I am currently a postdoc at the Research Institute for Symbolic Computation in Linz. Previously, I spent two years as a postdoc at San Francisco State University, funded by the DFG, after doing my PhD at the Freie Universität Berlin.
This page collects my published work, including research in mathematics and computer science, software and more.
On my personal blog I write about all kinds of things that interest me. The latest posts are shown on the right.
Mathematics and Computer Science
Here is a list of my formal research publications. Note that on publications in mathematics, authors are always listed alphabetically.
Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems (2015) with Zafeirakis Zafeirakopoulos
An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics (2015)
Felix Breuer, An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics. In: Computer Algebra and Polynomials; Jaime Gutierrez, Josef Schicho, Martin Weimann, editors. Lecture Notes in Computer Science 8942, 1-29, 2015.
Scheduling Problems (2014) with Caroline J. Klivans
Enumerating Colorings, Tensions and Flows in Cell Complexes (2014) with Matthias Beck, Logan Godkin and Jeremy Martin
Matthias Beck, Felix Breuer, Logan Godkin, Jeremy L. Martin, Enumerating colorings, tensions and flows in cell complexes, Journal of Combinatorial Theory, Series A 122(4), 82-106, 2014.
Analytic Feature Selection for Support Vector Machines (2013) with Carly Stambaugh and Hui Yang
Carly Stambaugh, Hui Yang, Felix Breuer, Analytic Feature Selection for Support Vector Machines. In: Machine Learning and Data Mining in Pattern Recognition; Petra Perner, editor. Lecture Notes in Computer Science 7988, 219-233, 2013.
Ehrhart f*-coefficients of polytopal complexes are non-negative integers (2012)
Felix Breuer, Ehrhart f*-coefficients of polytopal complexes are non-negative integers, Electronic Journal of Combinatorics 19(4), P16, 2012.
Hypergraph Coloring Complexes (2012) with Aaron Dall and Martina Kubitzke
Felix Breuer, Aaron Dall, Martina Kubitzke, Hypergraph Coloring Complexes, Discrete Mathematics 312(16), 2407-2420, 2012.
Ehrhart theory, Modular flow reciprocity, and the Tutte polynomial (2012) with Raman Sanyal
Felix Breuer, Raman Sanyal, Ehrhart theory, Modular flow reciprocity, and the Tutte polynomial, Mathematische Zeitschrift 270(1), 1-18, 2012.
Counting Hexagonal Patches and Independent Sets in Circle Graphs (2012) with Paul Bonsma
Paul Bonsma, Felix Breuer. Counting Hexagonal Patches and Independent Sets in Circle Graphs, Algorithmica 63(3), 645-671, 2012.
Paul Bonsma, Felix Breuer. Counting Hexagonal Patches and Independent Sets in Circle Graphs. In: LATIN 2010: Theoretical Informatics; Alejandro López-Ortiz, editor. Lecture Notes in Computer Science Volume 6034, 603-614, 2010.
Bounds on the Coefficients of Tension and Flow Polynomials (2011) with Aaron Dall
Felix Breuer, Aaron Dall, Bounds on the Coefficients of Tension and Flow Polynomials, Journal of Algebraic Combinatorics 33(3), 465-482, 2011.
Viewing counting polynomials as Hilbert functions via Ehrhart theory (2010) with Aaron Dall
Felix Breuer, Aaron Dall. Viewing counting polynomials as Hilbert functions via Ehrhart theory. In: 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010). DMTCS, 413-424, 2010.
Staircases in Z2 (2010) with Frederik von Heymann
Felix Breuer, Frederik von Heymann, Staircases in Z2, INTEGERS 10, 807-847, 2010.
Uneven Splitting of Ham Sandwiches (2010)
Felix Breuer, Uneven Splitting of Ham Sandwiches, Discrete and Computational Geometry 43(4), 876-892, 2010.
Ham Sandwiches, Staircases and Counting Polynomials (2009)
PhD Thesis, Freie Universität Berlin, 2009.
