Physical Sciences and Mathematics Commons^™

The Eichler-Selberg Trace Formula For Level-One Hecke Operators, Alex Barron

Honors Theses

This paper explains the steps involved in the proof of the Eichler-Selberg Trace Formula for Hecke operators of level one. It is based on an appendix in Serge Lang's Introduction to Modular Forms written by Don Zagier, though I also draw heavily from sections of Toshitsune Miyake's Modular Forms and Xueli Wang's and Dingyi Pei's Modular Forms with Integral and Half-Integral Weights.

Section 2 summarizes the necessary background in the theory of modular forms. The material covered here is standard, so I've left out most of the details and proofs. Most of the section is based on Chapter VII of …

Metallic Mineral Mining In Maine, Kaitlyn Bernard

Honors Theses

In 2012 the Maine State Legislature passed a bill directing the Maine Department of Environmental Protection (DEP) to rewrite the regulations governing metallic mineral mining in Maine. The bill was introduced after pressure from Maine’s largest private land owner and timber company, J.D. Irving, Limited. The company has a lucrative mineral deposit on one of their landholdings in northern Maine and is interested in pursuing a mining development project. The bill aimed to streamline the regulatory framework around mining operations and make the permitting process more conducive to mineral development throughout the state. The 2012 Maine Metallic Mineral Mining Act …

Massive Quiescent Disk Galaxies In The Candels Survey, Aurora Y. Kesseli

Honors Theses

We used data from the GOODS-S field of the CANDELS survey in order to confirm previous studies that found that large fractions of high-redshift galaxies (z ∼ 2) are disk-dominated (McGrath et al. 2008; van der Wel et al. 2011). In the GOODS-S field we selected out all the massive quiescent disk galaxies by imposing a mass limit of M > 10¹⁰M_⊙ and a redshift range of 0.5 ≤ z ≤ 2.5, and then choosing the quiescent red galaxies from a color-color plot. Once we had our sample, we did a qualitative visual classification of each galaxy and …

Massive Gravity Theories, Greg Seyfarth

Honors Theses

We examine Fierz and Pauli's work in 1939 of adding a mass term to the Lagrangian for linearized gravity with the form ?? where h is a small perturbation away from flat spacetime and showing that the only value for ? which gives a ghost-free theory with the correct five degrees of freedom expected for a massive spin- 2 particle such as the graviton is ? [1]. We start by rederiving the Lagrangian formulation for classical electrodynamics and giving examples of a ghost. Then we solve the linearized massless gravity equations to show their two degrees of freedom. We perform …

Investigating The Interaction Of Zinc-Finger Peptides And Nicked Dna Using Phage Display, Rachel Maria Guerra

Honors Theses

Recognition of structural features of DNA such as gaps, nicks and abasic sites is critical for many DNA-binding proteins, such as those involved in DNA damage repair. This study explores a novel strategy to model these protein-DNA interactions using phage display. Phage display has been commonly used to identity zinc fingers that bind to DNA sequences, but selection of peptides that binding to specific DNA structures has not been reported in the literature. A phage library of 109 variants was created based on one of three zinc finger domains of the DNA repair protein poly (ADP-ribose) polymerase I. The library, …