Gábor Braun

I approach problems from a strong algebraic viewpoint, searching for structure and operations and how they combine. My interests span from abstract algebra through topology/geometry to convex optimization.

📬 Contact

office
Room 3035 at ZIB
Room MA MA605 at TUB
e-mail
languages
Hungarian, English, and German

🎓 Curriculum vitae

since 2021
Member of MATH+
since 2020
Researcher at ZIB
2013 to 2018
Researcher at GT
2011 to 2013
Lecturer at University of Leipzig
2009 to 2011
Researcher at DUE
2007 to 2010
Researcher at Alfréd Rényi Institute of Mathematics
2004 to 2007
Researcher at Eötvös Loránd University
2003 to 2004
Researcher at Alfréd Rényi Institute of Mathematics
2002 to 2003
Research Assistant at DUE
Apr 2003
Ph.D. in Mathematics at DUE
Jan 2002
M.Sc. in Mathematics at Eötvös Loránd University

📝 Publications and preprints

Preprints

  1. Braun, G., Pokutta, S., and Woodstock, Z. (2024). Flexible Block-iterative Analysis for the Frank-Wolfe Algorithm. [arXiv]
    [BibTeX]
    @misc{2024_BraunPokuttaWoodstock_Blockiterativeanalysis,
  archiveprefix = {arXiv},
  eprint = {2409.06931},
  primaryclass = {math.OC},
  year = {2024},
  author = {Braun, Gábor and Pokutta, Sebastian and Woodstock, Zev},
  title = {Flexible Block-iterative Analysis for the Frank-Wolfe Algorithm},
  date = {2024-09-11}
}
  2. Braun, G., Carderera, A., Combettes, C., Hassani, H., Karbasi, A., Mokhtari, A., and Pokutta, S. (2022). Conditional Gradient Methods. [arXiv]
    [BibTeX]
    @misc{2022_BraunEtAl_Conditionalgradient,
  archiveprefix = {arXiv},
  eprint = {2211.14103},
  primaryclass = {math.OC},
  year = {2022},
  author = {Braun, Gábor and Carderera, Alejandro and Combettes, Cyrille and Hassani, Hamed and Karbasi, Amin and Mokhtari, Aryan and Pokutta, Sebastian},
  title = {Conditional Gradient Methods},
  date = {2022-11-25}
}
  3. Braun, G., Pokutta, S., and Weismantel, R. (2022). Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections. [arXiv] [slides] [video]
    [BibTeX]
    @misc{2022_BraunPokuttaWeismantel_Alternatingminimization,
  archiveprefix = {arXiv},
  eprint = {2212.02933},
  primaryclass = {math.OC},
  year = {2022},
  author = {Braun, Gábor and Pokutta, Sebastian and Weismantel, Robert},
  title = {Alternating Linear Minimization: Revisiting von Neumann's Alternating Projections},
  slides = {https://pokutta.com/slides/20230327-icerm.pdf},
  video = {https://icerm.brown.edu/programs/sp-s23/w2/#schedule-item-4945},
  date = {2022-12-06}
}
  4. Braun, G., and Pokutta, S. (2021). Dual Prices for Frank–Wolfe Algorithms. [arXiv]
    [BibTeX]
    @misc{2021_BraunPokutta_DualpricesFrankwolfe,
  archiveprefix = {arXiv},
  eprint = {2101.02087},
  primaryclass = {math.OC},
  year = {2021},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Dual Prices for Frank–Wolfe Algorithms},
  date = {2021-01-06}
}
  5. Braun, G., Schultz, P., and Strüngmann, L. (2018). Decompositions of Torsion-free Abelian Groups. [arXiv]
    [BibTeX]
    @misc{2018_BraunSchultzStruengmann_Torsionfreedecompositions,
  archiveprefix = {arXiv},
  eprint = {1810.09644},
  primaryclass = {math.GR},
  year = {2018},
  author = {Braun, Gábor and Schultz, Phill and Strüngmann, Lutz},
  title = {Decompositions of Torsion-free Abelian Groups},
  date = {2018-10-23}
}
  6. Braun, G., and Pokutta, S. (2016). An Efficient High-probability Algorithm for Linear Bandits. [arXiv]
    [BibTeX]
    @misc{2016_BraunPokutta_Highprobabilitylinearbandits,
  archiveprefix = {arXiv},
  eprint = {1610.02072},
  primaryclass = {cs.DS},
  year = {2016},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {An Efficient High-probability Algorithm for Linear Bandits},
  date = {2016-10-06}
}
  7. Braun, G., and Pokutta, S. (2015). An Information Diffusion Fano Inequality. [arXiv]
    [BibTeX]
    @misc{2015_BraunPokutta_Informationdiffusionfano,
  archiveprefix = {arXiv},
  eprint = {1504.05492},
  primaryclass = {cs.IT},
  year = {2015},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {An Information Diffusion Fano Inequality},
  date = {2015-04-21}
}
  8. Braun, G., and Pokutta, S. (2009). A Polyhedral Approach to Computing Border Bases. [arXiv]
    [BibTeX]
    @misc{2010_BraunPokutta_PolyhedralApproach,
  archiveprefix = {arXiv},
  eprint = {0911.0859},
  primaryclass = {math.AC},
  year = {2009},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {A Polyhedral Approach to Computing Border Bases},
  date = {2009-11-04}
}
  9. Braun, G. (2008). Geometry of Splice-quotient Singularities. [arXiv]
    [BibTeX]
    @misc{2008_Braun_Splicequotientsingularities,
  archiveprefix = {arXiv},
  eprint = {0812.4403},
  primaryclass = {math.AG},
  year = {2008},
  author = {Braun, Gábor},
  title = {Geometry of Splice-quotient Singularities},
  date = {2008-12-23}
}

