Triangle Lectures in Combinatorics

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The Triangle Lectures in Combinatorics (http://www.math.ncsu.edu/TLC) conferences are held twice a year in or near the Research Triangle region of North Carolina. This proposal supports the Fall 2012 and Spring 2013 meetings.Combinatorics is a growing and important area of mathematics. The states of North Carolina, Virginia, South Carolina, Georgia, Kentucky and Tennessee have recently seen an influx of research strength in combinatorics and adjacent areas. In particular, there are remarkably many tenure-track researchers, senior researchers and graduate students in combinatorics and related fields at various colleges and universities within about 4--5 hours drive of the Research Triangle region of North Carolina (Raleigh, Durham, and Chapel Hill). A relatively large proportion of these researchers are from underrepresented groups. Since the Spring of 2010, we have organized one-day (Saturday) conferences, once a semester, under the name Triangle Lectures in Combinatorics, with the aim of fostering regular contact between researchers in North Carolina, Virginia, South Carolina, Georgia, Kentucky and Tennessee. Each conference has brought four outstanding mathematicians from around the country to give talks about some of the most significant and most exciting developments in combinatorics.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. The Triangle Lectures in Combinatorics workshops play numerous roles: they enhance the national infrastructure for research and education by creating and strengthening a regional network of interacting researchers; facilitate the dissemination of cutting-edge research ideas, methods and results among researchers in the Southeastern United States; promote the teaching and training of graduate students by exposing them to the perspectives of leading researchers; increase awareness and understanding of combinatorics, on the part of faculty and students in the Southeast; support the development of young faculty at various schools and help them build local support and research networks; broaden participation of underrepresented groups, particularly women; and foster research interactions among participants, leading to new research results.