Yu Hin (Gary) Au

Associate Professor (Academic Programming) Department of Mathematics and Statistics University of Saskatchewan Office: 239 McLean Hall E-mail: auP@math.Qusask.caR (with P,Q,R removed)

Hello! I am an Associate Professor in the Department of Mathematics and Statistics at the University of Saskatchewan. I have what's akin to a teaching-stream appointment (hence the "Academic Programming" designation in my position title), and am particularly focused on the design and delivery of our undergraduate programs and courses in mathematics and statistics.

Previously, I completed my Ph.D. in Combinatorics and Optimization at the University of Waterloo, under the supervision of Levent Tunçel. After that, I was an Assistant Professor at the Milwaukee School of Engineering for several years.

Research

My research interest mainly lies in discrete optimization. I like to study the theory and applications of linear, integer, and semidefinite programming, with a particular focus on analyzing lift-and-project methods and their power and limitations in tackling problems that arise from combinatorial optimization.

More broadly, I am easily attracted to most things discrete mathematics, such as problems in combinatorics and graph theory.

Some of my work to date:

• A Computational Search for Minimal Obstruction Graphs for the Lovász-Schrijver SDP Hierarchy (with Levent Tunçel) Submitted (2025) Preprint
• Stable Set Polytopes with Rank $|V(G)|/3$ for the Lovász-Schrijver SDP Operator (with Levent Tunçel) Submitted (2025) Preprint
• On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász-Schrijver SDP Hierarchy (with Levent Tunçel) Mathematical Programming, to appear (2024) Final version / Preprint
• Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operators (with Levent Tunçel) Mathematical Programming, to appear (2024) Final version / Preprint
• Decompositions of Unit Hypercubes and the Reversion of a Generalized Möbius Series Electronic Journal of Combinatorics 31 (2024), Article P2.26. Final version
• On Connections Between Association Schemes and Analyses of Polyhedral and Positive Semidefinite Lift-and-Project Relaxations (with Nathan Lindzey and Levent Tunçel) Submitted (2023) Preprint
• Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers Journal of Integer Sequences 24 (2021), Article 21.1.1. Final version
• Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube (with Fatemeh Bagherzadeh and Murray Bremner) Journal of Integer Sequences 23 (2020), Article 20.1.4. Final version
• Elementary Polytopes with High Lift-and-Project Ranks for Strong Positive Semidefinite Operators (with Levent Tunçel) Discrete Optimization 27 (2018), 103-129. Final version / Preprint
• Notes and Note-Pairs in Nørgård's Infinity Series (with Christopher Drexler-Lemire and Jeffrey Shallit) Journal of Mathematics and Music 11:1 (2017), 1-19. Final version / Preprint
• A Comprehensive Analysis of Polyhedral Lift-and-Project Methods (with Levent Tunçel) SIAM Journal on Discrete Mathematics 30(1) (2016), 411-451. Final version / Preprint
• Generalized de Bruijn Words for Primitive Words and Powers Discrete Mathematics 338(12) (2015), 2320-2331. Final version / Preprint
• Complexity Analyses of Bienstock-Zuckerberg and Lasserre Relaxations on the Matching and Stable Set Polytopes (with Levent Tunçel) Proceedings of the 15th Conference on Integer Programming and Combinatorial Optimization (2011), 14-26. Final version / Preprint
• Van der Waerden's Theorem and Avoidability in Words (with Aaron Robertson and Jeffrey Shallit) Integers 11 (2011), 61-76. Final version / Preprint
• On the Polyhedral Lift-and-Project Methods and the Fractional Stable Set Polytope (with Levent Tunçel) Discrete Optimization 6(2) (2009), 206-213. Final version / Preprint
• A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization Ph. D. thesis
• On the Polyhedral Lift-and-Project Rank Conjecture for the Fractional Stable Set Polytope M. Math thesis

Teaching

I personally find teaching math a deeply satisfying endeavour -- I get to share with others about a subject I'm fascinated with, and play a small part in my students' growth and success.

Desmos Demonstrations

I am avid user of Desmos in my teaching (as well as simply for my own amusement). Here are some Desmos demonstrations that fellow instructors and students may find enlightening. (Note that these were published in 2022, and thus does not take advantage of some of Desmos' more recent features.)

• Some Visual Proofs by Desmos
• Some Desmos Demonstrations for Introductory Math/Stats Courses

Courses Taught

Finally, here is the list of courses I have taught at various places:

University of Saskatchewan (2018-)

MATH 110 -- Calculus I MATH 116 -- Calculus II MATH 123 -- Calculus I for Engineers MATH 124 -- Calculus II for Engineers MATH 133 -- Engineering Mathematics I MATH 134 -- Engineering Mathematics II MATH 163 -- Introduction to Mathematical Reasoning MATH 266 -- Linear Algebra I MATH 336 -- Mathematical Modelling I STAT 103 -- Elementary Probability STAT 242 -- Statistical Theory and Methodology

Milwaukee School of Engineering (2014-2017)

MA 120 -- Precalculus Mathematics MA 136 -- Calculus I MA 137 -- Calculus II MA 231 -- Calculus III MA 232 -- Calculus IV MA 2310 -- Discrete Mathematics I MA 262 -- Probability and Statistics MA 343 -- Linear Programming MA 344 -- Nonlinear Programming MA 481 -- Game Theory

University of Waterloo (2012-2014)

CO 250 -- Introduction to Optimization MATH 235 -- Linear Algebra II MATH 215 -- Linear Algebra for Engineering