Conference proceedings

  1. Braun, G., Pokutta, S., Tu, D., and Wright, S. (2019). Blended Conditional Gradients: the Unconditioning of Conditional Gradients. Proceedings of the International Conference on Machine Learning, 97, 735–743. [URL] [arXiv] [summary] [slides] [poster] [code]
    [BibTeX]
    @inproceedings{2018_BraunPokuttaTuStephen_Blendedconditionalgradients,
  year = {2019},
  booktitle = {Proceedings of the International Conference on Machine Learning},
  volume = {97},
  pages = {735–743},
  url = {https://proceedings.mlr.press/v97/braun19a},
  archiveprefix = {arXiv},
  eprint = {1805.07311},
  primaryclass = {math.OC},
  author = {Braun, Gábor and Pokutta, Sebastian and Tu, Dan and Wright, Stephen},
  title = {Blended Conditional Gradients: the Unconditioning of Conditional Gradients},
  code = {https://github.com/pokutta/bcg},
  poster = {https://app.box.com/s/nmmm671jd72i397nysa8emfnzh1hn6hf},
  slides = {https://app.box.com/s/xbx3z7ws6dxvl3rzgj4jp6forigycooe},
  summary = {https://pokutta.com/blog/research/2019/02/18/bcg-abstract.html}
}
  2. Braun, G., Pokutta, S., and Zink, D. (2017). Lazifying Conditional Gradient Algorithms. Proceedings of the International Conference on Machine Learning, 70, 566–575. [URL] [arXiv] [slides] [poster]
    [BibTeX]
    @inproceedings{2016_BraunPokuttaZink_Lazifyinggradientalgorithms:1,
  year = {2017},
  booktitle = {Proceedings of the International Conference on Machine Learning},
  volume = {70},
  pages = {566–575},
  url = {https://proceedings.mlr.press/v70/braun17a},
  archiveprefix = {arXiv},
  eprint = {1610.05120},
  primaryclass = {cs.DS},
  author = {Braun, Gábor and Pokutta, Sebastian and Zink, Daniel},
  title = {Lazifying Conditional Gradient Algorithms},
  poster = {https://app.box.com/s/lysscdg17ytpz7mqr0tu2djffyqvkl6a},
  slides = {https://app.box.com/s/zsp0hixjz2ha23u1vuyosijjkjdh8k}
}
  3. Braun, G., and Strüngmann, L. (2017). Rigid ℵ₁-free Abelian Groups with Prescribed Factors and their Role in the Theory of Cellular Covers. Proceedings of the Groups, Modules, and Model Theory - Surveys and Recent Developments: In Memory of Rüdiger Göbel, 69–81. DOI: 10.1007/978-3-319-51718-6_4
    [BibTeX]
    @inproceedings{2017_BraunStrngmann_Rigidabeliangroups,
  year = {2017},
  booktitle = {Proceedings of the Groups, Modules, and Model Theory - Surveys and Recent Developments: In Memory of Rüdiger Göbel},
  pages = {69–81},
  doi = {10.1007/978-3-319-51718-6_4},
  author = {Braun, Gábor and Strüngmann, Lutz},
  title = {Rigid ℵ₁-free Abelian Groups with Prescribed Factors and their Role in the Theory of Cellular Covers}
}
  4. Braun, G., Pokutta, S., and Roy, A. (2016). Strong Reductions for Extended Formulations. Proceedings of the Conference on Integer Programming and Combinatorial Optimization, 9682, 350–361. DOI: 10.1007/978-3-319-33461-5_29 [arXiv]
    [BibTeX]
    @inproceedings{2015_BraunPokuttaRoy_Strongreductions:1,
  year = {2016},
  booktitle = {Proceedings of the Conference on Integer Programming and Combinatorial Optimization},
  month = jun,
  volume = {9682},
  pages = {350–361},
  doi = {10.1007/978-3-319-33461-5_29},
  archiveprefix = {arXiv},
  eprint = {1512.04932},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian and Roy, Aurko},
  title = {Strong Reductions for Extended Formulations}
}
  5. Braun, G., Brown-Cohen, J., Huq, A., Pokutta, S., Raghavendra, P., Roy, A., Weitz, B., and Zink, D. (2016). The Matching Problem Has No Small Symmetric SDP. Proceedings of the Symposium on Discrete Algorithms, 1067–1078. DOI: 10.1137/1.9781611974331.ch75 [arXiv]
    [BibTeX]
    @inproceedings{2015_BraunEtAl_MatchingproblemSdp:1,
  year = {2016},
  booktitle = {Proceedings of the Symposium on Discrete Algorithms},
  pages = {1067–1078},
  doi = {10.1137/1.9781611974331.ch75},
  archiveprefix = {arXiv},
  eprint = {1504.00703},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Brown-Cohen, Jonah and Huq, Arefin and Pokutta, Sebastian and Raghavendra, Prasad and Roy, Aurko and Weitz, Benjamin and Zink, Daniel},
  title = {The Matching Problem Has No Small Symmetric SDP}
}
  6. Braun, G., Pokutta, S., and Zink, D. (2015). Inapproximability of Combinatorial Problems Via Small LPs and SDPs. Proceedings of the Annual Symposium on Theory of Computing, 107–116. DOI: 10.1145/2746539.2746550 [arXiv] [video]
    [BibTeX]
    @inproceedings{2014_BraunPokuttaZink_Affinereductions:1,
  year = {2015},
  booktitle = {Proceedings of the Annual Symposium on Theory of Computing},
  month = jun,
