17 papers
On the image of Hitchin morphism for some classical groups on algebraic surfaces
Artan Sheshmani, Jianping Wang, Xiaopeng Xia
In this article, we study the image of the Hitchin morphism for some classical groups over an algebraic surface. The Hitchin morphism is a map from the moduli stack of -Higgs bu…
Derived Moduli Spaces of Nonlinear PDEs: Singular Propagations
Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau
We construct a sheaf theoretic and derived geometric machinery to study nonlinear partial differential equations and their singular supports. We establish a notion of derived micro…
Toric Landau-Ginzburg models in threefold divisorial contractions
Yang He, Artan Sheshmani
We investigate quantum periods and toric Landau-Ginzburg models under divisorial contractions of terminal Fano threefolds. Let be a divisorial contraction betwe…
Yau's Affine-Normal Descent for Large-Scale Unrestricted Higher-Moment Portfolio Optimization
Ya-Juan Wang, Yi-Shuai Niu, Artan Sheshmani +1
Unrestricted mean-variance-skewness-kurtosis portfolio optimization can capture asymmetry and tail risk, but sample-moment formulations become computationally impractical when the…
Yau's Affine Normal Descent: Algorithmic Framework and Convergence Analysis
Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau
We propose Yau's Affine Normal Descent (YAND), a geometric framework for smooth unconstrained optimization in which search directions are defined by the equi-affine normal of level…
Affine Normal Directions via Log-Determinant Geometry: Scalable Computation under Sparse Polynomial Structure
Yi-Shuai Niu, Artan Sheshmani, Shing-Tung Yau
Affine normal directions provide intrinsic affine-invariant descent directions derived from the geometry of level sets. Their practical use, however, has long been hindered by the…