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Research

Research Interests

I am a die-hard combinatorialist. I study combinatorial problems inspired by optimization, and am particularly interested in polytopes and their realization spaces. I use tools from applied algebraic geometry to study the correspondence between the algebraic properties of slack ideals and the geometric and combinatorial structure of the polytopes and matroids. I am also interested in the facial structure of other convex bodies arising in optimization, particularly in semidefinite programming, and how combinatorial reasoning can be extended to study these non-polyhedral convex sets. 

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I also have an interest in problems and objects arising from applications in digital communication. In the past, I have studied Golay sequences and arrays, peak sidelobe levels of binary sequences, and I wrote my Master's thesis on the subject of complex equiangular lines (also known as SIC-POVMs to those studying quantum information theory).

Research Interests
Papers
Conferences

Publications

with M. Chang-Lee, L. Colmenarejo, J. Elder, M. Supina, 

        B. Tenner

AMS Notices, vol 71 (11), Dec 2024.

with J. Gouveia

arXiv:2407.14764, 2024.

with Y. Chen, W. Hare

arXiv:2406.04530, 2024.

with Y. Chen, W. Hare

arXiv:2312.03169, 2023.

with J. Gouveia, A. Macchia

Journal of Symbolic Computation, vol 114, pp. 172-192, 2023.

with J. Gouveia, A. Macchia

Discrete & Computational Geometry,vol 69, pp 505-542, 2022.

with A. Macchia

in A.M. Bigatti, J. Carette, J.H. Davenport, M. Joswig, T. de Wolff (eds.) Mathematical Software - Proc. ICMS 2020, vol. 12097, pp. 222-231, 2020.

with N. Livchitz, B. Sert

arXiv:2007.12893, 2020.

with J. Gouveia, A. Macchia, R. R. Thomas

Journal of Pure and Applied Algebra, vol 224 (5), 2020.

with M. Brandt

Algebraic Combinatorics,  vol. 2 (4), pp. 663-681, 2019. 

with J. Gouveia, A. Macchia, R. R. Thomas

SIAM J. Discrete Math., vol 33 (3), pp. 1637–1653, 2019. 

with J. Jedwab 

Des. Codes Cryptogr., vol. 80, pp. 73–89, 2016.

with J. Jedwab

in C.J. Colbourn, ed., Springer Proceedings in Mathematics and Statistics vol 133, Algebraic Design Theory and Hadamard Matrices, pp. 159–169, 2015.

with J. Jedwab

J. Comb. Theory A, vol. 134, pp. 98-102, 2015. 

with F. Fiedler, J. Jedwab

J. Comb. Theory A,  vol. 117, pp. 589-597, 2010.

Activities

Since September 2022, I have been co-chair of the joint UBCO/SFU COCANA/CORDS Optimization Seminar which is funded by PIMS.

2024

Nov 2024: Algebra and Combinatorics Seminar, Tulane University, New Orleans, USA 

Oct 2024: AMS Sectional, UC Riverside, Riverside, USA (25 minute talk in Special Session on "Gender Equity in the Mathematical Sciences (GEMS) of Combinatorics")

Jul 2024: ISMP, Montréal, Canada (25 minute invited talk in session on "Advances in Combinatorial Optimization")

Jul 2024: Women in Combinatorics 5th Anniversary Conference, Canada, Virtual (Session Organizer)

May 2024: Maseeh Mathematics and Statistics Colloquium, Portland State University, Portland, USA

2023

Nov 2023: Combinatorics Seminar, Binghamton University,  Binghamton, USA, Virtual

Sept 2023: WCOM, Simon Fraser University, Canada (Program Committee Member)

Aug 2023: MAA MathFest, Tampa, USA (Project NExT Fellow)

Jun 2023: CanaDAM, University of Winnipeg, Canada (20 minute invited talk in "Design Theory and Coding Theory" minisymposium)

May 2023: Circuit Diameters and Augmentation: Recent Advances in Linear and Integer Optimization, CU Denver, Denver, USA (Invited Workshop Speaker)

Mar 2023: Gender Equity in the Mathematical Study (GEMS) of Combinatorics, American Institute of Mathematics, San Jose, USA (Invited Workshop Participant)

Jan 2023: JMM, Boston, USA (Project NExT Fellow)

2022

Aug 2022: MAA MathFest, Philadelphia, USA (Project NExT Fellow)

Jul 2022: Tutte Colloquium, University of Waterloo, Waterloo, Canada, Virtual

Jun 2022: CAIMS Annual Meeting, University of British Columbia Okanagan, Hybrid (Optimization theme organizer)

Apr 2022: Emergent Research: The PIMS Postdoctoral Fellow Seminar, Canada, Virtual 

Mar 2022: Operations Research/COCANA Seminar, Simon Fraser University, Canada 

Feb 2022: Discrete Math Seminar, University of Massachusetts, Amherst, USA, Virtual 

Feb 2022: Cominatorics and Geometry Seminar, UW, Seattle, USA 

2021

Dec 2021: CMS Winter Meeting, Vancouver, Canada, Virtual (Attendee)

Sept 2021: Gender Equity in the Mathematical Study (GEMS) of Combinatorics, Virtual (Attendee)

Aug 2021: SIAM Conference on Applied Algebraic Geometry, Texas A&M, College Station, USA, Virtual (25 minute invited talk in "Symbolic Combinatorics"session)

Jul 2021: Convex Geometry Minicourse, MPI Leipzig, Germany, Virtual (Organizer)

Jun 2021: Workshop on Mathematics and Racial Justice, MSRI, Berkeley, USA, Virtual (Attendee)

