RTG: Research in Combinatorics

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The Research Training Group (RTG) in Combinatorics at UIUC will establish a number of activities involving researchers at all career stages ranging from undergraduate students to senior faculty. The project takes advantage of the combined strength and leadership of UIUC's faculty in multiple areas of a venerable field. The RTG has five PIs (Balogh, Di Francesco, Kedem, Kostochka, and Yong) and one senior personnel (Ford), which includes three speakers of the International Congress of Mathematicians (ICM). The depth and breadth of faculty, courses, and events at UIUC combinatorics is unique in the United States, as it includes algebraic combinatorics, graph theory and additive number theory. Thereby, students experience a broad range of education and options before deciding upon on their thesis direction. This fundamentally and positively affects recruitment and retention of domestic students, and in particular women and underrepresented minorities (URM). This claim is supported by a recent 2017 AMS award to the UIUC mathematics department as a whole. This RTG award is the first for the UIUC mathematics department, and is therefore of special impact. It tremendously strengthens UIUC's position to educate and train US students overall. Given the importance and applicability of combinatorics, it tangibly contributes to America's mathematical and scientific prominence. The RTG will provide a unifying structure for the development of researchers and to foster collaborations. Activities of the RTG include research workshops, new research seminars, conferences, and undergraduate mentoring. The strengths of UIUC combinatorics faculty are in two major areas: 1. Probabilistic and Extremal Combinatorics (Balogh, Kostochka), and 2. Algebraic, Geometric and Physical Combinatorics (Di Francesco, Kedem, Yong). All RTG faculty apply their work to other STEM fields, specifically physics and theoretical computer science. Ford (senior personnel) is a world leader in the related area of additive number theory. The primary purpose of this RTG is to support combinatorics graduate students. It funds conference travel for undergraduate students, graduate students, and postdocs. The program will be bolstered by a biannual combinatorics lecture series. More external contact will come from four annual summer schools layered with related conferences (ALGECOM and the Graduate Student Combinatorics Conference) organized by RTG faculty. The RTG supports non-local participation of students and (especially early career) faculty at RTG events. The award also vastly expands ICLUE (Illinois Combinatorics Lab for Undergraduate Experience), which is a novel UIUC career-long research and mentoring program. The RTG will hire four postdocs. These postdocs will not only assist in planned activities but also benefit from the intellectual environment offered by this research training group.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.