  pages = {107–116},
  doi = {10.1145/2746539.2746550},
  archiveprefix = {arXiv},
  eprint = {1410.8816},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian and Zink, Daniel},
  title = {Inapproximability of Combinatorial Problems Via Small LPs and SDPs},
  video = {https://youtu.be/MxLEticZ8RY}
}
  7. Braun, G., and Pokutta, S. (2015). The Matching Polytope Does Not Admit Fully-polynomial Size Relaxation Schemes. Proceedings of the Symposium on Discrete Algorithms, 837–846. DOI: 10.1137/1.9781611973730.57 [arXiv]
    [BibTeX]
    @inproceedings{2014_BraunPokutta_Matchingpolytope,
  year = {2015},
  booktitle = {Proceedings of the Symposium on Discrete Algorithms},
  pages = {837-846},
  doi = {10.1137/1.9781611973730.57},
  archiveprefix = {arXiv},
  eprint = {1403.6710},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {The Matching Polytope Does Not Admit Fully-polynomial Size Relaxation Schemes}
}
  8. Braun, G., Firorini, S., and Pokutta, S. (2014). Average Case Polyhedral Complexity of the Maximum Stable Set Problem. Proceedings of the Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 28, 515–530. DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.515 [URL] [arXiv]
    [BibTeX]
    @inproceedings{2013_BraunSamuelPokutta_Averagepolyhedralcomplexity:1,
  year = {2014},
  booktitle = {Proceedings of the Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques},
  month = sep,
  volume = {28},
  pages = {515–530},
  doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.515},
  url = {https://drops.dagstuhl.de/opus/volltexte/2014/4720},
  archiveprefix = {arXiv},
  eprint = {1311.4001},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Firorini, Samuel and Pokutta, Sebastian},
  title = {Average Case Polyhedral Complexity of the Maximum Stable Set Problem}
}
  9. Braun, G., Pokutta, S., and Xie, Y. (2014). Info-greedy Sequential Adaptive Compressed Sensing. Proceedings of the Allerton Conference on Communication, Control, and Computing (Allerton), 858–865. DOI: 10.1109/ALLERTON.2014.7028544 [arXiv]
    [BibTeX]
    @inproceedings{2014_BraunPokuttaYao_Infogreedycompressedsensing:1,
  year = {2014},
  booktitle = {Proceedings of the Allerton Conference on Communication, Control, and Computing (Allerton)},
  pages = {858–865},
  doi = {10.1109/ALLERTON.2014.7028544},
  archiveprefix = {arXiv},
  eprint = {1407.0731},
  primaryclass = {cs.IT},
  author = {Braun, Gábor and Pokutta, Sebastian and Xie, Yao},
  title = {Info-greedy Sequential Adaptive Compressed Sensing},
  date = {2014-07-02}
}
  10. Braun, G., and Pokutta, S. (2013). Common Information and Unique Disjointness. Proceedings of the IEEE Symposium on Foundations of Computer Science, 688–697. [URL]
    [BibTeX]
    @inproceedings{2016_BraunPokutta_CommoninformationDisjointness:1,
  year = {2013},
  booktitle = {Proceedings of the IEEE Symposium on Foundations of Computer Science},
  pages = {688–697},
  url = {https://eccc.weizmann.ac.il/report/2013/056},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Common Information and Unique Disjointness},
  date = {2013-04-05}
}
  11. Braun, G., and Pokutta, S. (2012). An Algebraic Approach to Symmetric Extended Formulations. Proceedings of the International Symposium on Combinatorial Optimization, 7422, 141–152. DOI: 10.1007/978-3-642-32147-4_14 [arXiv]
    [BibTeX]
    @inproceedings{2012_BraunPokutta_Algebraicsymmetricformulations,
  year = {2012},
  booktitle = {Proceedings of the International Symposium on Combinatorial Optimization},
  month = apr,
  volume = {7422},
  pages = {141–152},
  doi = {10.1007/978-3-642-32147-4_14},
  archiveprefix = {arXiv},
  eprint = {1206.6318},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {An Algebraic Approach to Symmetric Extended Formulations},
  date = {2012-06-27}
}
  12. Braun, G., Firorini, S., Pokutta, S., and Steurer, D. (2012). Approximation Limits of Linear Programs (beyond Hierarchies). Proceedings of the IEEE Symposium on Foundations of Computer Science, 480–489. DOI: 10.1109/FOCS.2012.10 [arXiv]
    [BibTeX]
    @inproceedings{2012_BraunSamuelPokuttaSteurer_Approximationlimits:1,
  year = {2012},
  booktitle = {Proceedings of the IEEE Symposium on Foundations of Computer Science},
  pages = {480–489},
  doi = {10.1109/FOCS.2012.10},
  archiveprefix = {arXiv},
  eprint = {1204.0957},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Firorini, Samuel and Pokutta, Sebastian and Steurer, David},
  title = {Approximation Limits of Linear Programs (beyond Hierarchies)},
  date = {2012-04-04}
}

