RESEARCH INTERESTS

I am a die-hard combinatorialist. My current research is in geometric combinatorics with connections to applied algebraic geometry and optimization. I am studying slack ideals of polytopes and matroids. In particular, we are interested in correspondence between the algebraic properties of the slack ideals and the geometric and combinatorial structure of the polytopes and matroids. 

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I also still like to think about problems and objects that have 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).

PUBLICATIONS

• A. Macchia and A. Wiebe, "Slack Ideals in Macaulay2," arXiv: 2003.07382, 2020.

• J. Gouveia, A. Macchia and A. Wiebe,  "Combining realization space models of polytopes," arXiv:2001.11999, 2020

• J. Gouveia, A. Macchia, R. R. Thomas and A. Wiebe, ''Projectively unique polytopes and toric slack ideals'' Journal of Pure and Applied Algebra (to appear), arXiv:1808.01692, 2018. 

• M. Brandt and A. Wiebe, ''The slack realization space of a matroid'' Algebraic Combinatorics,  vol 2 no. 4,  p. 663-681, 2019. 

• J. Gouveia, A. Macchia, R. R. Thomas and A. Wiebe, ''The slack realization space of a polytope,'' SIAM J. Discrete Math., vol 33(3), 1637–1653, 2019. 

• J. Jedwab and A. Wiebe, ''Constructions of complex equiangular lines from mutually unbiased bases,'' Des. Codes Cryptogr., vol. 80 pp. 73–89, 2016.

• J. Jedwab and A. Wiebe, ''A simple construction of complex equiangular lines,'' in C.J. Colbourn, ed., Springer Proceedings in Mathematics and Statistics vol 133, Algebraic Design Theory and Hadamard Matrices, pp. 159–169, 2015. 

• J. Jedwab and A. Wiebe, ''Large sets of complex and real equiangular lines,'' J. Comb. Theory A vol. 134 pp. 98-102, 2015. 

• A. Wiebe, ''Constructions of complex equiangular lines,'' M.Sc. Thesis, Simon Fraser University, 2013.

• F. Fiedler, J. Jedwab and A. Wiebe, ''A new source of seed pairs for Golay sequences of length 2^m,'' J. Comb. Theory A vol. 117 pp. 589-597, 2010.

ACTIVITIES

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

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

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

• Februrary 2020: Research Seminar on Discrete and Convex Geometry, Technische Universität Berlin, Germany

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

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

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

• October 2019: Discrete Geometry Seminar, Freie Universität Berlin, Germany

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

• June 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 talk in "Combinatorial Optimization" invited minisymposium)

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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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• August 2018: Visiting student, University of Coimbra, Portugal

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

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

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

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

• March 2018: Discrete Geometry Seminar, Freie Universität Berlin, Germany

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

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• October 2017: Geometric and topological combinatorics: Modern techniques and methods, MSRI, Berkeley, California (Attendee)

• September 2017: Introductory Workshop: Geometric and Topological Combinatorics, MSRI, Berkeley, California (Attendee)

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

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

• July 2017: Applied Macaulay2 Tutorials, Georgia Institute of Technology, Atlanta, Georgia (Attendee)

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• November 2016: Combinatorial Potlatch, Seattle University, Seattle, Washington (Attendee)

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

• January 2016: Joint Meetings, Seattle, Washington (Attendee)

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

CODE

​Here is the current version of a Macaulay2 package that can be used to construct and manipulate slack ideals. If you find errors in it, please email me. 
Examples files from The slack realization space of a matroid will be posted here soon.

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