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Here you can find some information on all the students who are currently doing research with me (both graduate and undergraduate). If you are interested in these projects, there are always more problems to be asked and worked on! Feel free to stop by my office (if you are a Clarkson student) or send me an email at aluttman@clarkson.edu. |
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Aaron Luttman’s Student Research Page |
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Email: aluttman@clarkson.edu |
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Current Research Students (School Year 2009-2010) |
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Current Student Research Projects |
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Former Research Students |
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Here are some of my currently available student research projects. If you are interested in any of these, feel free to contact me.
Pure Math Projects: · Investigating the existence of functions in algebras of Lipschitz functions on compact metric spaces. (Undergraduate) · Investigating how eigenvalues determine the properties of matrices and of bounded linear operators on Banach spaces. (Undergraduate) · Classifying spectral-preserver maps between Banach algebras (Graduate)
Applied Math Projects: · Computing statistical properties of temperature and precipitation data (PRISM) for the purpose of analyzing regional climate change. (Undergraduate) · Developing optical flow methods for turbulent flows in order to approximate mass transport from video data. (Undergraduate or Graduate) |
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SUNY-Clarkson Mathematics REU, Summer 2010 Project |
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My summer 2010 SUNY-Clarkson REU team will be working on a project related to identifying and classifying matrices through information about the eigenvalues of combinations of matrices. This is a project that sits at the intersection of analysis, algebra, and linear algebra, so, while the only required pre-requisite is linear algebra, any background in analysis or abstract algebra will also be helpful. If you don’t have that background, don’t worry! Once we have the classification for matrices, we will extend our results to general bounded linear operators on Banach spaces, including teaching you what that means. If you have any questions about the REU, contact the program director, Dr. Joel Foisy. Also check out the REU website! |
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Bio: I will be a freshman in the fall and plan on majoring in mathematics here at Clarkson, as well as participating in the Honors Program. I graduated salutatorian in a senior class of 440 from Frontier Central High School of Hamburg, NY and have earned potentially 30 college credits. Throughout high school I was a middle school math tutor, member of the International Club, and student of the Hamburg Dance Center. |
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Research: My research this summer is in preparation for a STEM summer institute workshop for middle school teachers that will show how to incorporate math modeling into the middle level curriculum. Specifically, I am studying the possibility of adding extracurricular activities through the analysis of the multiple factors that determine if a particular activity can or should be added. |
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Bio: I was born and raised in Pittsfield, Massachusetts. Now I study math at Clarkson, where I found Aaron. In my free time I enjoy riding my bike and playing bass. |
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Research: I'm currently interested in identification on algebras of continuous functions and uniform algebras. I'd like to classify polynomials of two variables by what information is needed about this polynomial evaluated at a given continuous function f and each member of a norm-restricted class of continuous functions to completely determine f. |
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Bio: I am currently a senior at Clarkson seeking dual degrees in Electrical Engineering and Physics (with a math minor). I hail from Vermont and love the brief summer months afforded to Potsdam. When I am not doing school work or research I am often outside playing ultimate frisbee or soccer, biking through the woods, or playing pick up games in various other sports. |
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Research: My primary interests are signals and image processing. My current work is in image processing and incorporates optical flow analysis of video data. The data in question is an infrared video of a leaf undergoing photosynthesis. The approaches for optical flow use variational optimization methods to find the change (as a vector field) between frames of the video. |
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Bio: My name is Kristopher Lee and I'm currently a graduate student at Clarkson University. I'm originally from Long Island, but I don't have the accent. Other than mathematics, I spend most of my time writing/playing/listening to heavy metal music. |
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Research: I'm interested in analyzing maps, not assumed to be linear, between uniform algebras that preserve some structure, i.e. the norm or the spectrum. The essential tool to this work is a result known as Bishop's Lemma and I'm interested in extending this result to other algebras. |
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Bio: I am in my last year of undergraduate study, double-majoring in Mathematics and Theatre at Bethany Lutheran College in Minnesota. Aside from math, I just about live in the theatre, though I also enjoy reading, traveling, and being active outdoors. Hiking, biking, and eating ice cream are some of my favorite non-research activities from my summer of research at Clarkson University. |
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Research: I am doing research in operator algebras on Banach spaces, looking for ways to identify operators given some specific eigenvalue information. In the finite-dimensional case, this is just working with matrices: we identify a matrix by looking at subsets of the eigenvalues of combinations of this matrix with collections of rank-one matrices. In the infinite-dimensional case, we use subsets of the spectrum of similar combinations with simple tensors to identify an operator. |
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Bio: I graduated as the 2009 valedictorian of South Glens Falls Senior High School located in South Glens Falls, NY. In the fall of 2009, I will be a freshman Honors student at Clarkson University and will be entering into the University Studies program. I plan to obtain a minor in mathematics. |
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Research: This summer I had the opportunity to work on pre-frosh research. My research involves working with mathematical models to show and predict the spread of disease. This is related to three main subclasses of those who are susceptible to, infected with, and recovered (or immune) from a disease. |
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Bio: I am Benjamin Ritz, and no, there’s no relation to the crackers or the hotel. I’m a pre-frosh Summer Researcher here at Clarkson. I’m looking to be a Chemical Engineering major, possibly doubling with Mathematics. This is, unsurprisingly, my first research opportunity, and I look forward to seeing it through and experiencing it. |
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Research: As far as research, my exact task is, thus far, unknown to me. However, I am going to be working with mathematical modeling, most likely modeling a problem that affects Middle or High School students, as I am freshly out of that setting and can provide insight into the student mindset.
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