Seattle University
Saturday, November 19, 2022
About the Conference
The Cascadia Combinatorial Feast (formerly known as the Combinatorial Potlatch) is an annual, 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.
In 2020, we decided to change the name of the conference. The original name, Potlatch, referred to a ceremonial feast among certain First Nations of the northwest Pacific coast. You can read more about Potlatches here.
This fall's conference will be hosted in person by the Department of Mathematics at Seattle University on Saturday, November 19, 2022.
Significant funding is being provided by the Pacific Institute for the Mathematical Sciences. Their support is gratefully acknowledged.
More information, including a history and links to previous conferences, is at the Cascadia Combinatorial Feast Home Page.
Schedule
All talks will be held in SINE 100. See the Getting There section for exact locations and directions.
A tentative schedule follows.
- 10:00 AM Registration, Bagels and Coffee
- 11:00 AM Opening Remarks
- 11:10 AM Cynthia Vinzant, Determinantal representations and the principal minor map
- 12:15 PM Lunch at Poquito's
- 2:30 PM Hays Whitlatch, Counting power domination sets in complete $m$-ary trees
- 3:00 PM Cookies and Coffee
- 3:30 PM Imre Barany, Pairwise intersecting convex sets and cylinders in $R^3$
- 5:00 PM Happy Hour
Talks and Abstracts
Cynthia Vinzant, University of Washington
Determinantal representations and the principal minor map
The principal minor map takes an $n$ by $n$ matrix to the vector of its $2^n$ principal minors. The quest for an algebraic description of the image of this map dates back to the 19th century classical algebraic geometry and was reinvigorated by work of Holtz-Sturmfels and Lin-Sturmfels. In this talk, I will describe a connection between this map and certain classes of determinantal representations. For symmetric and Hermitian matrices, this results in a set-theoretic description of the image of the principal minor map using the orbit of a finitely-many polynomial equations and inequalities under a large group action and recovers Oeding's characterization of the principal minors of symmetric complex matrices as the variety of the orbit of Cayley's hyperdeterminant. I will also give a combinatorial obstruction to show that that no such finite characterization is possible for general matrices. This is based on joint work with Abeer Al Ahmadieh.
Hays Whitlatch, Gonzaga University
Counting power domination sets in complete $m$-ary trees
Motivated by the question of computing the probability of successful power domination by placing $k$ monitors uniformly at random, in this talk we discuss a recursive formula to count the number of power domination sets of size $k$ in a labeled complete $m$-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time. This is joint work with Gonzaga professor Katharine Shultis, and students Sviatlana Kniahnitskaya, Michele Ortiz and Olivia Ramirez.
Imre Barany, Renyi Mathematical Institute, Budapest and University College, London
Pairwise intersecting convex sets and cylinders in $R^3$
We prove that given a finite collection of cylinders in $R^3$ with the property that any two of them intersect, there is a line intersecting an alpha-fraction of the cylinders where $\alpha=1/14$. This is a special case of a recent and exciting conjecture. I will present several open problems related to that conjecture.
Registration
The Cascadia Combinatorial Feast has no registration fees. And we like it that way. The host institutions provide facilities, coffee and food for the breaks, and some support for speakers' travel.
Getting There
All talks will be held in SINE 100. SINE is Seattle University’s new Sinegal Center for Science and Technology, located on the southwest corner of 12th Ave and Marion Street. The building is in the central portion of the campus map, and can be identified by searching for "SINE" in the pull-down menu. Please note that we expect only the west side doors of SINE will be unlocked on the day of the conference; these doors are on the opposite side of the building from 12th Avenue.
Detailed driving directions to Seattle University are here. If you're coming from the north on I-5, take exit 165A, turn left on James, then left again on 12th Avenue. When you get to East Marion Street, turn left for \$17 parking, and right for free or \$12 parking (see below).
On-campus parking is available in the Pigott lot (P5 in the campus map). This is just north of SINE on East Marion Street. Parking is $17 per day and payable using the Pay by Phone app or at the physical pay station using a credit card. Be sure not to park in any of the reserved spaces.
The closest (private, off-campus) parking lot is on the north side of Marion Street between 12th and 13th avenues. This lot is $12 per day. Street parking is generally free east of 12th Avenue, but you must move your car every two hours to avoid a parking ticket.
Lodging
We have rooms reserved at the Silver Cloud Hotel Broadway, for the nights of November 18 and 19.
- Book with the hotel directly at 206 325 1400.
- Make sure to mention “Cascadia Combinatorial Feast” when making your reservation, to get the discounted rate.
Mugs
These are free to partcipants, but restricted to one per participant.
The logo was designed by Cobus Swarts, and the cost of the mugs was shared by the Coast Combinatorics Conference fund and the Department of Mathematics at Western Washington University.
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Dining and Happy Hour
We've made reservations for no-host lunch and happy hour at two local restaurants, both within easy walking distance of campus. We very much hope you can join other participants, and your guests are welcome to join us also.
Lunch: Poquito's, 1000 E Pike Street. We've negotiated a (heavily subsidized) fixed price of \$20 (US dollars!) for the taco bar. This includes tacos, enchiladas and salads, but not drinks, which you can pay for separately.
Happy Hour: The Chieftain, 908 12th Avenue
Organizers
- Nancy Ann Neudauer, Pacific University, nancy (at) pacificu (dot) edu, Program Chair
- Amites Sarkar, Western Washington University, amites.sarkar (a) wwu (dot) edu, Communications Chair
- Allison Henrich, Mark MacLean and David Neel, Seattle University, Local Arrangements Committee