Full articles

  1. Braun, G., Guzmán, C., and Pokutta, S. (2024). Corrections to “Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization Via Information Theory.” IEEE Transactions on Information Theory, 70, 5408–5409. DOI: 10.1109/TIT.2024.3357200
    [BibTeX]
    @article{2024_BraunGuzmanPokutta_Oraclecomplexity,
  year = {2024},
  journal = {IEEE Transactions on Information Theory},
  date = {2024-06-21},
  month = jul,
  volume = {70},
  pages = {5408-5409},
  doi = {10.1109/TIT.2024.3357200},
  author = {Braun, Gábor and Guzmán, Cristóbal and Pokutta, Sebastian},
  title = {Corrections to “Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization Via Information Theory”}
}
  2. Braun, G., Pokutta, S., and Zink, D. (2019). Affine Reductions for LPs and SDPs. Mathematical Programming, 173, 281–312. DOI: 10.1007/s10107-017-1221-9 [arXiv]
    [BibTeX]
    @article{2014_BraunPokuttaZink_Affinereductions,
  year = {2019},
  journal = {Mathematical Programming},
  volume = {173},
  pages = {281–312},
  doi = {10.1007/s10107-017-1221-9},
  archiveprefix = {arXiv},
  eprint = {1410.8816},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian and Zink, Daniel},
  title = {Affine Reductions for LPs and SDPs}
}
  3. Braun, G., Pokutta, S., and Zink, D. (2019). Lazifying Conditional Gradient Algorithms. The Journal of Machine Learning Research, 20(71), 1–42. [URL] [arXiv]
    [BibTeX]
    @article{2016_BraunPokuttaZink_Lazifyinggradientalgorithms,
  year = {2019},
  journal = {The Journal of Machine Learning Research},
  volume = {20},
  number = {71},
  pages = {1–42},
  url = {https://jmlr.org/papers/v20/18-114.html},
  archiveprefix = {arXiv},
  eprint = {1610.05120},
  primaryclass = {cs.DS},
  author = {Braun, Gábor and Pokutta, Sebastian and Zink, Daniel},
  title = {Lazifying Conditional Gradient Algorithms}
}
  4. Braun, G., Pokutta, S., and Roy, A. (2018). Strong Reductions for Extended Formulations. Mathematical Programming, 172, 591–620. DOI: 10.1007/s10107-018-1316-y [arXiv]
    [BibTeX]
    @article{2015_BraunPokuttaRoy_Strongreductions,
  year = {2018},
  journal = {Mathematical Programming},
  month = nov,
  volume = {172},
  pages = {591–620},
  doi = {10.1007/s10107-018-1316-y},
  archiveprefix = {arXiv},
  eprint = {1512.04932},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Pokutta, Sebastian and Roy, Aurko},
  title = {Strong Reductions for Extended Formulations}
}
  5. Braun, G., Brown-Cohen, J., Huq, A., Pokutta, S., Raghavendra, P., Roy, A., Weitz, B., and Zink, D. (2017). The Matching Problem Has No Small Symmetric SDP. Mathematical Programming, 165, 643–662. DOI: 10.1007/s10107-016-1098-z [arXiv]
    [BibTeX]
    @article{2015_BraunEtAl_MatchingproblemSdp,
  year = {2017},
  journal = {Mathematical Programming},
  month = oct,
  volume = {165},
  pages = {643–662},
  doi = {10.1007/s10107-016-1098-z},
  archiveprefix = {arXiv},
  eprint = {1504.00703},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Brown-Cohen, Jonah and Huq, Arefin and Pokutta, Sebastian and Raghavendra, Prasad and Roy, Aurko and Weitz, Benjamin and Zink, Daniel},
  title = {The Matching Problem Has No Small Symmetric SDP}
}
  6. Braun, G., Guzmán, C., and Pokutta, S. (2017). Unifying Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization. IEEE Transactions on Information Theory, 63(7), 4709–4724. DOI: 10.1109/TIT.2017.2701343 [arXiv]
    [BibTeX]
    @article{2014_BraunGuzmanPokutta_Lowerboundsoraclecomplexity,
  year = {2017},
  journal = {IEEE Transactions on Information Theory},
  month = jul,
  volume = {63},
  number = {7},
  pages = {4709-4724},
  doi = {10.1109/TIT.2017.2701343},
  archiveprefix = {arXiv},
  eprint = {1407.5144},
  primaryclass = {math.OC},
  author = {Braun, Gábor and Guzmán, Cristóbal and Pokutta, Sebastian},
  title = {Unifying Lower Bounds on the Oracle Complexity of Nonsmooth Convex Optimization}
}
  7. Braun, G., Jain, R., Lee, T., and Pokutta, S. (2017). Information-theoretic Approximations of the Nonnegative Rank. Computational Complexity, 26, 147–197. DOI: 10.1007/s00037-016-0125-z [URL]
    [BibTeX]
    @article{2017_BraunRahulTroyPokutta_Informationtheoreticnonnegativerank,
  year = {2017},
  journal = {Computational Complexity},
  volume = {26},
  pages = {147–197},
  doi = {10.1007/s00037-016-0125-z},
  url = {https://eccc.weizmann.ac.il/report/2013/158},
  author = {Braun, Gábor and Jain, Rahul and Lee, Troy and Pokutta, Sebastian},