Finding Fullerene Patches in Polynomial Time (2009) with Paul Bonsma
Paul Bonsma, Felix Breuer. Finding Fullerene Patches in Polynomial Time. In: Algorithms and Computation: 20th International Symposium, ISAAC 2009; Yingfei Dong, Ding-Zhu Du, Oscar Ibarra, editors. Lecture Notes in Computer Science Volume 5878, 750-759, 2009.
Gauss Codes and Thrackles (2006)
Diploma Thesis, FU Berlin, 2006.
Domino-Pflasterungen und Aztekensterne (2006) with Daria Schymura
Felix Breuer, Daria Schymura, Domino–Pflasterungen und Aztekensterne, Mathematische Semesterberichte 53(1), 81 - 99, 2006.
Fund I/O is both: exploratory research and a practical business model. The premise: crowdfunding and novel payment solutions can be used to put theoretical mechanisms for the private provision of public goods to real-world use.
There is no research paper on Fund I/O available yet, but I am keeping an open notebook on both my theoretical findings and practical considerations on my blog. If you want to read more, this is the post to start with. A full list of posts on Fund I/O can be found here.
I am currently active in the following two software projects.
Polyhedral Omega is a solver for linear Diophantine systems that I am currently developing with Zafeirakis Zafeirakopoulos. It computes symbolic cone and rational function representations of the set of all integer solutions to a system of linear inequalities. See our paper for details. The current implementation is based on Sage.
Substance / Lens
Substance is a technology stack for reading and writing professional web-first publications. It includes the Lens reader for Substance documents, which is part of the online portals of publishers such as eLife. I am contributing mathematical features to the project.
In the past, I have maintained two open source software projects.
Qute is a text editor for Windows/Linux/Mac OS built around Markdown and MathJax. It offers TeX support and per-paragraph preview of markup (including typeset formulas)! It also an experiment in the visual aesthetics of text editing. There also is a version of Qute for Android, but that one offers fewer features.
InkBoard is an experimental pen-centric on-screen keyboard which I designed and implemented. It was written in Clojure and is available as open-source software. It is part of the larger InkCode project.
Also, I have been involved in several open source software projects, some of which are worth mentioning.
Heretix was a source based GNU/Linux distribution, whose package manager was implemented as a Ruby script. I helped writing packages, maintaining the website and integrating a documentation system into the package manager itself. Heretix has been discontinued.
Using Intuitive Geometry (2011)
In the fall term of 2011 I volunteered to teach Math 890 at San Francisco State University. The title of the course was "Using Intuitive Geometry - Using Geometric Intuition" and it dealt mainly with discrete geometry.
Along with Peter Krautzberger and Frederik von Heymann, I am one of the co-founders of Mathblogging.org. Mathblogging.org is a blog aggregator for the mathematical blogging community. By providing an index of math blogs, editorial content and technological infrastructure we help readers from any background discover the mathematical blogosphere.
Geometry, the Majority Vote and the Power of Agenda Control
After serious police violence against Occupy protesters in the Bay Area, I joined mathematicians at UC Berkeley in organizing a teach-in. We gave public lectures on mathematical topics with a connection to polictics. I spoke on "Geometry, the Majority Vote and the Power of Agenda Control".
Der kleine Gauß (2010) with Peter Krautzberger
As an experiment in communicating mathematics Peter and I created this video about the intuitive meaning of Gauss' sum formula.
Feldenkrais' Spontaneous Action and Laozi's Wuwei (2012)
Felix Breuer, Feldenkrais' Spontaneous Action and Laozi's Wuwei, Journal of Daoist Studies 5, 169 - 183, 2012.
Now and then I have been writing fiction.
Eine inszenierte Revolte (2007)
17 Gen r (2000)
"17 Gen r" is a fragment of a novel. I brought this project pretty far (beyond 100,000 words), but in the end I did not finish it.
Ein Jahr (1999)
The short story "Ein Jahr" was published in an anthology in 1999.