Title: The emergence of stable spatiotemporal patterns in a mean-field model for neuronal activity. Abstract: In this work we use numerical simulations and bifurcation theory techniques to study the emergence of stable spatiotemporal patterns in a mean-field model for neuronal activity. We identify sufficient conditions on the model’s parameters for the generation of traveling waves (TWs), standing waves (SWs) and modulated waves (MWs). We show how the relative contribution of the intrinsic...

Title : On conjugate systems with respect to completely positive maps Abstract : In 2010, Dabrowski showed that a von Neumann algebra generated by self-adjoint operators is a factor when they admit a conjugate system. We extend this to the operator-valued case by defining an operator valued partial derivative and conjugate systems with respect to completely positive maps. We study operator-valued cumulants using the lattice of non-crossing partition and provide a cumulant characterization for...

Estimating Entanglement Entropy in Neutral Atom Arrays

Topic: Moving Spike Patterns in a Chemotaxis Model and Oscillatory Traveling Waves in a Traffic Flow Model

Short Bio: Professor  Dongbin Xiu received his Ph.D degree from Division of Applied Mathematics of Brown University in 2004. He joined the Department of Mathematics of Purdue University in 2005. In 2013, he moved to the University of Utah as a Professor in the Department of Mathematics and Scientific Computing and Imaging (SCI) Institute. In 2016, He moved to The Ohio State University as Professor of Mathematics and Ohio Eminent Scholar. He received NSF CAREER award in 2007 and was elected to...

Title: Number theory and cryptography   Abstract:  In this presentation Professor Ye will survey his work and progress in number theory since his last colloquium talk in the department. Topics include the Riemann zeta function, automorphic L-functions, their functoriality, upper bounds, and zero statistics, computational number theory, and its applications to cyberspace security or insecurity.   Short Bio: Professor Yangbo Ye is a professor of Mathematics with expertise in number theory and...