Systems of Lines: Applications of Algebraic Combinatorics

Monday-Friday, August 10-14, 2015

Kinnicutt Hall, Salisbury Labs
Worcester Polytechnic Institute
Worcester, MA

WPI Mathematical Sciences Department

UPDATE: See below for links to papers and other outcomes of our meeting!

On behalf of the organizers, WPI and the NSF, thanks to all speakers and participants for a wonderful workshop. That's all folks!

We gratefully acknowledge critical financial support from the US National Science Foundation and Worcester Polytechnic Institute.

This mathematical research workshop entitled "Systems of Lines: Applications of Algebraic Combinatorics" will be held at Worcester Polytechnic Institute from August 10, 2015 to August 14, 2015. This workshop will bring together experts from around the world who study three subjects that are not obviously related but have deep connections between them. The organizers aim to foster cross-collaboration among mathematicians, computer scientists and physicists in order to identify common problems, tools and techniques among seemingly disparate applications of mathematics.

Experts in algebraic combinatorics apply tools from algebra, graph theory and optimization to study error-correcting codes, spherical codes and highly regular designs for use in statistics and computer science. In combinatorics, systems of lines include root systems, two-graphs, unbiased Hadamard matrices, antipodal distance-regular graphs, and Q-bipartite association schemes, among other structures.

Quantum information theorists face problems of measuring and (approximately) replicating finite-dimensional quantum systems in their work on quantum algorithms, quantum cryptography and quantum state tomography. Signal processing experts employ compressive sensing to efficiently reconstruct a sparse signal through undersampling in a carefully designed manner. Data scientists now use ideas from compressive sensing for dimension reduction and the efficient handling of very large data sets. The workshop will include talks from all three viewpoints and will allow ample time for discussion and collaboration.

By bringing people together from compressive sensing, quantum information theory, and algebraic combinatorics, this workshop will enable the application of tools and results from each area to the other and help identify the outstanding problems common to all three subdisciplines.

Schedule and Abstracts:

Titles and Abstracts can be found here.

Here the current schedule for workshop, with an exciting lineup of high-quality talks, yet leaving plenty of time for collaboration and discussion:


All talks will be held in Kinnicutt Hall, Salisbury Labs

NEW! Links to slides of selected talks:

All speakers are listed below, in chronological order of presentation. If the speaker has consented to having their slides posted here, those slides may be accessed by clicking the link labeled "SLIDES".

Directions, Parking and Accommodations:


You can find directions and information about parking at WPI hereFurther details will be posted here as we get closer to the date of the meeting.

WPI provides an extensive list of nearby hotels, but our recommended hotels are the Marriott Courtyard Worcester and the Hilton Garden Inn Worcester. Both of these are within walking distance of the meeting room, but the Marriott is much closer.

We have negotiated a discounted rate of $134 (plus taxes) per night for the Marriott Courtyard. To get the discount, please tell them that you are with the "WPI Workshop on Lines" at WPI. The rooms here are large, so we encourage you to share rooms if budget is an issue for you (and we'd be happy to help -- just send e-mail to Bill). [Hotel details: Courtyard by Marriott Worcester, 72 Grove Street, Worcester, MA 01605 Phone: (508)363-0300 Fax: (508)363-3563 (Sales Manager: Tricia Elkins)]

The Worcester Regional Airport (ORH) handles only a small number of flights. Most visitors to Worcester fly into Logan International Airport (BOS) in Boston. Other options include Providence, Rhode Island (PVD), Manchester, New Hampshire (MHT), and Bradley near Hartford, Connecticut (BDL). Please note: If any part of your airfare is to be reimbursed, it must be ticketed on a US carrier. It may be code-shared with anoth airline, but the ticket must have the US carrier's flight number.

Worcester Airport Limousine (, 800-660-0992 ) and Knight's Airport Limousine (, 800-822-5456) provide door-to-door transport from nearby airports to locations in and around Worcester. Call them to compare pricing.

There are many options for food near campus. WPI's Campus Center offers a small food court with a few mainstream options. Highland Street offers 8 restaurants on a 1/4 mile stretch: Subway, Sahara (Lebanese), Tech Pizza, Sole Proprietory (seafood), Boynton (upscale pub food), Thai Time, Dragon Dynasty (Chinese), Boomers Subs and Pizza. For a more extensive selection of Worcester restaurants, start here. In particular, if you have a car,try out the many restaurants on Shrewsbury Street.

The presentations will take place in Kinnicutt Hall, which is Room 115 in Salisbury Labs. Salisbury is building number 28 on this map and is adjacent to the water fountain at the center of the campus. (Please note that Salisbury Labs has a different building number on other WPI maps.)

Here is a list of local accommodations, and a list of area dining (although the meeting includes breakfast, lunch and dinner for registered participants).

If you are in need of further assistance, contact Bill Martin.

Special Events:

  • Wednesday afternoon excursion options include touring the Worcester Art Museum (free admission) and hiking Mount Wachusett (no cost)
  • Thursday evening conference dinner in Higgins House
  • Friday night optional trip to Boston to attend a baseball game between the Boston Red Sox and the Seattle Mariners (tickets will cost roughly $70, train is roughly $15; must request in advance)
  • There are many other things to do in the Worcester area if you arrive early or stay an extra day or two. See this link for some suggestions. For instance, the Commonwealth Shakespeare Company is providing free performances of "King Lear" on the Boston Common every night up until August 9th. Check here for detils.

Discrete Mathematics Days in the Northeast:

Just a few weeks after the workshop, WPI will host Discrete Math Day at WPI on September 12, 2015.

As you may know, this is part of a series of one-day conferences, titlted "Discrete Mathematics Days in the Northeast".   Information on previous meetings in the series can be found here. A less complete list of recent and future meetings can be found here.

Organizers: Alexander Barg (Maryland), Randy Paffenroth (WPI), Bill Martin (WPI)

We appreciate financial support from the National Science Foundation Division of Mathematical Sciences, with additional support from WPI's Department of Mathematical Sciences.



Followup and Impact

Preprints which were at least partially influenced by the workshop: