I work as a research associate in the Naito Laboratory at Harvard University, with Professor Xiaowei Zhuang in the departments of Chemistry and Physics. I also continue my affiliation with the Photonics Center of Boston University, where I worked in the group of Professor Bennett Goldberg and Selim Ünlü. I also work on a number of independent research projects, in various stages of completion, with the hope of culminating with publication in an academic journal.

Some day I hope to have more content on this part of my site, including links to individual project pages, with more information, publications, references, and so forth. I will also be adding a collection of Standard Operating Procedures (SOPs) that I've been writing for various laboratory tasks one might encounter in a physical chemistry, optics, or materials science laboratory. For the moment, here's a listing of the various projects with which I'm involved.

Zhuang Group Projects

Goldberg/Ünlü Group Projects

• Rotating Aperature Interference Nanoscopy
• Spectral Self-Interference Fluoresence Spectroscopy (conference paper)
• Optical Waveguide Phase Tomography
• Evanescent Waveguide Biosensing (project page)
  
• High-Resolution Diffraction Grating Fabrication

Independent Research

• Mathematics of Pile Shuffling (more information)
• 2-D Constant Aspect Ratio Strip Packing (more information)
  
• The History of the Discovery of the Electron (with John Straub, more information)
  
• The History of Avogadro's Number (with John Straub, more information)
• Dissociation of Sodium Chloride (more information)
• Digital Libraries (more information)
  
• University Mathematics Education (more information)
  
• University Science Education (more information)
  
• Raphael Semmes (more information)
  
• George Johnstone Stoney (more information)
  
• Miscellaneous Topics (more information)

Pile Shuffling
I've become interested in the mathematics of pile shuffling, which is a technique for shuffling a deck of cards. One takes the top m cards from a deck of n cards and so makes m separate piles. One then sequentially places the next m cards from the n-m cards remaining in the deck on top of the m cards, thus ending up with m piles of n/m cards, assuming that m is a factor of n, or one ends up with m - n mod m piles with one fewer card. The separate piles are then recombined into a deck of n cards in a new ordering and the process is repeated. The technique poses a number of interesting mathematical questions, since unlike the riffle shuffle, even in practice this technique is completely deterministic. How many shuffles are required to get a random ordering? How does the size of n and m effect the result after multiple iterations? Can the original ordering of the deck ever be regained by accident? Mathematica is used heavily in this investigation.

2-D Constant Aspect Ratio Strip Packing
The one dimensional bin packing problem is well researched. The goal is to "pack" a set of one dimensional objects of varying lengths, l_i, into the fewest bins each of a finite size L, such that all l_i <= L. A number of variations on this problem exist, and it has been well studied because of its important applications, particularly in the allocation of computer memory. This problem can also be easily generalized to two and higher dimensions. A related problem is that of two dimensional strip packing, also sometimes known as the cutting stock problem because of its application to clothing manufacturers who wish to minimize the length of cloth they must use to cut out a variety of patterns. For the case where the patterns are rectangular and the cloth is a finite, given width the problem is well studied, and there exist a number of excellent algorithms that give an upper bound on the length required to fit all of the patterns with the least wasted space. I've become interested in a novel variant of this problem that I call the constant aspect ratio strip packing problem, wherein the rectangular patterns are allowed to scale both larger and smaller, so long as the aspect ratio is maintained. The goal is to pack a set of rectangles into an area of a given aspect ratio such that the entire area is covered, and so that there's a minimum variance in the percent size increase or decrease of each of the component rectangles. This problem has not been studied because it does not arise naturally in the study if computer architecture nor does it have immediate industrial applications. However, it is an inherently interesting problem, and does have some applications, such as in the generation of a collage from a set of computer images, which is how the problem was first suggested to me.

History of the Electron
After a lecture demonstration in chemistry class, Professor John Straub and I became interested in the history of the discovery of the electron, and why certain experiments were not performed at the turn of the century. We have been actively pursuing this topic over the last several years and intend to publish the results of our research within two years.

Avogadro Constant
In the course of our investigation concerning the development of the electron Professor Straub and I became very interested various methods of measuring Avogadro's Number (Loschmidt's Number is equivalent). The enormous variety in both experimental and theoretical methods for the calculation of this very important chemical constant are quite astonishing, and also very illustrative of the history of chemistry in the late nineteenth and early twentieth centuries. We are currently compiling a graph of various measures of this constant over time, complete with the appropriate error bars, to demonstrate the specifically non-monotonically converging nature of chemical metrology.

Dissociation of Sodium Chloride
My interest is the dissociation or solvation of sodium chloride has grown out of a paper (Pavel Jungwirth, "How Many Waters does it Take to Dissolve a Rock Salt Molecule?" Journal of Physical Chemistry A, 104, 145, 2000) I read in the fall of 2000, as I was taking a physical chemistry course. I investigated this problem both by delving back into the experimental and theoretical literature, as well as performing ab initio calculations of the gas-phase dissociation in various water clusters, using PC-Spartan Plus, a software package made by Wavefunction Inc. In this investigation I found that Spartan is essentially useless for serious physical chemistry research, although it does have very intriguing possibilities in the teaching of organic, and possibly physical, chemistry. I also found that there were many serious methodological errors in Jungwirth's paper, and that the generally accepted criteria for dissociation of ions in solutions is somewhat unsatisfactory. I've recently revisited this problem as part of the graduate class on quantum mechanics I took in the fall of 2001, and I am performing new ab initio calculations with the far more powerful Gaussian 98W, and with a better understanding of quantum mechanics and electronic structure. The solvation of sodium chloride is an example of a little-researched area of chemical physics that I am very interested in, called mesoscopic chemistry, or the chemistry of clusters. While behaviors and interaction at the macroscopic and microscopic levels are comparatively well understood, this understanding has not translated cleanly into intermediate regimes. For example, while one can classify a macroscopic collection as belonging to a particular phase of matter (solid, liquid, gas, etc.) and it is clear that a single water molecule, for instance, cannot be so classified, it is unclear what meaning this concept has for a water cluster. I believe that this will be an increasingly important area of research.

