PROGRAM

"Analogies between algebraic number theory and graph theory" by Daniel Vallieres, California State University, Chico. 

Since its introduction in 1859, the Riemann zeta function and its generalizations, such as the Dedekind zeta function, have been objects of intense study.  Many other zeta functions arise in mathematics, perhaps most notably the Hasse-Weil zeta function associated with a curve over a finite field, whose properties are comparatively more tractable. In the 1960s, Ihara introduced a zeta function that can now be interpreted as being associated with a finite graph. In this talk, a few analogies between number theory and graph theory are discussed, with an emphasis on results involving special values of zeta and L-functions.

"How hard is it to untie your shoes?" by Edgar Bering, San Jose State University.

Knot theory is the mathematical study of knots and links. Two fundamental, computational problems regarding knots are the unknotting problem: deciding when a tangled mess is actually knotted. Generalizing this is the trivial sublink problem: given a link (a collection of possibly interacting knots) and an integer k, determine if the link has k components that are both unknotted and not linked to one another. Computational complexity theory gives us a way of precisely describing “how hard” a problem is. The family of NP problems is one of particular interest: roughly, it is the class of problems whose solutions are easily checked. This talk sketches some of the background about knots and links, relates some of the history of these computational problems, and presents a new, elementary proof that the trivial sublink problem is NP-hard. This new proof is due to Tancer, and is written down in a paper by Cheng, Chlopecki, Nazar,  and Samperton.

Discussion Under the Oaks. "Group worthy curve sketching" by Martha Brislen, Sonoma State University.

I loved curve sketching as a calculus student, but as a teacher, I saw students approaching it in a very procedural manner. While they were quite competent at running the first and second derivative tests and could come up with reasonable graphs, they weren't able to connect what we'd learned about increasing and decreasing behavior or concavity with the procedures they were doing. In this activity we do a cooperative curve sketching task I've designed to get students talking about what they're doing, and we have a discussion about group-worthy tasks.

Social Gathering and annual five minute business meeting.

Organizers: Elaine Newman, Thomas Mattman.