Yu Hin (Gary) Au

Assistant Professor
Department of Mathematics and Statistics
University of Saskatchewan

Office: 239 McLean Hall
E-mail: auP@mathQ.usask.caR
(with P,Q,R removed)


I am currently an Assistant Professor in the Department of Mathematics and Statistics at the University of Saskatchewan.

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. In particular, I like to study the theory and applications of linear, integer and semidefinite programming, and problems in closely related areas such as graph theory and approximation algorithms. Currently, I'm focused on analyzing lift-and-project methods, and their power and limitations in tackling problems that arise from combinatorial optimization.

I have also worked on several problems in combinatorics, and am easily attracted by most things discrete mathematics in general.

Some of my work to date:

Matchings, hypergraphs, association schemes, and semidefinite optimization
Preprint (2020)
(with
Nathan Lindzey and Levent Tunçel)

Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers
Preprint (2020)

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
PhD thesis

On the Polyhedral Lift-and-Project Rank Conjecture for the Fractional Stable Set Polytope
M.Math thesis


Teaching

I find incredible joy in communicating Mathematics with others, so it's only natural that I enjoy teaching immensely. Below is a list of courses I have taught / am currently teaching / am going to teach.

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 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