He is an expert in the field of Computational Discrete Mathematics, but his research encompasses a diverse set of topics including his work in (pure) Convex and Discrete Geometry, Algebraic Combinatorics, and Combinatorial Commutative Algebra, as well as his (applied) work in Combinatorial Optimization, Algorithms and Data Science. In addition to more than 100 published research papers, he has co-written two graduate level textbooks: `` Triangulations: Structures for Algorithms and Applications'' (Springer, with J. Rambau and F. Santos) and `` Algebraic and Geometric Ideas in the Theory of Discrete Optimization'' (SIAM, with R. Hemmecke and M. Koeppe). The first being a treatise about combinatorics of triangulations of polytopes and the second an introduction to the state of the art in algebraic-geometric algorithms in optimization.
In general, he enjoys rethinking Mathematics in terms of algorithmic questions and understanding how computers can be ``taught'' to discover or prove theorems (e.g., automatically produce rational generating functions from geometric counting questions). He approaches difficult computational problems using tools from Algebra, Combinatorics, and Convex Geometry, and Topology. He believes in the exciting future of interdisciplinary work. Some of his favorite mathematical objects are polytopes, which are multidimensional generalizations of polygons and cubes (some pretty ones seen in the pictures above).
His research has been recognized in several ways: He was awarded an Alexander von Humboldt Fellowship in 2004, the 2010 INFORMS computer society prize, a 2013 John von Neumann professorship at the Technical University of Munich, and in 2020 he won the Farkas Prize of the INFORMS optimization society. De Loera is both a fellow of the American Mathematical Society (AMS 2014) and a fellow of the Society of Industrial and Applied Mathematics (SIAM 2019).
De Loera has been plenary or semi-plenary speaker at many major scientific conferences including, the Joint Math Meetings, SIAM annual meeting, the National Mathematics Festival, MAA Mathfest, AMS and MAA regional meetings, COMBINATEXAS, CANADAM, FPSAC and MOPTA. He has presented more than 100 invited scientific colloquia in well-known academic institutions such as MIT, Caltech, Oxford Univ., UC Berkeley, UCLA, Cambridge Univ.,TU Munchen, MAA Carriage House, Claremont-McKenna College, IBM, and Courant Institute NYU. He has also given more than 100 seminars at academic departments around the world. He has received many national and international grants to support his work, including from NSF, NSA, CONACYT, and IBM.
He is an associate editor of the journals ``SIAM Journal of Discrete Mathematics'' and the ``Boletin de la Sociedad Matematica Mexicana'' and a former editor of ``SIAM journal of Applied Algebra and Geometry'' and ``Discrete Optimization''. He has also served the mathematics community as member of the scientific program of IPCO, LATIN and SOCG. He has also served in many committees and organizer of dozen of mathematical conferences, workshops and many event with an emphasis in promoting mathematics for underserved communities. E.g, recently he served in the AMS committee of Education, as well as Vice-Chair of the UC Davis Mathematics Department and Faculty Assistant to the Dean of Mathematical and Physical Sciences in undergraduate matters. He was elected to the AMS executive council in 2015 and has coorganized over 30 workshops and events, from many small regional meetings (e.g. AMS meetings) to two large semester-long MSRI programs ``Discrete and Computational Geometry'' (2003) and ``Geometric and Topological Combinatorics (2017). He is currently in the Scientific board of AIM and served in the scientific board of ICERM.
For his dedication to outstanding mentoring and teaching he received the 2003 UC Davis Chancellor's fellow award, the 2006 UC Davis award for diversity, the 2007 Award for excellence in Service to Graduate students by the UC Davis graduate student association, the 2013 Chancellor's award for mentoring undergraduate research. In 2017, the Mathematical Association of America Golden Section Award and in 2018 he won the UC Davis College of Letters and Science Distinguished Teaching Award. He has successfully supervised fifteen Ph.D students, eight postdoctoral scholars, and over 60 undergraduates doing research projects. He is very proud of all the hundreds of successful students who have shared mathematics with him over the years. He is grateful to them for teaching him so much.