2010 — 2014 
Shader, Bryan [⬀] Hall, Christopher Williford, Jason 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Rocky Mountain Algebra, Combinatorics and Number Theory Days
This project supports a 3year sequence of regional conferences in Algebra, Combinatorics & Number Theory. The goals of the conferences are to encourage and stimulate research efforts of regional PhD students in mathematics and computer science, to foster collaborations among senior researchers and students, and to further strengthen the developing group of researchers in the Rocky Mountain region in the focus areas. A tentative list of topics is: 2010 Topic: Expander graphs, Speaker: H.A. Helfgott (University of Bristol); 2011 Topic: Finite Geometry and its applications, Speakers: Gary Ebert (University of Delaware) and William Kantor (University of Oregon); 2012 Topic: Algebraic Graph theory applied to complex networks, Speakers: Sebi Ciaoba (University of Delaware). Each conference will have two plenary speakers. Those listed have already confirmed their participation. The remaining slots will be filled in consultation with the speakers to support the chosen topic.
Graduate student involvement will be a high priority. Graduate students will be encouraged to present their research, and the schedule will be designed with breakouts and problem sessions so that faculty can offer suggestions and direction to the students. Creating an environment to foster new collaborations will be another priority, and the topics and speakers have been chosen because of their timeliness and the high potential for collaborations with regional faculty. The project provides funds to defray some of the travel expenses for speakers and participants. Priority for travel funds will go to minority applicants and graduate students. The project will (a) provide an encouraging environment for young researchers and graduate students, (b) inform researchers of some of the latest developments in Algebra, Combinatorics and Number Theory, and (c) strengthen collaborative, and interdisciplinary research ties among mathematicians in the Rocky Mountain region.

0.964 
2013 — 2014 
Williford, Jason 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Rocky Mountain Summer School 2013: Algebraic Graph Theory
The program "Algebraic Graph Theory" will run from June 1728, 2013, at the University of Wyoming. This summer school is part of an annual program sponsored by the Rocky Mountain Mathematics Consortium (RMMC). The purpose of this program is to introduce graduate students and researchers to topics in algebraic graph theory and their applications, foster collaboration, and build ties between young researchers. Daily lectures will provide the participants with background in the subject, and contributed talks and problem sessions in the afternoon will reinforce the lectures and give the participants a chance to work together on open problems.
The use of algebraic techniques to solve graph theory problems has been a very fruitful approach, and continues to have applications beyond pure mathematics to physics, computer science, biology and statistics. The topics covered include spectral graph theory with applications to quantum computing, association schemes with applications to design and coding theory, and graph polynomials with applications to the Potts model and DNA selfassembly. The aim is for a diverse body of student and researchers. Participation of members of groups underrepresented in mathematics is encouraged and supported.
More information about the program can be found at:
http://www.uwyo.edu/jwilliford/rmmc2013/rmmc_2013.html

0.964 
2014 — 2017 
Williford, Jason 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
QPolynomial Schemes, Coherent Configurations, and Applications
Combinatorics is a broad area of mathematics that has found applications to many other fields such as computer science, statistics, physics, and chemistry. Association schemes and coherent configurations give a unified framework for several areas of combinatorics, such as coding theory, the statistical design of experiments, and finite geometry. This work has the potential to shed light on many problems in other areas of combinatorics, including those mentioned above as well as extremal graph theory. This project will further explore the rich connections between algebra and combinatorics, and help demarcate new directions, problems, and questions, thereby stimulating further interest in the area. Broader impacts include a sharpening of mathematical tools for applications in industry, training of highly qualified graduate students for academia and industry, and undergraduate research opportunities.
The interaction between linear and abstract algebra and combinatorics has been a very fruitful area of study and continues to find applications beyond pure mathematics, in physics, computer science, and statistics. In this project, the PI and his team study association schemes and coherent configurations. The first part of the project is a study of association schemes with the socalled Qpolynomial property, a property formally dual to the notion of a distanceregular graph. While distanceregular graphs have been well studied, until the last decade little attention was paid to schemes with the Qpolynomial property that did not also arise from distanceregular graphs. Recent results suggest that these objects are of interest in and of themselves, and that the surprising structure of these schemes merits further exploration. The PI will continue the search for new examples of Qpolynomial schemes, with particular emphasis on those that arise from groups. The search will be complemented by work to characterize Qpolynomial schemes. The second part of the project concerns extending results of association schemes to the more general notion of coherent configurations, a natural generalization of association schemes. In particular, the PI will explore further applications of the recently discovered semidefinite bound in coherent configurations.

