Bob Krueger
Carnegie Mellon University, Department of Mathematical Sciences
Contact: rkrueger at andrew.cmu.edu
Office: Wean Hall 7216
I started an NSF postdoc at Carnegie Mellon University in Fall 2024, sponsered by Prasad Tetali. I finished my math Ph.D. at the University of Illinois, Urbana-Champaign in Summer 2024, advised by József Balogh, where I held an NSF Graduate Research Fellowship. I earned undergraduate degrees at Miami University, where I majored in math and physics, and minored in statistics and computer science, and I was mentored by Louis DeBiasio.
My research interests generally lie in extremal and probabilistic combinatorics. At UIUC, I helped organize the Combinatorics Literature Seminar at UIUC, the Graph Theory and Combinatorics Seminar at UIUC, and CMPS, a two-time virtual meeting between UIUC, Iowa State, and University of Montana.
- Lipschitz functions on weak expanders [arXiv],
with Lina Li, Jinyoung Park
- Triangle Percolation on the Grid [arXiv] [Discrete & Computational Geometry],
with Igor Araujo, Bryce Frederickson, Bernard Lidický, Tyrrell B. McAllister, Florian Pfender, Sam Spiro, Eric Nathan Stucky.
Started at GRWC.
- Realizable Standard Young Tableaux [arXiv],
with Igor Araujo, Alexander E. Black, Amanda Burcroff, Yibo Gao, Alex McDonough.
Started at GRWC.
- On oriented cycles in randomly perturbed digraphs [arXiv] [Combinatorics, Probability & Computing],
with Igor Araujo, József Balogh, Simón Piga, Andrew Treglown.
- A sharp threshold for a random version of Sperner's Theorem [arXiv] [Accepted to Random Structures & Algorithms],
with József Balogh.
- Sharp threshold for the Erdős-Ko-Rado theorem [arXiv] [Random Structures & Algorithms, 2023],
with József Balogh, Haoran Luo.
- Lower bounds on the Erdős-Gyárfás problem via color energy graphs [arXiv] [Journal of Graph Theory, 2023],
with József Balogh, Sean English, Emily Heath.
- A note about monochromatic components in graphs of large minimum degree [arXiv] [DMGT, 2021],
with Louis DeBiasio.
- Generalized Ramsey numbers: forbidding paths with few colors [arXiv] [Electronic Journal of Combinatorics, 2020].
Product of CUNY's combinatorics REU.
- Partitioning the power set of [n] into C_k-free parts [arXiv] [Electronic Journal of Combinatorics, 2019],
with Eben Blaisdell, András Gyárfás, Ronen Wdowinski.
Completed during my 'Budapest' semester.
- Long monochromatic paths and cycles in 2-colored bipartite graphs [arXiv] [Discrete Mathematics, 2020],
with Louis DeBiasio.
- Large monochromatic components in multicolored bipartite graphs [arXiv] [Journal of Graph Theory, 2019],
with Louis DeBiasio, Gábor N. Sárközy.
- Monochromatic balanced components, matchings, and paths in multicolored complete bipartite graphs [arXiv] [Journal of Combinatorics, 2020],
with Louis DeBiasio, András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy.
- Hamiltonian cycles in k-partite graphs [arXiv] [Journal of Graph Theory, 2019],
with Louis DeBiasio, Dan Pritikin, Eli Thompson.
My first project, done at Miami.
Advising and Teaching
- List coloring with requests for planar graphs
Project done by undergraduates I advised at the IGL in Fall 2023.
- Manipulation in voting theory [IGL wiki].
Project done by local high school students I advised at the IGL in Summer 2022.
- Edge-colorings without small substructures [IGL wiki].
Project done by undergraduates I advised at the IGL in Spring 2022.
- Investigations in combinatorial game theory [IGL wiki].
Project done by local high school students I advised at the IGL in Summer 2020.
- Firefighting on the Hexagonal Grid and on Infinite Trees [arXiv] [Discrete Applied Mathematics, 2021].
Written by undergraduates I advised at the IGL in Spring 2020. See the IGL wiki for a poster and presentation.
- Recitation Sections at UIUC: Calculus I (Fall 2019, Fall 2020), Calculus II (Spring 2020).
Ranked outstanding by my students in Fall 2020.
Games