Richard Crago, Civil Engineering

What does Discovery mean to you?

Coming up with a hypothesis that you think might work, testing it against data, and finding that it does in fact work. In my research, that’s the nature of discovery. My research deals with estimating evaporation and transpiration from land surfaces using remotely gathered data from satellites. This is very useful for estimating the amount of water available during the growing season. . . My master’s thesis advisor presented the project to me, and I looked into it and found that I was very interested in the subject area. What’s great about research at Bucknell is that we can pick projects of personal interest. Even if we can’t get our research published, we can still work with a student on something we find fascinating.

Pete Brooksbank, Mathematics

Pete Brooksbank

photo from bucknell.edu

 Is there any way you could in laymen’s terms structure one of the algebraic problems you are trying to solve using these really advanced and complicated models?
"Sure. Maybe a good thing to think about is the familiar Rubik’s cube. With the cube, there six different faces that you can rotate, and there are many different configurations that you can generate from these face rotations. Rather amusingly, Ideal Toy, the original manufacturers of the cube, wrote on the packaging that there are more than 3 billion configurations. This sounds like an awful lot, but in fact they underestimated the actual number by a factor of about 10 billion! The challenge, if you’ve ever played with the cube, is to take a scrambled configuration and return it to its original solved state. People who are good at this come up with various "macros" that move the cube from more scrambled to less scrambled states, with each successive state being a better approximation of the solved cube. In this way they are able rather quickly to reach the solved state. Of course, when human beings solve the cube, they are really using a lot of geometric insight and visual recognition. However, you can also think of the cube problem in purely algebraic terms: underlying it is an example of the kind of algebraic problem that I’m interested in. Specifically, you have a couple of fixed symmetries of the cube, namely the face rotations, and you are given a scrambled configuration of the cube. Your job is to unscramble this configuration back to the solved one. The catch is that you don't have a physical cube to work with! All you have is the algebraic description of what these different face rotations are doing. Well, you can in fact program a computer to do this, but it’s not going to produce the optimal solution because you have not told it that there's a cube behind the problem. Thus, the computer cannot have the same geometric intuition as human beings. Rather, it works only with the algebraic structure. Despite this apparent handicap, computer algorithms can solve the cube almost effortlessly using a moderate number of moves. So that’s one type of problem that I'm interested in. It’s an example of a "constructive word problem" for algebraic objects called "groups". There are far more general versions of that problem, and highly refined methods for solving them. As these methods go, the Rubik’s cube problem is child’s play: the computer can solve the cube in the blink of an eye. In my work, I deal with vastly larger algebraic objects whose underlying structure is far more complex than that of the cube."

Chris Martine, Biology

Professor Martine talks about plant biology and gives us a tour of the greenhouse. If you find this interesting, be sure to check out Martine's YouTube series linked at the end of the video!

Richard Henne-Ochoa, Education

What's been your biggest "aha!" moment of your research career?
“The biggest “aha!” moment of my research career occurred when I truly recognized the sophistication of language-minoritized childrens' verbal artistry and efficacy. More particularly, when I started to look closely at the forms and functions of Native American kids’ English language use, it was plain to me that I wasn’t witnessing just impoverished versions of what adults speak. What I saw was very complicated, sophisticated, and efficacious talk—in its own right! When I realized that Native American kids' talk had this kind of richness and power, I knew I was really on to something big. Ideologies in the dominant U.S. culture of what constitutes good speaking or good language use can be pretty narrow and limited to the extent that grammatical correctness is the main standard against which language use is measured. If we just open our eyes and ears to the ways of speaking used in different cultures, including the use of English in those cultures, we realize that there is such a wide array of beautifully artistic and highly efficacious talk, ways of speaking that most of us are not accustomed to hearing.  There’s so much to learn about these ways of speaking. I'm trying to get at that everyday, what language-minoritized kids can do with language. I am especially interested in what they can do with language that isn't school sanctioned, language use that schools don’t see as legitimate or worthy. I'm looking at ways of speaking that are not considered “correct" by school standards but are, according to local cultural standards, just as expressive, just as artistic, just as efficacious as any language use that is validated in formal educational environments. When these non-dominant ways of speaking by language-minoritized kids are empirically specified, educators can then tap into these funds of linguistic knowledge and skill and build bridges to ways of speaking English that have more widespread social and cultural capital.”

Jeff Langford, Mathematics

What is your research?

I study heat flow and problems in math and physics using techniques of pure math. Most of the time I work on a problems that have physical motivation. My main interest is in the mathematical techniques that are used to tackle these problems.

Here is one example of a problem. Imagine a perfectly square room with perfectly insulated walls, so no heat can enter or leave the room. Now draw 16 floor tiles: half generate heat, and the other half absorb heat.Then create a second room, with the same size and insulation as the first. Move all of the hot tiles together in each column. The conjecture is that the second room will have a larger gap between the maximum and minimum temperature than the first. I proved this correct a few years ago, and I’m currently working on writing up my solution for the same problem in higher dimensions.

The most interesting part of my research to me are the techniques I use to solve these problems. I’m not a physicist, but I like to think I have good intuition for solving the problems.

What do you do when you get stuck?

If I get stuck with this research I try one of two things. First, I can try to solve an easier problem. Sometimes, solving that problem will give me insight or techniques that can carry over to the harder problem. Another option is to search the literature for similar problems. I focus my attention on the techniques that other researches use and try to adjust them to fit in my situation. Sometimes, I get lucky, and find something useful.

Karen Castle, Chemistry

Professor Karen Castle of Chemistry discusses her research and gives a quick tour of her lab.

Discovering Lasers

Eric Tillman, Chemistry

What got you interested in your research? 

Professor Tillman conducts research on mechanistic polymers. As a graduate student Professor Tillman joined a research group where they made polymers and they tried to convert these polymers into cyclic polymers. They had the challenge of designing, understanding, and then using these reactions to build something specific. This research group interested him in polymer research, and since Professor Tillman really liked organic chemistry. According to Professor Tillman, "Polymer chemistry is just really applied organic chemistry, and I really liked the process of learning organic chemistry and then applying what I learned in organic chemistry to make polymers." In his research group at Bucknell, he tries to use organic chemistry reactions to link polymer chains together.