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I am an associate professor at UBC's Sauder School of Business. I am thankful to be an associate member of the CS department at UBC.
Previously, I worked as a postdoc at ETH Zürich at the Institute for Operations Research in Robert Weismantel's group. I received my Ph.D. in Applied Math and Stats at Johns Hopkins University under the supervision of Amitabh Basu. In 2016, I worked with Zuse Institute Berlin and the Deutsche Bahn to model train schedules.
My current research interests lie in discrete optimization, with a major focus on the theory of integer programming. I am particularly interested in identifying tools from topology, combinatorics, and number theory that can be applied to problems in integer optimization.
My email is joseph.paat 'at' ubc 'dot' ca. Here is my CV.
"All this is quite genuine mathematics, and has its merits; but it is just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly) which a real mathematician tends to despise." --- A Mathematician's Apology by G.H. Hardy ---
Teaching
At UBC
BASC 550 - Operations
COMM 204 - Logistics and Operations Management
COMM 612 - Advanced Topics in Optimization (A topic course)
2023 W2 - A focus on modeling practices for mathematical programming; Co-taught with Julia Yan.
COMM 616 - Optimization Theory and Applications (A topic course)
2021 W1 - A focus on integer and linear programming
COMM 618 - Discrete Optimization II (A topic course)
2022 W1 - A focus on machine learning in discrete optimization
2023 W1 - A focus on combinatorial optimization
At ETH
401 - Geometric Integer Programming
At JHU
EN 553.112 - Statistical Analysis II
EN 553.171 - Discrete Mathematics
Selected professional service
INFORMS Optimization Society, Vice -chair of Integer and Combinatorial Optimization, 2025 - Present
Associate Editor, Discrete Optimization, 2022 - Present
Committee of the Mixed Integer Programming Society [Secretary 2022-2025; Chair 2025-2026]
Chair of the Organizing Committee of the Mixed Integer Programming Workshop, 2024
Research
Submitted articles
The column number for 3-modular matrices Joint work with Zach Walsh and Luze Xu
A characterization of unimodular hypergraphs with disjoint hyperedges Joint work with Marco Caoduro and Meike Neuwohner
Journal articles and refereed conference proceedings
Performance of the offer-everything policy Operations Research, 2025 Joint work with Tim Huh and Maurice Queyranne
Extended formulations for the integer hull of strictly Delta-modular cographic polyhedral cones Operations Research Letters, 2025Joint work with Zach Walsh and Luze Xu
The MIP Workshop 2023 Computational Competition on ReoptimizationMathematical Programming Computation, 2024Joint work with Suresh Bolusani, Mathieu Besançon, Ambros Gleixner, Timo Berthold, Claudia D'Ambrosio, Gonzalo Muñoz, and Dimitri Thomopulos.
A characterization of maximal homogeneous-quadratic-free setsMathematical Programming, 2024A conference version appeared here in Proceedings of IPCO 2023Joint work with Gonzalo Muñoz and Felipe Serrano
Compressing Branch-and-Bound TreesMathematical Programming, 2024A conference version appeared here in Proceedings of IPCO 2023Joint work with Gonzalo Muñoz and Álinson S. Xavier
On the column number and forbidden submatrices of Delta-modular matrices SIAM Journal on Discrete Mathematics, 2024 Joint work with Ingo Stallknecht, Zach Walsh, and Luze Xu
Proximity and flatness bounds for linear integer optimization Mathematics of Operations Research, 2023Joint work with Marcel Celaya, Stefan Kuhlmann, and Robert Weismantel
A Colorful Steinitz Lemma with Applications to Block Integer ProgramsMathematical Programming, 2023Joint work with Timm Oertel and Robert Weismantel
Polynomial upper bounds on the number of differing columns of Delta-modular integer programsMathematics of Operations Research, 2022Joint work with Jon Lee, Ingo Stallknecht, and Luze Xu
Improving the Cook et al. Proximity Bound Given Integral Valued Constraints Proceedings of IPCO 2022 Joint work with Marcel Celaya, Stefan Kuhlmann, and Robert Weismantel
Constructing lattice-free gradient polyhedra in dimension two
Mathematical Programming, 2021A conference version appeared in Proceedings of IPCO 2020Joint work with Miriam Schlöter and Emily SpeakmanThe integrality number of an integer program
Mathematical Programming, 2021A conference version appeared in Proceedings of IPCO 2020Joint work with Miriam Schlöter and Robert WeismantelThe distributions of functions related to parametric integer optimization
SIAM Journal on Applied Algebra and Geometry, 2020Joint work with Timm Oertel and Robert WeismantelImproving proximity bounds using sparsity
Proceedings of ISCO 2020Joint work with Jon Lee, Ingo Stallknecht, and Luze XuSparsity of integer solutions in the average case
Proceedings of IPCO 2019There are some typos in the IPCO version. The corrected version is here on the arXivJoint work with Timm Oertel and Robert WeismantelNonunique lifting of integer variables in minimal inequalities
SIAM Journal on Discrete Mathematics, 2019Joint work with Amitabh Basu and Santanu S. DeyThe structure of the infinite models in integer programming
Mathematics of Operations Research, 2019.A conference version was published in IPCO 2017 hereJoint work with Amitabh Basu, Michele Conforti, and Marco Di SummaDistances between optimal solutions of mixed-integer programs
Mathematical Programming, 2018Joint work with Robert Weismantel and Stefan WeltgeConflict-free railway track assignment at depots
Journal of Rail Transport Planning & Management, 2018Joint work with Brady Gilg, Torsten Klug, Rosemarie Martienssen, Thomas Schlechte, Christof Schulz, Sinan Seymen, and Alexander TeschApproximation of corner polyhedra with families of intersection cuts
SIAM Journal on Optimization, 2018A conference version was published in IPCO 2017 hereJoint work with Gennadiy Averkov and Amitabh BasuExtreme functions with an arbitrary number of slopes
Mathematical Programming, 2017A conference version was published in IPCO 2016 here Joint work with Amitabh Basu, Michele Conforti, and Marco Di SummaOperations that preserve the covering property of the lifting region
SIAM Journal on Optimization, 2015Joint work with Amitabh BasuInvolve, a Journal of Mathematics, 2017Joint work with Hwa Jeong Lee, Lew Ludwig, and Amanda PeifferAn infinite family of knots whose mosaic number is realized in non-reduced projections
Journal of Knot Theory and Its Ramifications, 2013Joint work with Erica Evans and Lew LudwigPage updated
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