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)

** 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. 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

* 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 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 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.

* 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

* 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

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

* Divij Garg (Metea Valley High School in Aurora, IL; mentors Shiliang Gao, Y.)

* Paul Graham (Physics student)

* Matt Ho

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

* Elizaveta Kalinina

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

* 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 '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.

* 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.

* Dinglong Wang '24 (mentor: Y) Will be in the ICLUE summer program in Summer '22.

* 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

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

* Yichi Zhang (Electrical Engineering student)

* Zhuo Zhang Will participate in the summer '22 program on combinatorics and representation theory lead by Y.