I hope you're having a good day!

I am an assistant 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

At ETH

At JHU

Selected professional service

Associate Editor, Discrete Optimization, 2022 - Present

Secretary of the Mixed Integer Programming Society, 2022 - Present

Chair of the Organizing Committee of the Mixed Integer Programming Workshop, 2024

Research

Submitted articles


A characterization of unimodular hypergraphs with disjoint hyperedges Joint work with Marco Caoduro and Meike Neuwohner
On the performance of the offer everything policy  Joint work with Tim Huh and Maurice Queyranne

Journal articles and refereed conference proceedings


Extended formulations for the integer hull of strictly Delta-modular cographic polyhedral cones Accepted in Operations Research Letters, 2024.Joint work with Zach Walsh and Luze Xu 
The MIP Workshop 2023 Computational Competition on ReoptimizationMathematical Programming Computation, 2024.Joint 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, 2024.A conference version appeared here in Proceedings of IPCO 2023Joint work with Gonzalo Muñoz and Felipe Serrano
Compressing Branch-and-Bound TreesMathematical Programming, 2024.A 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 Speakman

The integrality number of an integer program

Mathematical Programming, 2021A conference version appeared in Proceedings of IPCO 2020Joint work with Miriam Schlöter and Robert Weismantel

The distributions of functions related to parametric integer optimization

SIAM Journal on Applied Algebra and Geometry, 2020Joint work with Timm Oertel and Robert Weismantel

Improving proximity bounds using sparsity

Proceedings of ISCO 2020Joint work with Jon Lee, Ingo Stallknecht, and Luze Xu

Sparsity 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 Weismantel

Nonunique lifting of integer variables in minimal inequalities

SIAM Journal on Discrete Mathematics, 2019Joint work with Amitabh Basu and Santanu S. Dey

The 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 Summa

Distances between optimal solutions of mixed-integer programs

Mathematical Programming, 2018Joint work with Robert Weismantel and Stefan Weltge

Conflict-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 Tesch            

Approximation 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 Basu

Extreme 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 Summa

Operations that preserve the covering property of the lifting region

SIAM Journal on Optimization, 2015Joint work with Amitabh Basu

Knot mosaic tabulation

Involve, a Journal of Mathematics, 2017Joint work with Hwa Jeong Lee, Lew Ludwig, and Amanda Peiffer

An 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 Ludwig