  title = {Information-theoretic Approximations of the Nonnegative Rank}
}
  8. Braun, G., Firorini, S., and Pokutta, S. (2016). Average Case Polyhedral Complexity of the Maximum Stable Set Problem. Mathematical Programming, 160(1), 407–431. DOI: 10.1007/s10107-016-0989-3 [arXiv]
    [BibTeX]
    @article{2013_BraunSamuelPokutta_Averagepolyhedralcomplexity,
  year = {2016},
  journal = {Mathematical Programming},
  month = mar,
  volume = {160},
  number = {1},
  pages = {407–431},
  doi = {10.1007/s10107-016-0989-3},
  archiveprefix = {arXiv},
  eprint = {1311.4001},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Firorini, Samuel and Pokutta, Sebastian},
  title = {Average Case Polyhedral Complexity of the Maximum Stable Set Problem}
}
  9. Braun, G., and Pokutta, S. (2016). Common Information and Unique Disjointness. Algorithmica, 76(3), 597–629. DOI: 10.1007/s00453-016-0132-0 [URL]
    [BibTeX]
    @article{2016_BraunPokutta_CommoninformationDisjointness,
  year = {2016},
  journal = {Algorithmica},
  month = feb,
  volume = {76},
  number = {3},
  pages = {597–629},
  doi = {10.1007/s00453-016-0132-0},
  url = {https://eccc.weizmann.ac.il/report/2013/056},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Common Information and Unique Disjointness}
}
  10. Braun, G., and Pokutta, S. (2016). A Polyhedral Characterization of Border Bases. SIAM Journal on Discrete Mathematics, 30(1), 239–265. DOI: 10.1137/140977990 [arXiv]
    [BibTeX]
    @article{2009_BraunPokutta_BorderbasesOrderidealsPolyhedral,
  year = {2016},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {30},
  number = {1},
  pages = {239–265},
  doi = {10.1137/140977990},
  archiveprefix = {arXiv},
  eprint = {0912.1502},
  primaryclass = {math.AC},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {A Polyhedral Characterization of Border Bases}
}
  11. Braun, G., and Strüngmann, L. (2016). Examples of Non-dual Subgroups of the Baer–Specker Group. Houston Journal of Mathematics, 42(3), 723–739.
    [BibTeX]
    @article{2016_BraunStrngmann_Nondualsubgroups,
  year = {2016},
  journal = {Houston Journal of Mathematics},
  volume = {42},
  number = {3},
  pages = {723–739},
  author = {Braun, Gábor and Strüngmann, Lutz},
  title = {Examples of Non-dual Subgroups of the Baer–Specker Group}
}
  12. Braun, G., Firorini, S., Pokutta, S., and Steurer, D. (2015). Approximation Limits of Linear Programs (beyond Hierarchies). Mathematics of Operations Research, 40(3), 756–772. DOI: 10.1287/moor.2014.0694 [arXiv]
    [BibTeX]
    @article{2012_BraunSamuelPokuttaSteurer_Approximationlimits,
  year = {2015},
  journal = {Mathematics of Operations Research},
  month = aug,
  volume = {40},
  number = {3},
  pages = {756-772},
  doi = {10.1287/moor.2014.0694},
  archiveprefix = {arXiv},
  eprint = {1204.0957},
  primaryclass = {cs.CC},
  author = {Braun, Gábor and Firorini, Samuel and Pokutta, Sebastian and Steurer, David},
  title = {Approximation Limits of Linear Programs (beyond Hierarchies)}
}
  13. Braun, G., Pokutta, S., and Xie, Y. (2015). Info-greedy Sequential Adaptive Compressed Sensing. IEEE Journal of Selected Topics in Signal Processing, 9(4), 601–611. DOI: 10.1109/JSTSP.2015.2400428 [arXiv]
    [BibTeX]
    @article{2014_BraunPokuttaYao_Infogreedycompressedsensing,
  year = {2015},
  journal = {IEEE Journal of Selected Topics in Signal Processing},
  month = jun,
  volume = {9},
  number = {4},
  pages = {601–611},
  doi = {10.1109/JSTSP.2015.2400428},
  archiveprefix = {arXiv},
  eprint = {1407.0731},
  primaryclass = {cs.IT},
  author = {Braun, Gábor and Pokutta, Sebastian and Xie, Yao},
  title = {Info-greedy Sequential Adaptive Compressed Sensing}
}
  14. Braun, G., and Strüngmann, L. (2015). The Independence of the Notions of Hopfian and Co-Hopfian Abelian P-groups. Proeedings of the American Mathematical Society, 143, 3331–3341. DOI: 10.1090/proc/12413
    [BibTeX]
    @article{2015_BraunStrngmann_HopfianCohopfian,
  year = {2015},
  journal = {Proeedings of the American Mathematical Society},
  month = apr,
  volume = {143},
  pages = {3331-3341},
  doi = {10.1090/proc/12413},
  author = {Braun, Gábor and Strüngmann, Lutz},
  title = {The Independence of the Notions of Hopfian and Co-Hopfian Abelian P-groups}
}
  15. Braun, G., and Pokutta, S. (2014). A Short Proof for the Polyhedrality of the Chvátal-Gomory Closure of a Compact Convex Set. Operations Research Letters, 42(5), 307–310. DOI: 10.1016/j.orl.2014.05.004 [arXiv]
