Research

I am broadly interested in online algorithms and other information-theoretic questions in algorithms, convex geometry, convex optimization, and combinatorial optimization.

Publications

• Robust Secretary and Prophet Algorithms for Packing Integer Programs
  with Anupam Gupta, Marco Molinaro, and Sahil Singla, SODA 2022.
• Lipschitz Selectors may not Yield Competitive Algorithms for Convex Body Chasing
  with Anupam Gupta and Marco Molinaro, Discrete and Computational Geometry 2022.
• Necessary and Sufficient Conditions for Rank-One Generated Cones
  with Fatma Kılınç-Karzan and Alex Wang, Mathematics of Operations Research, 2022.
• Dimension-Free Bounds for Chasing Convex Functions
  with Anupam Gupta and Guru Guruganesh, COLT 2020.
• Chasing Convex Bodies with Linear Competitive Ratio
  with Anupam Gupta, Guru Guruganesh, and Ziye Tang, SODA 2020.

  Awarded SODA 2020 Best Paper

• A Nearly-Linear Bound for Chasing Nested Convex Bodies
  with Sebastien Bubeck, Michael Cohen, Anupam Gupta, and Yin Tat Lee, SODA 2019.
• Covers in Partitioned Intersecting Hypergraphs
  with Ron Aharoni, European Journal of Combinatorics 2016.

Presentations

• Chasing convex bodies with linear competitive ratio.
  • SODA 2020
  • CMU Math Graduate Student Seminar, Nov. 2019
  • CMU Theory Lunch, Nov. 2019
• Chasing nested convex bodies.
  • SODA 2019
  • CMU Theory Lunch, Nov. 2018
• Rank-one generated spectral cones defined by two homogeneous linear matrix inequalities.
  
  • INFORMS 2017

Click for slides.

Teaching

Carnegie Mellon University

2021	Fall	21-256 Multivariate Analysis	Instructor
2021	Spring	21-240 Matrix Algebra	TA
2020	Fall	21-228 Discrete Mathematics	TA
2020	Spring	21-122 Integration and Approximation	Lead TA
2019	Fall	21-228 Discrete Mathematics	TA
2019	Summer	21-120 Differential and Integral Calculus	Instructor
2019	Spring	21-127 Concepts of Mathematics	Lead TA
2018	Fall	21-228 Discrete Mathematics	TA
2018	Summer	21-120 Differential and Integral Calculus	Instructor
2018	Spring	21-292 Operations Research	TA
2017	Fall	21-259 Calculus in 3D	TA
2017	Spring	21-259 Calculus in 3D	TA
2016	Fall	21-257 Methods and Models for Optimization	TA

University of Chicago

2013	Spring	MATH 13200-13300 Elementary Functions and Calculus	TA
2012	Fall	MATH 11200 Studies in Mathematics	TA

My teaching portfolio is available upon request.

ARML

Contact

Email	cargue@andrew.cmu.edu (work) westernpaarml@gmail.com (ARML)
Office	Wean Hall 6207
Mail	Department of Mathematics Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213

CV