Test polynomials, retracts, and the Jacobian conjecture
Testing log K-stability by blowing up formalism
Testing S-duality conjecture and exceptional bundles
The $m-$dissimilarity map and representation theory of $SL_m$
The $p$-rank of the reduction $\rm{mod}\, p$ of jacobians and Jacobi sums
The $S^1$ fixed points in Quot-schemes and mirror principle computations
The $\ell$-adic Dualizing Complex on an Excellent Surface with Rational Singularities
The $ξ$-stability on the affine grassmannian
The $τ$-invariant and elimination
The 'corrected Durfee's inequality' for homogeneous complete intersections
The (-1) twist
The (local) lifting problem for curves
The (unexpected) importance of knowing $α$
The 0-th stable A^1-homotopy sheaf and quadratic zero cycles
The 2-dimensional jacobian conjecture via Klein's program
The 2-Factoriality of the O'Grady Moduli Spaces
The 3-cuspidal quartic and braid monodromy of degree 4 coverings
The 3-fold vertex via stable pairs
The 5-canonical system on 3-folds of general type
The A-infinity algebra of an Elliptic Curve and the j-invariant