Digital Libraries
As a member of the Faculty of Arts and Sciences Standing Committee on the Library at Harvard University, and an avid user of libraries, I've thought a great deal about how libraries are changing with the advent and implementation of new technologies, particularly digital imaging and searching algorithms. My interest in "digital libraries" is actually representative of a greater interest in computing in the humanities in general. I've done some working performing frequency analyses of Ancient Greek literature, comparing technical aspects of Plato's imitations of Lysias' oratory in the Phaedrus, to Lysias' own corpus, using Plato's other works as a control, to see if Plato was aiming for fidelity or humor in his imitation of Lysias. I've also worked a bit with Professor Mark Schiefsky of the Classics department at Harvard University on his Archimedes project, and I am a contributor to the Voice of the Shuttle internet project. I'm also interested in strategies of searching the internet, and the place of the internet in contemporary research.

College Mathematics Education
While a student of calculus and differential equations some years ago, I became interested in college mathematics education, specifically introductory mathematics education. I wondered whether the standard two-semester introductory sequence of single-variable differential and integral calculus was still the best choice for the first college mathematics courses, which not only asks questions about calculus and discrete mathematics (the latter being a candidate to replace calculus as the standard introductory course) but also of the aims of college mathematics educations for various kinds of students. I am kept current in this area by the seminars on mathematics education organized by Professor Daniel Goroff of the Derek Bok Center for Teaching and Learning at Harvard University, and I am in the process of developing a complete argument covering how discrete mathematics better fulfills the purpose of college mathematics for many students.

College Chemistry Education
My interest in science education at the university level is related to my interest in mathematics education in so far as I am trying to rethink the purpose of science training for various kinds of university students. But the particular concerns of chemistry education are quite different from those of mathematics. I am interested in several accepts of college chemistry education: the structure and variety of general chemistry courses; the use of technology, specifically quantum mechanical modeling software, in the teaching of introductory organic chemistry; the place of and structure of physical chemistry in the curriculum; the discontinuity between introductory and advanced textbooks.

Raphael Semmes
An extremely well-read and well-educated Confederate solider, Semmes was both an admiral and general for the CSA. His memoirs of both the Mexican War and the Civil War are fascinating, and he holds an unusual position as a modern solider and as a southern gentleman imbued with notions of honour. I've written extensively, but as of yet unpublished, concerning this most interesting figure from the American Civil War.

George Johnstone Stoney
While researching the history of the discovery of the electron, I found that an Irish scientist, G.J. Stoney had actually coined the term electron, some years before J.J. Thomson's discovery of the particle. Stoney had a fascinating career as an extremely creative scientist, but is often not so well known any longer, and there's lots of biological research yet to be done on his career.

Randomness of Run Support
It is often said that the number of wins and losses that a baseball pitcher accumulates over a year is a poor measure of that pitchers worth, since the number of runs that his own team scores behind him is out of his control. Sometimes, the number of runs that the opposing team scores is also out of his control because of errors committed by his defense. Thus the earned run average (ERA, the number of earned runs the pitcher would allow in an average nine-inning game) is widely touted as a more fair metric to evaluate the performance of a pitcher. But some say that pitchers with a low ERA, few wins, and many losses, are not just saddled with bad luck, but just don't quite know how to win--how to turn up the intensity when the going gets tough. Some are more charitable and suggest that teams play different behind certain pitchers--either not scoring as many runs as they might otherwise because they know they don't necessarily have to in order to win, or playing sloppy defense because the pitcher takes an inordinately long time in between pitches. I'm currently looking at a large set of statistical data to see how random run support really is.

Seat Location in Lectures
Do students learn better if they sit closer to the front of the lecture hall? Will they learn better if forced to sit closer to the front? How do final grades correlate with the number of absences in a class?

Historiography of Greek Mathematics
What is the best way to segment and categorize ancient Greek mathematics? Should practical arithmetic, geometry, number theory, logic, and geometric algebraic be looked at as separate disciplines? Did the last even really exist in Greek mathematics? This is at once the central question and the starting question in the history of Greek mathematics, and one that occupies a great deal of my thoughts, and a great deal of my academic courses in the history of science. Ultimately, it is from the historiography of Greek mathematics, that my "continuity theory" of science originates.

Linguistics of Computer Languages
Computer programming languages have a number of striking similarities with natural languages in both form and development. However, unlike natural languages where the focus is almost always on verbal communication, programming languages, and most other formal languages (such as mathematical notation, or symbolic logic) lack a well defined phonetic system and require a completely unforgiving orthography. The study of programming linguistics is interesting from a purely theoretical computer science or theoretical linguistics standpoint, but also has important practical application, as it becomes significantly more important for a greater proportion of the population to learn and use computer programing languages.

Chinese Expatriate Names
I've become interested in what kinds of personal names Chinese people living outside of China use. I've made an ethnographic study of this question, drawing on responses from a set of college-aged students of Chinese ethnicity living in the greater Boston area. I am planning to significantly expand the ethnographic aspect of this study, and combine it with the significant theoretical apparatus that I've constructed as a project in a Chinese anthropology course I took in the fall of 2000.

Byron and Ancient Greece
A very long time ago, when I was in high school, I wrote a paper about the influence of Ancient Greek literature and thought on Lord George Gordon Noël Byron, the great English poet (and my favourite English poet). I continue to be interested in this topic, although I am not currently actively revising my paper.