Jun 2021: CMS Summer Meeting, Ottawa, Canada, Virtual (Attendee)

May 2021: CanaDAM, Canada, Virtual (Attendee)

May 2021: WCOM, University of British Columbia Okanagan, Canada, Virtual (Attendee)

May 2021: Combinatorics Seminar, KTH, Stockholm, Sweden, Virtual 

May 2021: AMS Sectional, San Francisco State University, California, Virtual, (25 minute invited talk in ''Special Session on Algebraic and Combinatorial Aspects of Polytopes'')

Apr 2021: Graduate student meeting on Applied Algebra and Combinatorics​, University of Copenhagen, Denmark, Virtual, (25 minute contributed talk) 

Apr 2021: (Polytop)ics, MPI Leipzig, Germany, Virtual (Attendee)

Apr 2021: Discrete Math Seminar, Simon Fraser University, Canada, Virtual

Apr 2021: Algebraic Combinatorics Seminar, University of Waterloo, Canada, Virtual

Feb 2021: Introductory Workshop: Combinatorial Algebraic Geometry, ICERM, Virtual, (Attendee)

2020

Dec 2020:  Women in Combinatorics Colloquium, Virtual

Jul 2020: ICMS 2020, TU Braunschweig, Germany, Virtual, (Attendee)

May 2020 (POSTPONED): Chow Lectures, Max Planck Institute, Leipzig, Germany (introductory lecture)

Apr 2020 (POSTPONED): Graduate student meeting on Applied Algebra and Combinatorics​, University of Copenhagen, Denmark (contributed talk)

Mar 2020: Combinatorial Coworkspace — a session in algebraic and geometric combinatorics, Haus Bergkranz, Kleinwalsertal, Austria (Invited participant)

Feb 2020: Research Seminar on Discrete and Convex Geometry, Technische Universität Berlin, Germany​​​

2019

Dec 2019: Research Retreat of the Thematic Einstein Semester "Algebraic Geometry - Varieties, Polyhedra, Computation", Döllnsee, Germany (Attendee)

Dec 2019: Women in Symbolic Algebra and Computations, Bad Dürkheim, Germany (20 minute invited talk)

Dec 2019: Einstein Workshop on Polytopes and Algebraic Geometry, Freie Universität Berlin, Germany (Organizer)

Oct 2019: Discrete Geometry Seminar, Freie Universität Berlin, Germany

Oct 2019: Opening conference of the Thematic Einstein Semester "Algebraic Geometry - Varieties, Polyhedra, Computation", Freie Universität Berlin, Germany (Attendee)

Jun 2019: International Conference on Network Games, Tropical Geometry, and Quantum Communication, Zuse Institute Berlin, Germany (Attendee)

May 2019: CanaDAM, Simon Fraser University, Vancouver, Canada (20 minute invited talk in "Combinatorial Optimization" minisymposium)​

2018

In Autumn 2018, I started a graduate student optimization seminar at the University of Washington. I organized the seminar for the 2018-2019 academic year. 

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Aug 2018: Visiting student, University of Coimbra, Portugal

Jul 2018: ISMP, Bordeaux, France (25 minute talk in ''Algebraic and geometric aspects of semidefinite programming'' session)

Jun 2018: ECCO 18, Barranquilla, Colombia (25 minute talk in ''Polytopes'' session)

May 2018: Discrete Math Seminar, Simon Fraser University, Burnaby, Canada

Apr 2018: AMS Sectional Meeting, Portland State University, Portland, USA (25 minute talk in ''Special Session on Commutative Algebra'')

Mar 2018: Discrete Geometry Seminar, Freie Universität Berlin, Germany

February-March 2018: Visiting Student, MPI, Leipzig, Germany (50 minute talk in ''Seminar on Nonlinear Algebra'')​​​

Oct 2017: Geometric and topological combinatorics: Modern techniques and methods, MSRI, Berkeley, USA (Attendee)

Sep 2017: Introductory Workshop: Geometric and Topological Combinatorics, MSRI, Berkeley, USA (Attendee)

Aug 2017: Bridging Continuous and Discrete Optimization Boot Camp, Simons Institute for the Theory of Computing, Berkeley, USA (Attendee)

Aug 2017: SIAM Conference on Applied Algebraic Geometry, Georgia Institute of Technology, Atlanta, USA (25 minute talk in minisymposium on ''Semidefinite Optimization and Convex Algebraic Geometry'')

Jul 2017: Applied Macaulay2 Tutorials, Georgia Institute of Technology, Atlanta, USA (Attendee)​

2017

Nov 2016: Combinatorial Potlatch, Seattle University, Seattle, USA (Attendee)

Aug 2016: Summer School on Real Algebraic Geometry and Optimization, Georgia Institute of Technology, Atlanta, USA (Attendee)

Jan 2016: Joint Meetings, Seattle, USA (Attendee)​

2016

​Jan 2015: Mathematics of Communications: Sequences, Codes and Designs Workshop, BIRS, Banff, Canada (Attendee)

2015

Students

Ph. D.

2024 - 

Yiwen Chen, UBCO

M. Sc.

2024 - 

Kaioke Begay, UBCO

2023 -

Jeremiah Yoder, UBCO

2022 - 2024

Undergraduate

May - Aug 2024

Zahra Kagda, UBCO (URA)

May - Jul 2024

Aniket Pandey, UBCO (Mitacs Globlink Research Intern)

May - Aug 2023

Nathania Hendradjaja, UBCO (Work Study)

Students
Code

Code

​Here is the current version of a Macaulay2 package that can be used to construct and manipulate slack ideals. It is also available with the current distribution of Macaulay2. If you find errors in it, have questions or suggestions, please email me. 

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