Mathematics Research
Convex Analysis at Infinity: A Generalized Differentiation Framework
This paper introduces a generalized differentiation theory at infinity specifically for convex sets and functions. It extends fundamental convex analysis concepts—tangent cones, normal cones, and subdifferentials—into the context of infinity, maintaining convexity and linking with recession analysis…
Bridging Exceptional Orthogonal Polynomials and Quasi-Orthogonality via Degree-Skipping Constructions
Bailey and Gavrilov construct monic orthogonal polynomial sequences that omit exactly one degree using linear combinations of classical polynomial families (e.g., Hermite, Laguerre, Jacobi), extending the conceptual framework of Exceptional Orthogonal Polynomials (XOPs). The core result establishes …
A Sporadic srg(120,56,28,24) Finally Explained via Ovoids, Spreads, and Overlarge Steiner Systems
Of the three non-isomorphic strongly regular graphs with parameters (120,56,28,24) whose automorphism groups act primitively on vertices, two belong to well-known classical families, but the third has remained poorly understood. Adriaensen et al. resolve this gap by constructing the sporadic graph f…
Infinitely Many High-Dimensional Hyperbolic Groups with Exotic Finiteness Properties Constructed via Right-Angled Coxeter Subgroups
Italiano, Migliorini, and Ng construct, for every cohomological dimension d ≥ 3, infinitely many quasi-isometry classes of hyperbolic groups that algebraically fibre with finitely presented kernel. The groups are realized as finite-index subgroups of right-angled Coxeter groups, and their L²-Betti n…
Spectral Analysis Yields Global Well-Posedness for Coupled Navier–Stokes–Biot Systems with Poro-Viscoelastic Media
Binz, Hieber, and Roy establish strong global well-posedness for a 3D fluid–poro-viscoelastic interaction system coupling incompressible viscous flow (Navier–Stokes) with a poro-viscoelastic medium (Biot) via Beavers–Joseph–Saffman interface conditions. The proof strategy is spectral-analytic rather…
Closed-Form Lower Expectations Under TV Distance and Chi-Squared Divergence Uncertainty Sets
De Bock (2026) derives closed-form expressions for lower expectations over uncertainty sets defined by total variation (TV) distance and chi-squared divergence balls around a probability mass function on a finite set. These results belong to the imprecise probability / robust Bayesian framework, whe…
First Explicit Multi-Monopole Constructions on Non-Product 3-Manifolds via Adiabatic Limit Theorem
The multi-spinor generalization of the Seiberg-Witten equations on 3-manifolds — known as multi-monopoles — fails to yield a topological invariant because solution counts jump discontinuously across parameter-space boundaries called chambers (wall-crossing). Existing constructions were too limited t…
Yudovich Theory Extended to Heterogeneous Euler-Type Systems via Micropolar Fluid Reduction
This paper establishes global well-posedness at low regularity for a 2D reduced micropolar fluid model with zero viscosity, coupling an Euler-type equation for velocity with an advection-diffusion equation for a scalar microrotation field. The authors prove global existence and uniqueness of Yudovic…
Morel-Voevodsky Localization Extended to Complex Analytic Stacks, Enabling a Full 6-Functor Motivic Formalism
Roy Magen proves the analog of the Morel-Voevodsky localization theorem in the setting of complex analytic stacks, a foundational result previously established only in algebraic geometry. This localization theorem serves as a key ingredient for the 6-functor formalism of complex analytic motivic hom…
Biharmonic Subdivision for Manifold Data Interpolation
This paper introduces a biharmonic interpolatory subdivision framework to enhance data fairness and smoothness on Riemannian manifolds. It extends the six-point Deslauriers-Dubuc stencil from the Euclidean setting to constant-curvature surfaces, establishing fourth-order smoothness. The methodology …
Profinite Completion Equivalence for Aspherical Manifolds
This paper demonstrates that smooth, closed, connected aspherical manifolds with "good" fundamental groups are cobordant and have congruent signatures modulo 8 if their profinite completions are isomorphic. Additionally, the spin structure is preserved under this isomorphism. The findings extend to …