The Department of Mathematics at University of Hawaii at Manoa has long had an informal graduate program in logic, lattice theory, and universal algebra (People, Courses, Description) going back to Alfred Tarski’s 1963 student William Hanf.

We are offering the following course rotation (courses repeating after two years):

Semester Course number Course title Instructor
Fall 2015 MATH 649B Graduate Seminar Kjos-Hanssen
Spring 2016 MATH 649 Applied Model Theory Ross
Fall 2016 MATH 654 Graduate Introduction to Logic Beros
Spring 2017 MATH 657 Computability and Complexity Khan
Fall 2017
Spring 2018 MATH 649 Applied Model Theory Ross

It is also recommended that students familiarize themselves with undergraduate level logic, which is offered on the following schedule:

Semester Course number Course title Instructor
Fall 2012 MATH 454 Axiomatic Set Theory Kjos-Hanssen
Spring 2013 MATH 455 Mathematical Logic
Fall 2014 MATH 454 Axiomatic Set Theory Ross
Spring 2015 MATH 455 Mathematical Logic Khan
Spring 2016 MATH 454 Axiomatic Set Theory Khan
Spring 2017 MATH 455 Mathematical Logic Ross
Spring 2018 MATH 455 Mathematical Logic Khan
Fall 2018 MATH 454 Axiomatic Set Theory ?

#### Faculty teaching in the program

David A. Ross, Professor
Bjørn Kjos-Hanssen, Professor
Mushfeq Khan, Temporary Assistant Professor 2014-2018
Achilles Beros, Temporary Assistant Professor 2015-2018

# Marriott’s doctoral defense

John Marriott, a student of Prof. Monique Chyba, will defend his doctoral dissertation on September 5.

#### Abstract

This work addresses the contrast problem in nuclear magnetic resonance as a Mayer problem in
optimal control. This is a problem motivated by improving the visible contrast in magnetic resonance
imaging, in which the magnetization of the nuclei of the substances imaged are first prepared by
being set to a particular con figuration by an external magnetic field, the control. In particular we
examine the contrast problem by saturation, wherein the magnetization of the first substance is
set to zero. This system is modeled by a pair of Bloch equations representing the evolution of the
magnetization vectors of the nuclei of two di fferent substances, both influenced by the same control
field.
More…

# The zeros of entire functions

Graduate student Rintaro “Yoshi” Yoshida will defend the degree of Ph.D. on Thursday May 2, 2:00pm, in Keller 301.

We invite the reader to consider the entire function whose restriction to $\mathbb R$ is pictured above:
$$\varphi_{_{1/5}}(x) = \sum_{k=0}^\infty \frac{x^k}{(k!)^{(6/5)}}$$
Do you think this function has any non-real zeros? Does it belong to the Laguerre-Pólya class? See the draft dissertation for answers.