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====== Michael Gene Dobbins ======

mɑɪkəl dʒin dɑbɪnz

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I will be joining the [[http://www2.math.binghamton.edu|math department]] at Binghamton University in New York State in the autumn 2015. My primary research interests are discrete geometry, convexity, combinatorics, topology, and foundations. My preferred programming language is Haskell. Recently, I have been a post-doctoral researcher for [[http://gaia.postech.ac.kr|GAIA]] in South Korea where I have been working with [[http://otfried.org/index.html|Otfried Cheong]] and [[http://mathsci.kaist.ac.kr/~andreash/newpage/home.html|Andreas Holmsen]]. I received my PhD from [[https://math.temple.edu|Temple University]] in 2011. My advisor was [[https://math.temple.edu/~rivin|Igor Rivin]].

===== Contact =====

Email: dobbins(AT)postech.ac.kr\\ 

===== Publications =====


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Michael Gene Dobbins. A point in a nd-polytope is the barycenter of n points in its d-faces. Inventiones Mathematicae, to appear. [[http://doi.org/10.1007/s00222-014-0523-2|DOI]] [[http://arxiv.org/abs/1312.4411|arXiv]]

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Michael Gene Dobbins, Andreas Holmsen, and Alfredo Hubard. Regular systems of paths and families of convex sets in convex position. Transactions of the American Mathematical Society, to appear. [[http://arxiv.org/abs/1307.0909|arXiv]]

Michael Gene Dobbins. Realizability of polytopes as a low rank matrix completion problem. Discrete and Computational Geometry, 51(4): 761-778, 2014. [[http://doi.org/10.1007/s00454-014-9599-0|DOI]] [[http://arxiv.org/abs/1012.3905|arXiv]]

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Michael Gene Dobbins, Andreas Holmsen, and Alfredo Hubard. The Erdős-Szekeres problem for non-crossing convex sets. Mathematika, 60(2): 463-484, 2014 [[http://doi.org/10.1112/S0025579314000072|DOI]] [[http://arxiv.org/abs/1305.2266|arXiv]]

Luis Barba, Jean Lou De Carufel, Otfried Cheong, Michael Gene Dobbins, Rudolf Fleischer, Akitoshi Kawamura, Matias Korman, Yoshio Okamoto, János Pach, Yuan Tang, Takeshi Tokuyama, Sander Verdonschot, and Tianhao Wang. Weight balancing on boundaries and skeletons. In Proceedings of the 30th Symposium on Computational Geometry, Kyoto, Japan, 2014.

Michael Gene Dobbins, Heuna Kim. Packing segments in a convex 3-polytope is NP-hard. In Proceedings of the 30th European Workshop on Computational Geometry, Ein-Gedi, Israel, 2014.

===== Preprints =====

Michael Gene Dobbins. Antiprismless, or: reducing combinatorial equivalence to projective equivalence in realizability problems for polytopes. [[http://arxiv.org/abs/1307.0071|arXiv]]

Michael Gene Dobbins, Andreas Holmsen, and Alfredo Hubard. Realization spaces of arrangements of convex bodies. [[http://arxiv.org/abs/1412.0371|arXiv]]

Boris Aronov, Otfried Cheong, Michael Gene Dobbins, and Xavier Goaoc. The Number of holes in the union of translates of a convex set in three dimensions. [[http://arxiv.org/abs/1502.01779|arXiv]]