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 interests mainly lie 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:

• On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász-Schrijver SDP Hierarchy Preprint (2024) (with Levent Tunçel)
• Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operators Mathematical Programming A (2024), 1-36. (with Levent Tunçel)
• Decompositions of Unit Hypercubes and the Reversion of a Generalized Möbius Series Electronic Journal of Combinatorics 31 (2024), Article P2.26.
• On Connections Between Association Schemes and Analyses of Polyhedral and Positive Semidefinite Lift-and-Project Relaxations Preprint (Revised Dec. 2023) (with Nathan Lindzey and Levent Tunçel)
• Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers Journal of Integer Sequences 24 (2021), Article 21.1.1.
• Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube Journal of Integer Sequences 23 (2020), Article 20.1.4. (with Fatemeh Bagherzadeh and Murray Bremner)
• Elementary Polytopes with High Lift-and-Project Ranks for Strong Positive Semidefinite Operators Discrete Optimization 27 (2018), 103-129. (with Levent Tunçel)
• Notes and Note-Pairs in Nørgård's Infinity Series Journal of Mathematics and Music 11:1 (2017), 1-19. (with Christopher Drexler-Lemire and Jeffrey Shallit)
• A Comprehensive Analysis of Polyhedral Lift-and-Project Methods SIAM Journal on Discrete Mathematics 30(1) (2016), 411-451. (with Levent Tunçel)
• Generalized de Bruijn Words for Primitive Words and Powers Discrete Mathematics 338(12) (2015), 2320-2331.
• Complexity Analyses of Bienstock-Zuckerberg and Lasserre Relaxations on the Matching and Stable Set Polytopes Proceedings of the 15th Conference on Integer Programming and Combinatorial Optimization (2011), 14-26. (with Levent Tunçel)
• Van der Waerden's Theorem and Avoidability in Words Integers 11 (2011), 61-76. (with Aaron Robertson and Jeffrey Shallit)
• On the Polyhedral Lift-and-Project Methods and the Fractional Stable Set Polytope Discrete Optimization 6(2) (2009), 206-213. (with Levent Tunçel)
• 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 enjoy teaching math immensely -- it's deeply satisfying to talk about what you love!

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:

• 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