Illinois Combinatorics Lab for Undergraduate Experiences (ICLUE)

Director: Alexander Yong

This program (initiated Spring 2017) is for undergraduate students who are seriously interested in graduate school in mathematics. Activities can take various forms, including:

* Research projects

* Combinatorics education initiatives (visiting local high schools)

* Seminars with academic visitors

* Conference travel

This is was originally an *unpaid* mentorship program. However, thanks to NSF RTG DMS 1937241, we have support for US citizens and permanent residents that are UIUC undergraduates. The mentoring faculty include Jozsef Balogh, Philippe Di Francesco, Kevin Ford, Rinat Kedem, Alexandr Kostochka, and Alexander Yong. Please see the combinatorics RTG site for more information. Generally speaking, a strong performance in a class by one of the faculty is a prerequisite. You may also contact one of the faculty and/or Alexander Yong for more information.

Products of ICLUE:

Symmetric group representations and Z (Anshul Adve and Alexander Yong)

Vanishing of Littlewood-Richardson polynomials is in P (Anshul Adve, Colleen Robichaux and Alexander Yong)

Complexity, combinatorial positivity, and Newton polytopes (Anshul Adve, Colleen Robichaux and Alexander Yong)

Reduced word enumeration, complexity, and randomization (Cara Monical, Benjamin Pankow, Alexander Yong)

An estimation method for game complexity (Alexander Yong, David Yong)

Multiplicity-free key polynomials (Reuven Hodges, Alexander Yong) used software developed by David Brewster and Husnain Raza (summer 2020)

Coxeter combinatorics and spherical Schubert geometry (Reuven Hodges, Alexander Yong) used software developed by David Brewster, Jiasheng Hu, and Husnain Raza (summer 2020).

Newell-Littlewood numbers II: extended Horn inequalities (Shiliang Gao, Gidon Orelowitz, Alexander Yong) used software developed by David Brewster (summer, Fall 2020).

Generalized permutahedra and Schubert calculus (Avery St. Dizier, Alexander Yong) used software developed by Husnain Raza (Fall 2020).

Maximum determinant and permanent of sparse 0-1 matrices (Igor Araujo, Jozsef Balogh, and Yuzhou Wang) (Fall 2020)

Proper permutations, Schubert geometry, and randomness (David Brewster, Reuven Hodges, and Alexander Yong) (Fall 2020)

Member outcomes:

* Anshul Adve was awarded a 2019 Goldwater fellowship at UCLA for work done through ICLUE. He attended a U. Chicago REU in summer of 2019. He is a 2021 Hertz Fellowship finalist (one of 48 named in the nation, and the only one in mathematics). He also was awarded an NSF graduate fellowship in 2021. He will start his math PhD at Princeton in Fall 2021.

* David Brewster will be funded by an NSF RTG to work in the ICLUE program in Summer 2020 and Fall 2020.

* Anna Chlopecki '20 will be attending a math REU at Brown in the summer of 2019; accepted to multiple private and public math PhD programs and will start a math doctoral degree at Purdue in Fall 2020.

* Zhaobidan (Amy) Feng '18 is pursuing a PhD in math at Texas A+M

* Matthew Faust '18 is pursuing a PhD in math at Texas A+M

* Ananth Koppol is funded by an NSF RTG to work in ICLUE in Fall 2020

* Thien Le '19 is pursuing a PhD in CS at MIT

* Jeremy McMahan '18 is pursuing a PhD in CS at U. Wisconsin

* Husnain Raza is funded by an NSF RTG to work in ICLUE in Summer 2020 and Fall 2020.

* Steven Zhang '20 is attending Oxford for a graduate program offered jointly by the Mathematical Institute and the Department of Physics. In Fall 2021 he will return to the US for graduate study in mathematical physics at Stony Brook.

* Judy Chiang has been accepted to the University of Minnesota's Summer 2021 REU in Algebra, Combinatorics, and Representation Theory, Cornell's SPUR program, and MIT's SGI program. She will attend the latter program.

* David Brewster '21 has won the math department's H. Roy Brahana prize (Spring 2021)

* Mose Mizrahi '21 will move to ETH Zurich in the Fall of 2021 to begin graduate study in CS.

* Tue Do will be joining A. Yong's ICLUE group this summer on NSF RTG funding.

Members/Alumni:

* Anshul Adve (high school student; now undergraduate at UCLA; 2019 Goldwater Fellowship)

* David Brewster '21 (H. Roy Brahana prize winner)

* David Buksa

* Hongxuan Chen (Mentor: Balogh)

* Judy Chiang

* Anna Chlopecki (2019 REU at Brown, now in Math PhD at Purdue U)

* Elia Chudov

* Aaron Marcus Cunanan

* Tue Do

* Cathy Du

* Matthew Faust

* Zhaobidan (Amy) Feng (Now Math PhD at Texas A&M)

* Paul Graham (Physics student)

* Matt Ho

* Jiasheng Hu

* Elizaveta Kalinina

* Daniel Klovsky

* Ananth Koppol

* Thien Le (now CS PhD student at MIT)

* Nathan Lin

* Chinmaya Mahesh

* Jeremy McMahan (now CS PhD student at U. Wisconsin)

* Mose Mizrahi (moving in Fall for graduate school at ETH Zurich)

* Joaquin Padilla Montani (Austria)

* Jackie Oh

* Benjamin Pankow

* Husnain Raza

* Alexander Roe (mentor: Jozsef Balogh)

* Michael Sandler (Physics student)

* Ray Shang (high school student at IMSA)

* Lucas Trojanowski

* William Wang

* Yuzhou Wang (mentor: Balogh)

* Zihan Wang

* Jason Xia

* Qingqing Yang

* Steven Zhang

* Yichi Zhang (Electrical Engineering student)

Some other undergraduate research projects