    [BibTeX]
    @article{2012_BraunPokutta_Chvtalgomoryclosure,
  year = {2014},
  journal = {Operations Research Letters},
  month = jul,
  volume = {42},
  number = {5},
  pages = {307–310},
  doi = {10.1016/j.orl.2014.05.004},
  archiveprefix = {arXiv},
  eprint = {1207.4884},
  primaryclass = {math.CO},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {A Short Proof for the Polyhedrality of the Chvátal-Gomory Closure of a Compact Convex Set}
}
  16. Braun, G., and Göbel, R. (2012). Splitting Kernels Into Small Summands. Israel Journal of Mathematics, 188, 221–230. DOI: 10.1007/s11856-011-0121-6
    [BibTeX]
    @article{2012_BraunGoebel_Splittingkernels,
  year = {2012},
  journal = {Israel Journal of Mathematics},
  month = mar,
  volume = {188},
  pages = {221–230},
  doi = {10.1007/s11856-011-0121-6},
  author = {Braun, Gábor and Göbel, Rüdiger},
  title = {Splitting Kernels Into Small Summands}
}
  17. Braun, G., and Pokutta, S. (2012). Rigid Abelian Groups and the Probabilistic Method. Contemporary Mathematcs, 576, 17–30. DOI: 10.1090/conm/576 [arXiv]
    [BibTeX]
    @article{2011_BraunPokutta_Rigidabeliangroups,
  year = {2012},
  journal = {Contemporary Mathematcs},
  volume = {576},
  pages = {17–30},
  doi = {10.1090/conm/576},
  archiveprefix = {arXiv},
  eprint = {1107.2325},
  primaryclass = {math.GR},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Rigid Abelian Groups and the Probabilistic Method}
}
  18. Braun, G., and Trlifaj, J. (2011). Strong Submodules of Almost Projective Modules. Pacific Journal of Mathematics, 254(1), 73–87.
    [BibTeX]
    @article{2011_BraunTrlifaj_Strongsubmodules,
  year = {2011},
  journal = {Pacific Journal of Mathematics},
  month = nov,
  volume = {254},
  number = {1},
  pages = {73–87},
  author = {Braun, Gábor and Trlifaj, Jan},
  title = {Strong Submodules of Almost Projective Modules}
}
  19. Braun, G., and Pokutta, S. (2011). Random Half-integral Polytopes. Operations Research Letters, 39(3), 204–207. DOI: 10.1016/j.orl.2011.03.003 [URL]
    [BibTeX]
    @article{2011_BraunPokutta_Randomhalfintegralpolytopes,
  year = {2011},
  journal = {Operations Research Letters},
  month = may,
  volume = {39},
  number = {3},
  pages = {204–207},
  doi = {10.1016/j.orl.2011.03.003},
  url = {https://optimization-online.org/2010/11/2813},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Random Half-integral Polytopes}
}
  20. Braun, G., and Strüngmann, L. (2011). Breaking Up Finite Automata Presentable Torsion-free Abelian Groups. International Journal of Algebra and Computation, 21, 1463–1472. DOI: 10.1142/S0218196711006625
    [BibTeX]
    @article{2011_BraunStrngmann_FiniteautomataTorsionfree,
  year = {2011},
  journal = {International Journal of Algebra and Computation},
  volume = {21},
  pages = {1463–1472},
  doi = {10.1142/S0218196711006625},
  author = {Braun, Gábor and Strüngmann, Lutz},
  title = {Breaking Up Finite Automata Presentable Torsion-free Abelian Groups}
}
  21. Braun, G., and Pokutta, S. (2010). Rank of Random Half-integral Polytopes. Electronic Notes in Discrete Mathematics, 36, 415–422. DOI: 10.1016/j.endm.2010.05.053 [URL]
    [BibTeX]
    @article{2011_BraunPokutta_Randomhalfintegralpolytopes:1,
  year = {2010},
  journal = {Electronic Notes in Discrete Mathematics},
  date = {2010-08-01},
  month = aug,
  volume = {36},
  pages = {415–422},
  doi = {10.1016/j.endm.2010.05.053},
  url = {https://optimization-online.org/2010/11/2813},
  author = {Braun, Gábor and Pokutta, Sebastian},
  title = {Rank of Random Half-integral Polytopes}
}
  22. Braun, G., and Némethi, A. (2010). Surgery Formulas for Seiberg–Witten Invariants of Negative Definite Plumbed 3-manifolds. Journal Für Die Reine Und Angewandte Mathematik, 638, 189–208. DOI: 10.1515/CRELLE.2010.007 [arXiv]
    [BibTeX]
    @article{2010_BraunNmethi_Surgeryseibergwitten,
  year = {2010},
  journal = {Journal für die reine und angewandte Mathematik},
  month = jan,
  number = {638},
  pages = {189–208},
  doi = {10.1515/CRELLE.2010.007},
  archiveprefix = {arXiv},
  eprint = {0704.3145},
  primaryclass = {math.GT},
  author = {Braun, Gábor and Némethi, András},
  title = {Surgery Formulas for Seiberg–Witten Invariants of Negative Definite Plumbed 3-manifolds}
}
  23. Braun, G. (2008). The Cobordism Class of the Multiple Points of Immersions. Algebraic & Geometric Topology, 8, 581–601. DOI: 10.2140/agt.2008.8.581 [URL] [arXiv]
    [BibTeX]
