5 problems

Generic non-algebraicity conjecture for smooth Weierstrass cubics
Smooth Weierstrass cubic period-test conjecture. For a generic smooth real Weierstrass cubic, the compact oval is nonseparating and the exterior Cauchy transform of the domain boun…
openabelian-differentials cauchy-transforms elliptic-curves
0 responses
03
Multi-oval generic non-algebraicity conjecture for exterior Cauchy transforms
Multi-oval generic non-algebraicity conjecture. For a generic affine Euclidean realization, the exterior Cauchy transform of the domain bounded by any one of these ovals is non-alg…
openalgebraic-curves cauchy-transforms real-algebraic-geometry
0 responses
02
Separating/nonseparating algebraicity principle for exterior Cauchy transforms
Separating/nonseparating algebraicity principle. If $\gamma$ is separating, then the exterior Cauchy transform is algebraic. If $\gamma$ is nonseparating, then the exterior Cauchy…
openabelian-differentials algebraic-curves cauchy-transforms
0 responses
03
Dimension conjecture for quadratic motherbody equations
Dimension conjecture for quadratic motherbody equations. The set $\Omega_{P,Q}$ is a real semi-analytic variety of real dimension $n$ .
opencauchy-transforms measure-theory real-algebraic-geometry
0 responses
02
Balanced algebraic-function conjecture for positive motherbody measures
Balanced algebraic-function conjecture. Every such $P(\mathcal C,z)$ admits a positive motherbody measure.
openalgebraic-functions cauchy-transforms measure-theory
0 responses
02

5 problems

Generic non-algebraicity conjecture for smooth Weierstrass cubics

Multi-oval generic non-algebraicity conjecture for exterior Cauchy transforms

Separating/nonseparating algebraicity principle for exterior Cauchy transforms

Dimension conjecture for quadratic motherbody equations

Balanced algebraic-function conjecture for positive motherbody measures