using Drinfel’d twisters

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Jeffrey Kuan

Description: Abstract: The concept of 'universality' motivates a wide variety of probability and mathematical physics problems, going back to the classical central limit theorem. Most recently, the Kardar--Parisi--Zhang universality class has been proven to have Tracy--Widom fluctuations in the long-time asymptotics. In this talk, I will present a new universality result about the long-time asymptotics of so--called ``dynamic'' processes. The asymptotic fluctuations are related to the Tracy--Widom distribution. The proof will utilize a duality of Markov processes, which is constructed using Drinfel'd twisters of the quantum group U_q(sl_2), viewed as a quasi-triangular quasi-Hopf algebra. The orthogonality of the duality functions allow for an asymptotic analysis.