February 1-14, Distinguised Visiting Professor: Il Bong Jung, Kyung Pook National University
COLLOQUIUM Thursday, February 10 - 4:00 Olin 372
Title: Gaps between operator classes and examples
Abstract: We continue the first talk and, in addition, discuss recent research on bridges - classes falling between - the well known classes of hyponormal operators and subnormal operators. In particular, we consider k-hyponormal operators and weakly k-hyponormal operators.
Unsolved problems in mathematics can be discovered in some interesting places. We will begin by briefly discussing a few problems that I have stumbled upon, and will also consider the method of stumbling in each case. Then we will focus on one particular problem that came from a book my high school math teacher gave to me at graduation. The problem comes from combinatorics and involves integer-labeled graphs. No previous knowledge of graph theory will be assumed.
Operations research (OR) is a scientific approach to analyzing problems and making decisions. OR can be applied in virtually every area of business and government, from capital budgeting to airline scheduling. In this talk we begin by reviewing the standard solution methodologies for linear and integer programs. We then show how these methods can be extended to solve 0-1 quadratic programs.
The mathematical framework of quantum mechanics is a non-classical probability calculus. In this talk, I’ll compare this "quantum probability theory" with its classical precursor in the context of a very general, but very simple, and conceptually very conservative, extension of the latter. (Prerequisites: basic linear algebra and very basic probability theory. No knowledge of quantum mechanics will be presupposed.)
Although relatively new, the study of Configuration Spaces of (uncolored and colored) Graphs has produced interesting combinatorial and topological results. The field gets its motivation from real life applications like that in robotics. In this talk, I will give you a quick tour around these spaces and present some small results in regards to the connectedness of these spaces. Prerequisite: NONE, although some elementary graph theory knowledge may help
After playing a round or two of the card game SET (a family favorite in the speaker's home), we will consider some mathematical questions related to the game. The answers come from adapting our Calc III knowledge of the geometry of R^n to finite vector spaces and then doing some counting. The main ideas are adapted from an article by B. L. Davis and D. Maclagan in The Mathematical Intelligencer.
Abstract: In 1742, Goldbach conjectured that every positive integer greater than 2 is the sum of at most three prime numbers. Over 250 years later this conjecture is still unproven! An easier problem to answer is: Is every number the sum of at most 2 squares? How about three or four squares? Lagrange was the first to prove that every number was the sum of at most four squares. We will discuss his solution to this problem as well as some solutions to related problems.
COLLOQUIUM Tuesday May 3, 4:00 Olin 372
Title: "Special generators of C*-algebras I"
Abstract: This talk will give an introduction and overview of recent joint work with Paul McGuire about characterizing those bounded linear operators A on a Hilbert space such that C*(A) has a subnormal or hyponormal generator. When A is a "nice" operator, then the answer only depends on the "spectral picture" of A. Hence the answer takes a pleasing form as it involves describing which "pictures" satisfy the right conditions.
COLLOQUIUM (A more in-depth Talk) Wednesday May 4, 2:00 Olin 372
Title: "Special generators of C*-algebras II"
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