

2009  2013  PhD, Statistics, University of California, Berkeley, CA, USA  2013  2015  Simons Postdoctoral Fellow, Mathematics, University of Texas, Austin, TX, USA  Since 2015  Professor (W2, Bonn Junior Fellow), Mathematics, University of Bonn  Since 2015  Assistant Professor, Mathematics, University of Texas, Austin, TX, USA (on leave) 


I use tools from tropical geometry and probability to create novel applications of mathematics in economics, neuroscience and other sciences. I love revisiting old problems with new geometric insights. In the immediate future, I have three main research themes: applications of tropical geometry in economics, combinatorial stochastic processes, and applications of discrete mathematics in neuroscience.
0.1. Applications of Tropical Geometry: Tropical geometry connects algebraic geometry, combinatorics and optimization theory. I use it to tackle optimization problems from a new geometric perspective. In the past I have worked on pairwise ranking problems [1,2]. This motivates the classification of tropical eigenspaces [3], commuting matrices [4], culminating in [5], where I used techniques from commutative algebra to explicitly classify polytropes in dimension 3 and 4. Recently, this tool again proves valuable in other areas of economics, namely, auction theory [6] and mechanism design [7]. I am working on extensions of the results in [7] to Bayesian mechanisms and multiplayer settings, as well as related problems on tropical polynomials.
0.2. Random tropical polynomials and partitions. In [8], with Francois Baccelli, I proved a point process approximation for zeros of a random tropical polynomial with i.i.d coefficients. We obtain simpler proofs of past results on vertices of random polytopes in , which are special cases of our setup. The higher dimension generalization of this work is particularly interesting. In particular, the power of our proof in [8] lies in a newly discovered connection between combinatorial stochastic processes (CSP) and random polytopes in , and is closely related to my work with Jim Pitman on sizebiased permutations [9]. I am working on various extensions of this work [10], with applications in Bayesian clustering.
0.3. Discrete mathematics and neuroscience. In mathematical neuroscience, I use techniques from discrete mathematics to answer longstanding open questions in theoretical neuroscience, to provide theorems and algorithms for current analysis, and to inspire new developments in mathematics. Currently I have three separate projects with collaborators and master students: decoding grid cells by solving maxclique, classification of the disease Lupus using exchangeable random graph theory, and testing hypothesis on pairwise correlation in population code using lattice point enumeration algorithms.


[ 1] Ngoc Mai Tran
Pairwise ranking: choice of method can produce arbitrarily different rank order Linear Algebra Appl. , 438: (3): 10121024 2013 ISSN: 00243795 DOI: 10.1016/j.laa.2012.08.028[ 2] Ngoc Mai Tran
HodgeRank is the limit of Perron rank Math. Oper. Res. , 41: (2): 643647 2016 ISSN: 0364765X DOI: 10.1287/moor.2015.0744[ 3] Bernd Sturmfels, Ngoc Mai Tran
Combinatorial types of tropical eigenvectors Bull. Lond. Math. Soc. , 45: (1): 2736 2013 ISSN: 00246093 DOI: 10.1112/blms/bds058[ 5] Ngoc Mai Tran
Enumerating Polytropes arXiv preprint arXiv:1310.2012 2013[6] Ngoc Mai Tran, Josephine Yu
ProductMix Auctions and Tropical Geometry arXiv preprint arXiv:1505.05737 2015 [7] Robert Alexander Crowell, Ngoc Mai Tran
Tropical geometry and mechanism design arXiv preprint arXiv:1606.04880 2016 [8] Francois Baccelli, Ngoc Mai Tran
Zeros of random tropical polynomials, random polygons and stickbreaking Trans. Amer. Math. Soc. , 368: (10): 72817303 2016 ISSN: 00029947 DOI: 10.1090/tran/6565 [ 9] Jim Pitman, Ngoc M. Tran
Sizebiased permutation of a finite sequence with independent and identically distributed terms Bernoulli , 21: (4): 24842512 2015 ISSN: 13507265 DOI: 10.3150/14BEJ652[ 10] Francois Baccelli, Ngoc M. Tran
Iterated Gilbert Mosaics and Poisson Tropical Plane Curves arXiv preprint arXiv:1610.08533 2016[11] Ralph Morrison, Ngoc M. Tran
The tropical commuting variety Linear Algebra Appl. , 507: : 300321 2016 ISSN: 00243795 DOI: 10.1016/j.laa.2016.05.039



2001  Gold Medal U13, Hanoi Chess Competition  2004  Premier’s Award for Allround Excellence, NSW, Australia  2006  Margaret Pitcher Prize in Mathematics, University of Newcastle, NSW, Australia  2006  Summer Scholar, Australian National University, Canberra, ACT, Australia  2006  Head of College, International House, University of Newcastle, NSW, Australia  2007  SAS Institute Prize in Statistics, University of Newcastle, NSW, Australia  2007  Dean’s List, University of Newcastle, NSW, Australia  2009  2015  Fellow, Vietnam Education Foundation  2013  2015  Postdoctoral Fellow, Simons Foundation  Since 2015  Bonn Junior Fellow, Hausdorff Center for Mathematics, Bonn 


2012  Tropical Mathematics and its Applications, Birmingham, England, UK  2012  Workshop for Women in Probability, Duke University, Durham, NC, USA  2013  Workshop on Mathematics of Partially Identified Objects, Oberwolfach  2014  Seminar on Stochastic Processes, San Diego, CA, USA  2014  Plenary Talk, CombinaTexas, Houston, TX, USA  2014  Conference on Algebraic Geometry and Optimization, Korea  2014  Workshop on Mathematics and Economics, Hokkaido, Japan  2015  Session on Probability and Applications, AMS Joint Meeting, San Antonio, TX, USA  2015  Session on Graph Theory, Combinatorics and Discrete Geometry, AMS Joint Meeting, San Antonio, TX, USA  2015  Computational and Systems Neuroscience (Cosyne), Salt Lake City, UT, USA  2015  Workshop on Nonlinear Algebra, Berlin  2015  Workshop on Algebraic and Stochastic Aspects in Graph Theory, Osnabrück  2016  Spring School on Combinatorial Stochastic Processes, Hanoi, Vietnam 


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