Speaker: Isaac Goldbring, UC Irvine.
Title: The Connes Embedding Problem, MIP*=RE, and the Completeness Theorem
Abstract: The Connes Embedding Problem (CEP) is arguably one of the most famous open problems in operator algebras. Roughly, it asks if every tracial von Neumann algebra can be approximated by matrix algebras. In 2020, a group of computer scientists proved a landmark result in complexity theory called MIP*=RE, and, as a corollary, gave a negative solution to the CEP. However, the derivation of the negative solution of the CEP from MIP*=RE involves several very complicated detours through C*-algebra theory and quantum information theory. In this talk, I will present joint work with Bradd Hart where we show how some relatively simple model-theoretic arguments can yield a direct proof of the failure of the CEP from MIP*=RE while simultaneously yielding a stronger, Gödelian-style refutation of CEP. No prior background in any of these areas will be assumed.
Title: Non-deterministic Automatic Complexity of Fibonacci words
Abstract: Automatic complexity rates can be thought of as a measure of how random words can be for some given automaton (machine). By creating a scale between 0 and 1 that ranges from predictable to complex, if the rate of a given word is strictly between 0 and 1/2 then we call it indeterminate. In this paper we show that for an infinite Fibonacci word the non-deterministic automatic complexity can be no greater than 1/Φ^2.
Kuykendall Hall 210
Title: Low($\Pi^0_1$-IM) = $\Delta^0_1$
Abstract: My dissertation investigated $\Pi^0_1$-immune sets, i.e. those
that have no co-enumerable subset. This talk continues that work, first
connecting it to modern notions of computability-theoretic lowness. Then
I settle (in the affirmative) a conjecture that my dissertation left
open: only the computable sets fail to co-enumerate a $\Pi^0_1$-immune
Rukiyah Walker, Monday, November 13, 2:30 – 4:30 pm, Keller 403
Title: A Generalized Epidemiological Compartmental Model
Abstract: Epidemiological compartmental models are standard and important tools used to analyze the spread of infectious diseases. These models divide a population into distinct compartments, such as susceptible, infected, and recovered, based on their disease status. The behavior of the models can then be analyzed using methods from dynamical systems to better understand the spread of a particular disease. The ongoing COVID-19 pandemic highlighted the unpreparedness of societies worldwide in effectively responding to a devastating pandemic. Additionally, existing compartmental models often lack the capabilities to be applied to different diseases. Hence, the need to develop comprehensive models that can accurately predict the behavior of infectious diseases has become evident. In this work we propose a general compartmental model which has the potential to capture the behavior of specific diseases based on key parameters. We study the equilibria and stability of this model, as well as several submodels, by utilizing techniques from dynamical systems. Furthermore, we illustrate examples of varying fundamental parameters, such as transmission rates, latency periods, and more, with simulations for the different submodels that we will encounter.