Pure and applied mathematics including algebra, analysis, geometry, and combinatorics.
Metric-compatible coarse corrections transfer gradients across manifolds, reducing iterations and CPU time on Kohn-Sham, Gross-Pitaevskii, and segmentation problems.
A BBGKY argument couples entropy and Fisher-information inequalities to extend Lacker’s chaos method to smooth mean-field diffusions.
A modal DG solver stores the Vlasov distribution in tensor-train form, reaching 10⁴-scale compression on weakly nonlinear benchmarks.
A Pareto-frontier analysis of GABD estimators identifies an extended $(\phi,\gamma)$ divergence that minimizes asymptotic variance at a chosen breakdown point.
Lifting frameworks to the hyperbolic plane turns surface rigidity into a finite gain-graph condition with a 2|V|-edge tightness rule.
A Sturm--Liouville chaos basis makes derivative information orthogonal, improving Sobol index estimation on toy and flood models with small designs.
A structural proof shows that every poset with a planar diagram has dimension at most 96 se(P) + 672.
Local trajectory contracts and safety envelopes let agents join or leave without central coordination, validated with up to eight race cars.
A degeneracy argument for $C(k,\ell)$-free Hamiltonian digraphs proves $\chi(D) \leq k+\ell-1$ for $k+\ell \geq 6$, matching lower-bound examples.
Post-processing Lagrangian dual certificates with sparsification and SDP searches cuts an FGM N=3 active set from 16 multipliers to 6.
