Research archive

Preprint · Combinatorial group theory

A global girth obstruction for Garg–Mineyev taiko product structures

A global obstruction to the Garg–Mineyev triple-girth route to zero-divisor and unit counterexamples in group rings over F₂, proved through incidence geometry.

Preprint · Additive combinatorics

Iterated-sumset spectra: The complete exponent law and its rank geometry

Determines the growth exponent of the number of possible h-fold sumset sizes for fixed-size integer sets, together with sharp bounds for integer models preserving finite additive relations. Also proves the formula conjectured in OEIS A227589 for minimal labelings of identical four-sided dice that maximize the number of distinct sums.

Published

Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Bennett Chow, Michael Freedman, Henry Shin, Yongjia Zhang

Advances in Mathematics 372 (2020), 107303

Curvature estimates for four-dimensional gradient Ricci soliton singularity models, using geometric analysis and topological arguments.

Preprint · Algebraic combinatorics

Exchange identities and symmetric slices of the valley Delta conjecture

Exchange identities and symmetry for the area-zero and area-one slices of the valley Delta generating function.

Preprint · Extremal combinatorics

One extra edge forces Berge pancyclicity

Berge cycles of every length from a Hamiltonian Berge cycle and one additional edge, in the stated large-order uniformity regime.

Preprint · Algebra · Arithmetic geometry

Hilbert-90 quotient maps, torsion defects, and symmetric monodromy

Rational maps from Hilbert-90 descent: cancellation, torsion, and characteristic-zero monodromy.

Preprint · Number theory · Algebraic geometry

Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori

Trace distributions on cosets in cubic norm-one tori, including singular fibers and local branch geometry.

Preprint · Arithmetic geometry

Logarithmic source curves in polynomial fiber products

Geometry at infinity of polynomial fiber products, rational lifts, and their arithmetic counting behavior.

Preprint · Geometric analysis

Open full-metric formation and local marked first-order asymptotic moduli of FIK blowdown singularities

Formation of FIK singularities under Ricci flow and the local parameters governing their first-order asymptotic behavior.

Preprint · Analysis · Partial differential equations

From rough local mass to logarithmic spectral ladders for damped waves

Local damping mass, resolvent bounds, and decay, including spectral asymptotics near logarithmic damping wells.