0.964 
2014 — 2015 
Horn, Paul Ferrara, Michael Pfender, Florian (coPI) [⬀] Young, Michael (coPI) [⬀] Williford, Jason 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
The Rocky MountainGreat Plains Graduate Research Workshop in Combinatorics, July 27  August 9, 2014 @ University of Colorado At Denver
Combinatorics is a growing and important area of mathematics. The focus of combinatorics is the structure of discrete (as opposed to continuous) sets of objects. Combinatorics is critical to many areas of mathematics, and plays a key role in computational, scientific, and engineering applications. In part due to the legacy of Paul Erdos, combinatorics is a research field driven by collaboration. In order to provide graduate students in combinatorics a collaborative research opportunity and nurture longlasting research collaborations, we will organize the Rocky MountainGreat Plains Workshop Graduate Research Workshop in Combinatorics.
This award will support the Rocky MountainGreat Plains Workshop Graduate Research Workshop in Combinatorics (GRWC), which will be held in Denver, CO from July 28thAugust 8th, 2014, will involve approximately 30 graduate students, 4 postdoctoral researchers and 10 faculty in an intense twoweek collaborative research experience. Participants will work to solve important, relevant problems from graph theory, enumeration, combinatorial matrix theory, finite geometry and other modern subdisciplines of combinatorics. Students will prepare open problems prior to the workshop under the guidance of a faculty mentor from the organizing committee, which consists of faculty from the University of Colorado Denver, University of Denver, Iowa State University, the University of Wyoming and the University of Nebraska Lincoln. These problems will then either be presented at the workshop by their proposers or hosted on the workshop's secure problem wiki, and will be worked on by small groups of participating students, postdocs and faculty. For more information about the GRWC, including a detailed description of the workshop format please see the workshop website at http://sites.google.com/site/rmgpgrwc .

0.961 
2016 — 2019 
Williford, Jason Mcallister, Tyrrell 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Collaborative Research: Rocky MountainGreat Plains Graduate Research Workshops in Combinatorics
The Rocky MountainGreat Plains Graduate Research Workshop in Combinatorics (GRWC), will be held in Laramie, WY (2016), Denver, CO (2017) and Ames, IA (2018), building upon successful NSFfunded workshops in 2014 and 2015. Each workshop will involve approximately 39 graduate students and postdoctoral researchers, and 10 or more faculty members in an intense twoweek collaborative research experience. Participants will work to solve important, relevant problems from graph theory, enumeration, combinatorial matrix theory, finite geometry, and other modern subdisciplines of combinatorics. Students will prepare open problems prior to the workshop under the guidance of faculty mentors from the organizing committee, which consists of faculty from Iowa State University, the University of Colorado Denver, the University of Denver, the University of Nebraska Lincoln, and the University of Wyoming. These problems, presented at the workshop by their proposers or hosted on the workshop's secure problem wiki, will be worked on by small groups of participating students, postdocs, and faculty. For more information about the GRWC, including a detailed description of the workshop format, please see the workshop website at http://sites.google.com/site/rmgpgrwc
The goal of the collaborations at the heart of the GRWC is to produce highquality, publishable research on a variety of topics. Another longerterm goal of the workshop is to help student participants expand their professional research networks. A strong research network is often a crucial part of building a generative and sustainable research program, and establishing these connections at an early career stage can have a longterm positive effect on the quality, impact, and depth of a professional's research portfolio. Participation in the GRWC will allow students to cultivate a large professional network of peers from the combinatorics community with whom they will be able to interact and collaborate throughout their careers. The GRWC will also offer professional development workshops to help students and postdocs prepare for job searches and future careers in academia, industry, or government.

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