Dr. John F. Hamilton, Jr.		Dr. Dan Isaksen

	Dr. John F. Hamilton, Jr.
	Photographic Science and Technology Center, Kodak Research Labs, Rochester, NY
	Biography:	A graduate of Cornell University, John Hamilton received his Ph.D. in mathematics at Indiana University. In 1974, he accepted a position at the Kodak Research Laboratories where he applied mathematics to various problems in graphic arts (printing), medical imaging, clinical diagnostic imaging, and electronic digital imaging. He is a Research Fellow, a recipient of the Eastman Innovation Award (2003), a recipent of the Rochester Intellectual Property Law Association (RIPLA) Distinguished Inventor of the Year Award (2005), and a member of Kodak’s Distinguished Inventors Gallery with 42 patents in the area of digital image processing. Currently, he is developing novel image processing algorithms for Kodak's digital camera business, Kodak's sensor business, and related applications.
	Title:	Industrial Mathematics
	Abstract:	This talk is about the kind of problems found in "industry" and the role played by mathematicians in solving them. Most industrial problems are multi-disciplinary in nature and require the efforts of several people to find a solution. While math modeling is an important problem-solving skill, other "non-math" skills are equally important. These include good communication and the ability to deal with people from other areas of science and business. A brief summary is presented of actual problems encountered at Kodak.
	Title:	Digital Imaging and Mathematics
	Abstract:	Digital imaging abounds with opportunities to apply mathematics. Image processing, for example, makes use of vector spaces, linear shift invariant transformations, Fourier analysis, and convolution. The inherent noise processes in the physics of image capture include both Gaussian and Poisson distributed random variables. Finally, modeling the human visual system involves a vector space projection of spectral energy distributions to a three-dimensional subspace. The talk then takes the audience through the standard image processing steps that happen in a fraction of a second, each time a person pushes the button to take a digital picture.

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	Dr. Dan Isaksen
	Department of Mathematics, Wayne State University. Detroit MI
	Biography:	Dan Isaksen is an associate professor of mathematics at Wayne State University in Detroit, Michigan. He has been involved with REUs for many years in various capacities: as an undergraduate student, as a graduate advisor, and as a director. His mathematical interests concern applications of algebra to geometry and topology.
	Title:	Quaternions, Octonions, and Beyond
	Abstract:	There are three well-known real division algebras: the real numbers, the complex numbers, and the quaternions. The octonions are another real division algebra of dimension 8; it's more obscure than the other three but still classical. I will describe the octonions and explain some of their uses. These examples generalize into a famous family called the Cayley-Dickson algebras. I will discuss some of the properties of the 16-dimensional Cayley-Dickson algebra.

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