    @article{2008_Braun_Cobordismimmersions,
  year = {2008},
  journal = {Algebraic & Geometric Topology},
  month = may,
  number = {8},
  pages = {581–601},
  doi = {10.2140/agt.2008.8.581},
  url = {https://msp.warwick.ac.uk/agt/2008/08-01/p019.xhtml},
  archiveprefix = {arXiv},
  eprint = {math/0409574},
  primaryclass = {math.AT},
  author = {Braun, Gábor},
  title = {The Cobordism Class of the Multiple Points of Immersions}
}
  24. Braun, G., and Némethi, A. (2007). Invariants of Newton Non-degenerate Surface Singularities. Compositio Mathematica, 143, 1003–1036. [URL] [arXiv]
    [BibTeX]
    @article{2007_BraunNmethi_Newtonsingularities,
  year = {2007},
  journal = {Compositio Mathematica},
  number = {143},
  pages = {1003–1036},
  url = {https://journals.cambridge.org/action/displayAbstract?aid=1207944},
  archiveprefix = {arXiv},
  eprint = {math/0609093},
  primaryclass = {math.AG},
  author = {Braun, Gábor and Némethi, András},
  title = {Invariants of Newton Non-degenerate Surface Singularities}
}
  25. Braun, G., and Lippner, G. (2006). Characteristic Numbers of Multiple-point Manifolds. Bulletin of the London Mathematical Society, 38, 667–678. DOI: 10.1112/S0024609306018571
    [BibTeX]
    @article{2006_BraunLippner_Characteristicnumberscohomology,
  year = {2006},
  journal = {Bulletin of the London Mathematical Society},
  month = aug,
  number = {38},
  pages = {667–678},
  doi = {10.1112/S0024609306018571},
  author = {Braun, Gábor and Lippner, Gábor},
  title = {Characteristic Numbers of Multiple-point Manifolds}
}
  26. Blass, A., and Braun, G. (2005). Random Orders and Gambler’s Ruin. Electronic Journal of Combinatorics, 12(1), R23. [URL]
    [BibTeX]
    @article{2005_BlassBraun_Gamblerruins,
  year = {2005},
  journal = {Electronic Journal of Combinatorics},
  volume = {12},
  number = {1},
  pages = {R23},
  url = {https://combinatorics.org/Volume_12/Abstracts/v12i1r23.html},
  author = {Blass, Andreas and Braun, Gábor},
  title = {Random Orders and Gambler's Ruin}
}
  27. Braun, G., and Göbel, R. (2005). E-algebras Whose Torsion Part Is Not Cyclic. Proceedings of the American Mathematical Society, 133(8), 2251–2258 (electronic). [URL]
    [BibTeX]
    @article{2005_BraunGoebel_EalgebrasTorsion,
  year = {2005},
  journal = {Proceedings of the American Mathematical Society},
  volume = {133},
  number = {8},
  pages = {2251–2258 (electronic)},
  url = {https://ams.org/proc/2005-133-08/S0002-9939-05-07815-9/home.html},
  author = {Braun, Gábor and Göbel, Rüdiger},
  title = {E-algebras Whose Torsion Part Is Not Cyclic}
}
  28. Braun, G. (2005). Characterization of Matrix Types of Ultramatricial Algebras. New York Journal of Mathematics, 11, 21–33. [URL] [arXiv]
    [BibTeX]
    @article{2005_Braun_Matrixtypesultramatricial,
  year = {2005},
  journal = {New York Journal of Mathematics},
  volume = {11},
  pages = {21–33},
  url = {nyjm.albany.edu:8000/j/2005/11-2.html},
  archiveprefix = {arXiv},
  eprint = {math/0406302},
  primaryclass = {math.GR},
  author = {Braun, Gábor},
  title = {Characterization of Matrix Types of Ultramatricial Algebras}
}
  29. Braun, G. (2004). A Proof of Higgins’s Conjecture. Bulletin of the Australian Mathematical Society, 70(2), 207–212. [arXiv]
    [BibTeX]
    @article{2004_Braun_Higginsconjecture,
  year = {2004},
  journal = {Bulletin of the Australian Mathematical Society},
  volume = {70},
  number = {2},
  pages = {207–212},
  archiveprefix = {arXiv},
  eprint = {math/0312139},
  primaryclass = {math.GR},
  author = {Braun, Gábor},
  title = {A Proof of Higgins's Conjecture}
}
  30. Braun, G., and Göbel, R. (2003). Automorphism Groups of Nilpotent Groups. Archiv Der Mathematik, 80(5), 464–474. DOI: 10.1007/s00013-003-0802-4
    [BibTeX]
    @article{2003_BraunGoebel_Automorphismnilpotent,
  year = {2003},
  journal = {Archiv der Mathematik},
  volume = {80},
  number = {5},
  pages = {464–474},
  doi = {10.1007/s00013-003-0802-4},
  author = {Braun, Gábor and Göbel, Rüdiger},
  title = {Automorphism Groups of Nilpotent Groups}
}
  31. Braun, G., and Göbel, R. (2003). Outer Automorphisms of Locally Finite P-groups. Journal of Algebra, 264(1), 55–67.
    [BibTeX]
    @article{2003_BraunGoebel_OuterautomorphismsPgroups,
  year = {2003},
  journal = {Journal of Algebra},
  volume = {264},
  number = {1},
  pages = {55–67},
  author = {Braun, Gábor and Göbel, Rüdiger},
  title = {Outer Automorphisms of Locally Finite P-groups}
}

