Topological modular forms with level structure

The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to restrict to the cusps, providing multiplicative maps from Tmf with level structure to forms of K-theory. In particular, this allows us to construct a connective spectrum tmf_0(3) consistent with properties suggested by Mahowald and Rezk. This is accomplished using the machinery of logarithmic structures. We construct a sheaf of locally even-periodic elliptic cohomology theories, equipped with highly structured multiplication, on the log-\'etale site of the moduli of elliptic curves. Evaluating this sheaf on modular curves produces Tmf with level structure.Comment: 53 pages. Heavily revised, including the addition of a new section on background tools from homotopy theor

The spectra ko and ku are not Thom spectra: an approach using THH

We apply an announced result of Blumberg-Cohen-Schlichtkrull to reprove (under restricted hypotheses) a theorem of Mahowald: the connective real and complex K-theory spectra are not Thom spectra.Comment: 9 pages, 7 figure

Spontaneous Emission in Systems of Reduced Dimension

Matter coupled to light can emit photons. In the absence of an external field this process is known as spontaneous emission. The radiation properties depends in detail the nature of the emitter. In this thesis we consider a two level point-source emitter, and examine how the emission is affected by engineering the local environment. We begin by studying analytically how embedding an emitter in a multi-layer cylindrical structure with radius much smaller than the emission wavelength alters the intensity of the emitted light. We find that for carefully chosen metal-dielectric interfaces, the emission can be strongly enhanced by the plasmonic effect. With this intuition, we experimentally study an InGaN semiconductor quantum dot-in-wire structure as our two level emitter, and manipulate the local field environment by coupling to a lossy plasmonic cavity. We find that the strong enhancement of the field around the quantum dot due to the metal more than compensates for the non-radiative losses, leading to order-of-magnitude increases in the radiative spontaneous emission rate, as well as overall brightness. We then examine how the emission of light can be affected by other nearby emitters. The cooperative effects are strongly dependent on the dimension of the system which controls the electromagnetic mode overlap of the emitters. We present a unified formalism capturing how these cooperative effects change from one dimension to the next. Cooperative light scattering between emitters underpins collective effects such as super- and sub-radiance, and we numerically investigate how our previous results give rise to the key experimental signatures that can be used to identify those phenomena. Specifically, we study how the superadiant decay rate scales with the size of a $2$-dimensional atomic cloud, and how cooperative effects between a small number of emitters alter the emission spectrum of strongly driven resonance fluorescence.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144047/1/hityler_1.pd

A Functional Ecological Comparison of three Sponge Species from the Lower Florida Keys

The shallow, tidal flats off the islands of the lower Florida Keys represent a harsh environment for sessile marine invertebrates. This habitat is home to three taxonomically distinct sponge species that share similar rope morphologies: Cliona varians forma varians, Ircinia variabilis, and Neopetrosia subtriangularis. Despite sharing a habitat, these three species differ in their symbiont regime, with C. varians hosting dinoflagellate photosymbionts, and I. variabilis and N. subtriangularis hosting cyanobacterial photosymbionts. We conducted experiments to measure other ecological differences between these species. The sponges were all assayed for pumping rates using dye-video analysis and tissue samples were taken to compare the composition and functional genes of their microbiomes. The results indicated that N. subtriangularis had a significantly higher pumping rate than the other species. The microbiomes of the species varied, and the microbiome functional gene screening provided evidence that C. varians forma varians hosts nitrogen fixing bacteria, that I. variabilis hosts methane metabolizing bacteria, and that N. subtriangularis hosts nitric oxide reducing bacteria. More work is currently underway to examine the metabolism of these sponges, giving us insight into the unique ecology of this harsh habitat

Automorphic forms and cohomology theories on Shimura curves of small discriminant

We compute the homotopy groups of spectra associated by a theorem of Lurie to the Shimura curves of discriminants 6, 10, and 14, beginning with a computation of integral rings of automorphic forms on these curves. As an application, we find that a generalized truncated Brown-Peterson spectrum BP is an E_\infty ring spectrum at the prime 3.Comment: 46 pages, 3 figures. Updated versio

Varicella Zoster Virus Encephalitis

Varicella zoster virus in the adult patient most commonly presents as shingles. Shingles is a painful vesicular eruption localized to a specific dermatome of the body. One of the potential complications of this infection is involvement of the central nervous system causing encephalitis. An increased risk of this complication is associated with the immunocompromised patient. In this case report, we review the history and physical exam findings that should raise clinical suspicion for varicella zoster encephalitis, as well as the epidemiology, risk factors, treatment, and prognosis of this type of infection

“I get that ball and I am running…like nothing else is there with me”: an interpretative phenomenological analysis of rugby players’ experience of flow during game-play

Background: This research examines the flow experience of rugby players following game-play. A flow experience is when an individual becomes completely immersed in the task at hand, as the task is challenging enough to push the individual to perform at their optimum skill level. Limited research focuses on flow in competitive, team-based environments and the implications this has for team dynamics and wellbeing. Methods: Semi-structured interviews were conducted with five rugby players from the Old Northamptonians rugby club and was analysed using interpretative phenomenological analysis. Findings: Participants’ accounts highlighted three main aspects of flow which appeared to be relevant to competitive gameplay. This included communication, which was dependent on player position and role; perception of control, which focused on gaming restrictions and mind set; and time distortion; which was dependent on experience and perception of in-game challenges. Discussion: These findings help explain how rugby players individually experience flow, as well as how coaches may experience a flow states at the same time, but have a different perception of the experience. This research has implications for helping to promote flow experiences and to encourage individuals to become more aware of when they are experiencing flow, both in rugby game-play and in other aspects of their lives