FRIDAY Arrival. No formal activities planned. Set up campsites and join us for a "Meet and Greet" Social Gathering.
SATURDAY
10:00 AM "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, I will discuss a few analogies between number theory and graph theory, with an emphasis on results involving special values of zeta and L-functions.
11:00 AM "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. In this talk I’ll sketch some of the background about knots and links, relate some of the history of these computational problems, and present 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.
Noon Student Poster Session.
3:30 PM 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. So we'll be doing a cooperative curve sketching task I've designed to get students talking about what they're doing, and we'll have a discussion about group-worthy tasks.
8:00 PM Family Social Gathering and annual Five Minute Business Meeting.
SUNDAY Departure.
Directions: Dry Creek Campground (Site #2) at Whiskeytown Lake is west of Redding along Highway 299. See the maps page for details.
There is a $25 per vehicle park use fee (or display your National Parks And Federal Recreation Lands Pass). The fee can be paid online here, or at the Visitors' Center in the park. For the Congress, a small donation towards campground cost is the only registration fee. For further information, contact the organizers on the contact page.
In the event of a government shutdown: We are grateful to be able to host our conference in the Whiskeytown National Recreation Area each year, but if the government shuts down, we will have to move our conference at the last minute to a new location. We have a plan B, but haven't paid for it yet. Please check back here. We'll make the decision if needed by 5 PM on Thursday, Oct 2.