Jesus De Loera
University of California-Davis, CA·Mathematics & Statistics
Polytopes are many-sided geometric shapes, such as cubes and pyramids, extended to any number of dimensions. Polyhedra are their unbounded cousins.
- Fields
Mathematics & Statistics
Computer Science
- Topics
polytopes
polyhedra
combinatorics
- Grants
- 2 known grants, through Jul 2028
What they work on
- Study slices and shadows of polytopes, meaning their cross-sections and projections, using enumerative and extremal combinatorics with computer-aided experimentation.
- Develop a weighted, colored Ehrhart theory for counting lattice points, points with whole-number coordinates, inside polytopes.
- Investigate Baues complexes and constructions such as fiber polytopes, floating bodies and illumination bodies using geometric-topological combinatorics.
- Generate diverse, high-quality polyhedral samples with AI diffusion methods and reinforcement learning to support data-driven discovery of conjectures.
- Build Polyhedral-GPT, a large language model with a polyhedral transformer, and pair it with formal verification and SAT solvers to move from conjecture to checked proof.
More about the research
They are central to combinatorics, geometry and optimization. Fast computing with polytopes, for example, helps schedule airline crews and route planes. Yet some of the most basic questions about them remain open. This research attacks those questions directly. It also builds artificial intelligence (AI) tools that help mathematicians explore polytopes, form conjectures and check proofs.
Why it matters
Polytopes underlie optimization problems such as airline crew scheduling and plane routing. New results and software could help mathematicians and theoretical computer scientists who work with them. AI tools for generating examples, proposing conjectures and verifying proofs could speed mathematical discovery and show how AI can support rigorous reasoning.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Xiaoyu Huang
Temple University, PA·Mathematics & Statistics
Generate and curate large public datasets of number-theoretic and combinatorial objects, including a database of noncongruence modular forms for studying their arithmetic properties.
Alexander Diaz-Lopez
Villanova University, PA·Mathematics & Statistics
Describe the structure coefficients of the peak algebra, the numbers governing how its elements multiply, to better understand permutations grouped by their peak sets.
Swarat Chaudhuri
University of Texas at Austin, TX·Computer Science
Develop foundation model programming, which writes scientific hypotheses as programs combining symbolic rules with neural modules and foundation models, to extract interpretable concepts from images and video.
The school
University of California-Davis: 49 labs on PI Pages, $1.0B a year on research, 647 research doctorates a year.
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