🔬 Projects

Research Campus MODAL SynLab

SynLab researches mathematical generalization of application-specific advances achieved in the Gas-, Rail– and MedLab of the research campus MODAL. The focus is on exact methods for solving a broad class of discrete-continuous optimization problems. This requires advanced techniques for structure recognition, consideration of nonlinear restrictions from practice, and the efficient implementation of mathematical algorithms on modern computer architectures. The results are bundled in a professional software package and complemented by a range of high-performance methods for specific applications with a high degree of innovation.

SynLab
Apr 2020 to Mar 2025
13
59

🌍 Research Stays and Visits

Sep 2018
Mannheim University of Applied Sciences hosted by Lutz Strüngmann

👨‍🏫 Teaching

spring 2017
Tutor for engineering optimization at GT
autumn 2015
Tutor for modern optimization techniques at GT
autumn 2014
Tutor for modern optimization techniques at GT
spring 2013
Tutor for automata theory at University of Leipzig
spring 2013
Advisor for automata theory seminar at University of Leipzig
spring 2013
Tutor for calculus at University of Leipzig
autumn 2012
Tutor for Automata Theory Seminar at University of Leipzig
autumn 2012
Tutor for calculus at University of Leipzig
autumn 2012
Tutor for automata theory at University of Leipzig
spring 2012
Tutor for computability theory at University of Leipzig
spring 2012
Tutor for automata theory seminar at University of Leipzig
spring 2012
Tutor for algebraic automata theory at University of Leipzig
autumn 2011
Tutor for automata theory at University of Leipzig