Specialty exam presentation
Aaron Tamura-Sato

Modeling Brain Development from MRS Scans of Newborns

Magnetic resonance spectroscopy (MRS) experiments were performed on newborns to investigate the effects of drug-use on early infant brain development. We formulate a model to translate the metabolite concentrations from the scans to a measure of cellular activity for neurons and glial cells in order to compare development rates between different brain regions and between the control and exposed groups.

Let $W_e$ be the $e$th computably enumerable set in a standard enumeration.

For $A \subseteq N$ let $A^{[i]}=\{a: \langle a,i\rangle\in A\}$. Paul Nguyen explores the arithmetic complexity of
$$
E = \{e: (\exists !i) \quad W_e^{[i]}\text{ is infinite}\}.
$$
Specifically, whether $E$ is $\Sigma^0_n$ or $\Pi^0_n$, and whether it is $\Sigma^0_n$-hard or $\Pi^0_n$-hard, for $n\in\{1,2,3,4\}$.

[Added post-talk: He presented a completely satisfactory proof of the perhaps surprising result that $E$ is complete for the class of intersections of $\Sigma^0_3$ and $\Pi^0_3$ sets!]

TITLE Approximation by translates of powers of a continuous periodic
function

SPEAKER: Yitzhak Weit, University of Haifa

ABSTRCT: We characterize the set of real-valued, 2pi-periodic, continuous functions f for which the translation invariant subspace V(f) generated by f^n, n geq 0, is dense in C(T) where T denotes the unit circle. In particular, it follows that if f takes a given value at only one point ( which is necessarily its maximum or minimum) then V(f) is
dense in C(T). One observes that V(cos(t)) contains the orthogonal trigonometric
system {cos(kt) ,sin(kt)} hence it is dense in C(T). Our purpose is to characterize the
set of functions which share with cos(t) this propert.

TITLE Some Tips for UH Math Grad Students

SPEAKER: David Ross, UHM

TITLE TBA

SPEAKER: Thomas Hangelbroek, UHM

John Marriott will defend his doctoral dissertation, available at
http://math.hawaii.edu/home/theses/PhD_2013_Marriott.pdf.

Speaker: Thomas Hangelbroek

Title: A Gentle Introduction to Frames

Speaker: Daisuke Takagi (U. Hawaii, Manoa)

Title: Capturing stealthy swimmers and other adventures in fluid dynamics

Abstract: Fluid dynamics is a branch of applied mathematics concerned with fluids in motion. When a solid body propels itself through fluids the resultant motion is generally difficult to predict. Laboratory experiments reveal how microscopic particles can stealthily swim on surfaces, slide along walls, and slalom through obstacles. These observations are explained using a simple model that accounts for the fluid flow around each swimmer. I will discuss some broader implications of this work and possible directions for future research.