Combinatorial Potlatch 2012
Simon Fraser University
Saturday, November 17, 2012

The Combinatorial Potlatch is an irregularly scheduled, floating, one-day conference. It has been held for many years at various locations around Puget Sound and southern British Columbia, and is an opportunity for combinatorialists in the region to gather informally for a day of invited talks and conversation. While most who attend work in, or near, the Puget Sound basin, all are welcome.  Typically there are three talks given by speakers who are visiting or new to the area, along with breaks for coffee and lunch. Many participants remain for dinner at a local restaurant or pub.

The American Heritage Dictionary defines "potlatch" as: A ceremonial feast among certain Native American peoples of the northwest Pacific coast, as in celebration of a marriage or an accession, at which the host distributes gifts according to each guest's rank or status. Between rival groups the potlatch could involve extravagant or competitive giving and destruction by the host of valued items as a display of superior wealth. [Chinook Jargon, from Nootka p'achitl, to make a potlatch gift.]

This fall's Potlatch is being hosted by the Department of Mathematics at Simon Fraser University at their Harbour Centre in downtown Vancouver, British Columbia on Saturday, November 17, 2012.

Significant funding is being provided by Pacific Institute for the Mathematical Sciences (PIMS) and the Department of Mathematics at Simon Fraser University. Their support is gratefully acknowledged.

Schedule

All talks will be held in Labatt Hall, located in the Harbour Centre, with registration and breaks nearby. See the Getting There section for exact locations and directions.

• 10:00 AM Registration, Bagels and Coffee
• 11:00 AM Chris Godsil, Continuous Quantum Walks on Graphs
• 12:00 PM Lunch
• 2:00 PM Dan Drake, Higher Order Matching Polynomials and $d$-Orthogonality
• 3:00 PM Cookies, Coffee and Cokes
• 3:30 PM Ron Graham, The Combinatorics of Solving Linear Equations
• 4:30 PM Happy Hour, Dinner

Title: Continuous Quantum Walks on Graphs

Abstract: If $A$ is the adjacency matrix of a graph $X$, then the matrix exponential $U(t) = \exp(itA)$ determines what physicists term a continuous quantum walk. They ask questions such as: for which graphs are the vertices $a$ and $b$ and a $t$ such that $|U(t)_{a,b}|=1$? The basic problem is to relate the physical properties of the system with properties of the underlying graphs, and to study this we make use of results from the theory of graph spectra, number theory, ergodic theory$\dots$. My talk will present some of the progress on this topic.

Title: Higher Order Matching Polynomials and $d$-Orthogonality

Abstract: The classical combinatorial theory of the Hermite, Laguerre, and Chebyshev orthogonal polynomials interprets them as matching polynomials of certain classes of graphs. A matching of a graph is a collection of disjoint edges in the graph; a higher-order matching is a collection of disjoint paths of length $k$ in the graph. I will show how the ideas of higher-order matchings and $d$-orthogonality, developed separately, put together form a nice generalization of the combinatorial theory of Hermite, Laguerre, and Chebyshev polynomials.

Title: The Combinatorics of Solving Linear Equations

Abstract: One of the fundamental topics in combinatorics involves deciding whether some given linear equation has solutions with all its variables lying in some restricted set, and if so, estimating how many such solutions there are. In this talk, we will describe some of the old and new results in this area, as well as discuss a number of unsolved problems.

Registration

The Combinatorial Potlatch has no sponsoring organization and no budget. And we like it that way. Consequently, there are no registration fees because we wouldn't know what to do with them. You are on your own for meals and lodging, speakers travel at their own expense and the host institution provides facilities and food for the breaks. So expressions of appreciation to the speakers and the hosts are preferred and especially encouraged. Thanks.

Getting There

Simon Fraser's Harbour Centre is located at 515 West Hastings Street in downtown Vancouver (which is not the main campus). The venue for all talks, registration and breaks is Labatt Hall.

Detailed information on transportation and parking.

Dining and Happy Hour

You are encouraged to join other conference participants at the various meals and other events planned for the day.

• Breakfast before the first talk will include: bagels, cream cheese & other spreadables, fruit, fruit juices, muffins, tea & coffee.
• A no-host lunch is planned for Irish Heather, a nearby GastroPub. We will sit together, and order from a limited menu:
• Vegetarian Chilli with Garlic Bread ($11) • Italian Ham and Cheese Sandwich with Grilled Veg & Pesto Mayo served with a Cup of Vegetarian Minestrone ($10)
• Steak and Winter Vegetables, Slowly Cooked In Guinness From Our Taps, Then Made Into Pies In Our Bakery ($16) • Bangers & Mash ($15)
• Vegetarian Feature ($14) • Happy Hour will likely be in the bar at Waterfront Station. • They will be expecting us for a no-host dinner at Shabusen on Burrard Street. They have Japanese and Korean food (in particular, sushi and barbeque-at-the-table). The all-you-can-eat option is a terrific value. • Nearby Restaurants Social Events Luis and Rachel Goddyn will host a informal Potlatch Pre-Party at their home, for those in town on Friday night. You and company are invited! Details from Luis follow: • When: Friday, November 16, 6:00pm - midnight • Time: Drop in any time after 6:00pm. • Bring: Beverages and a snack to share, if you desire. • Format: Very informal, snacks will be available, but not a full meal. The guests will generally be mathematics-related folk and their friends. • Address: 4095 McGill St., Burnaby, 8 blocks North of Hastings St. on Gilmore Ave. • Map: http://math.sfu.ca/~goddyn/transitToGoddyns.pdf • Taxi: Is about$25.
• Transit: The #135 SFU/Burrard station leaves every 7 or 8 minutes. It takes about 20 minutes to Gilmore Avenue from Downtown. Then walk 8 short blocks North on Gilmore, or catch the C1 shuttle at Kooteney Loop.
• Contact: 604.431.6658, goddyn@sfu.ca

Organizers

• Rob Beezer, University of Puget Sound, beezer (at) ups (dot) edu, Communications Chair
• Nancy Ann Neudauer, Pacific University, nancy (at) pacificu (dot) edu, Program Chair
• Jonathan Jedwab, Simon Fraser University, jed (at) sfu (dot) ca, Local Arrangements Chair
Last updated: November 11, 2012, http://buzzard.ups.edu/potlatch/2012/potlatch2012.html