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, to appear in Electronic J. Combinatorics (2022) (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) Now published in Linear Algebra Appl. 645 (2022), 194-228.

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

Proper elements of Coxeter groups (Jozsef Balogh, David Brewster, and Reuven Hodges) (Fall 2021)

Mathscinet scraper for citations and publication count to assist UIUC's department Evaluation Task Force (but can be used for any list of mathematicians) (Spring 2022, Jason Xia '22)

Summer 2022 ICLUE program on Representation theory and Combinatorics (participants: Casey Appleton, Judy Chiang, Dylan Chiu, Dylan Roscow, Dinglong Wang, Zhuo Zhang)

Summer 2023 ICLUE program on Schubert combinatorics and geometry (ICLUE participants: Casey Appleton, Tasha Fellman, Alex Jin, Dylan Roscow, David Wallach, Maya Viswanathan)

On components of the square of a Weyl module (Shiliang Gao and Dinglong Wang), Fall 2023.

Member outcomes:

* Zhuo Zhang will participate in the REU at U. Chicago in Summer 2023. He also is a recipient of the 2022-2023 Lewis C. Hack Scholarship.

* 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. David will attend Harvard's PhD program in CS in Fall 2022.

* 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; Ananth graduated in '23 and is now working at Facebook

* 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.

* Dylan Roscow (mentor: Y.) will work with Yong on research in algebraic combinatorics during Summer 2022. * 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 (mentor: Y. and Avery St. Dizier) will attend the math PhD program at Minnesota in Fall 2023. Previously she attended the University of Minnesota's Summer 2022 REU in Algebra, Combinatorics, and Representation Theory. In Summer 2021 she was accepted to the same program, but also Cornell's SPUR program, and MIT's SGI program; she attended the latter program. In Fall 2021, Judy also was awarded an LAS Design and Career Scholarship to work with Prof. Avery St. Dizier. She was also awarded a James Scholar Preble Research Award (later) in Fall 2021 for this work. She was awarded a Lois M. Lackner prize in Spring 2022. In Summer 2022 she will attend the U. Minnesota Summer REU in combinatorics and is participating in the ICLUE 2022 summer program on representation theory and combinatorics.

* 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 and Dmitrios Tambakos are joining A. Yong's ICLUE group in summer '21 on NSF RTG funding.

Members/Alumni:

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

* Casey Appleton '25 (Mentor: Orelowitz, Y) RTG funded to participate in the ICLUE summer program on representation theory and combinatorics in Summer '22 lead by Y. Won the Elise Thomas Fraser Award Spring 2022 and the Elizabeth R. Bennet Scholarship in 2023. Funded for Summer and Fall 2023 as well as Spring 2024. In Summer 2024 he will attend the UMN Summer REU in Combinatorics and Algebra

* Richard Bi (Mentor: Peter Bradshaw)

* Brendan Biernacki (Mentor: Michael Wigal) Funded to work in ICLUE, Spring 2024.

* David Brewster '21 (H. Roy Brahana prize winner) (Mentors: Gao, Hodges, Orelowitz, Y.) Will attend Harvard's PhD program in CS starting Fall 2022.

* David Buksa

* Hongxuan Chen (Mentor: Balogh)

* Judy Chiang (Mentors: St. Dizier, Y) Multiple REUs and awards (see above). Will be participating in the '22 summer ICLUE program on representation theory and combinatorics.

* Dylan Chiu (Mentor Y) Will be participating in the '22 summer ICLUE program on representation theory and combinatorics.

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

* Elia Chudov

* Aaron Marcus Cunanan

* Anakin Dey '24 (mentor: Y). Anakin will attend an REU Summer '23 in Algebra at Texas State U. Anakin is funded to work in ICLUE for Spring 2024.

* Tue Do (mentors: Gao, Orelowitz, Y.)

* Cathy Du

* Dylan Chiu (mentor: Y) RTG funded to participate in the summer '22 program on combinatorics and representation theory lead by Y. * Matthew Faust

* Tasha Fellman '24 (mentor: Y) Supported by an ICLUE summer '23 stipend.

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

* Vish Ganesan (mentor: Michael Wigan) Stipend for Spring 2024.

* Divij Garg (Metea Valley High School in Aurora, IL; mentors Shiliang Gao, Y.) -- Divij is now an ICLUE member at UIUC. He will be attending an REU in astrophysics in Summer 2023 at Virginia Tech.

* Paul Ge (Mentor: Elizabeth Kelley) is working with Kelley on a problem in combinatorial game theory starting Summer 2023 and supported by an ICLUE stipend in Spring 2024.

* Paul Graham (Physics student)

* Matt Ho

* Jiasheng Hu '22 (will start a Software Engineering position at Google in Summer '22)

* Alex Jin '25 (mentor: Y) will work in ICLUE during Summer 2024

* Elizaveta Kalinina

* Daniel Klovsky '19 (completed a Master's degree in Statistics at UIUC in '22)

* Ananth Koppol '23 (mentor: Y) Facebook

* 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 '21 (mentor: Y) Published a paper with Monical and Y. in Electronic J. Combinatorics. Find him here on linkedin

* Husnain Raza '22 (mentors: Hodges, Y.)

* Alexander Roe (mentor: Jozsef Balogh)

* Dylan Roscow (mentor: Y) RTG funded to participate in the summer '22 program on combinatorics and representation theory lead by Y. Funded for Summer and Fall 2023 as well as Spring 2024.

* Michael Sandler (Physics student)

* Ray Shang (high school student at IMSA)

* Dmitrios Tambakos '22 (mentors: Gao, Orelowitz, Y.)

* Lucas Trojanowski '20 (mentor: Y) Completed a Master's degree in Applied Mathematics in '22. Will start a physics PhD at Maryland in Fall '22.

* Maya Viswanathan (mentor: Y) high school student from University Lab School.

* David Wallach (mentor: Y, Andy Hardt) studying reduced word combinatorics, 2022-2023 winner of the Salma Wanna award in the math department. Funded to work with the RTG in Summer, Fall 2023 and Spring 2024.

* Dinglong Wang '24 (mentor: Shiliang Gao, Y) Will be in the ICLUE summer program in Summer '22. Dinglong won a Josephine Chanler Scholarship (2022-2023). Completed a preprint ``On Components of the square of a Weyl module'' (https://arxiv.org/pdf/2312.12756.pdf) in December 2023.

* William Wang

* Yuzhou Wang (mentor: Balogh)

* Zihan Wang

* Jason Xia '22 (mentor: Y) Wrote code to analyze citation data of faculty. Will start a position at Duolingo after graduation.

* Qingqing Yang

* Annie Zeng (mentor: Peter Bradshaw) funded to work with the RTG in Fall 2023 and Spring 2024.

* Steven Zhang '20 Now a graduate student in physics at Stony Brook after a masters at Oxford.

* Yichi Zhang (Electrical Engineering student)

* Zhuo Zhang participated in the summer '22 program on combinatorics and representation theory lead by Y. In Summer 2023 he will participate in the Chicago REU.

Some other undergraduate research projects