A. Sheshmani

Counting higher-rank sheaves on toric threefolds

Nicolo Piazzalunga, Artan Sheshmani, Shing-Tung Yau

We develop an equivariant K-theoretic vertex formalism for a colored, abelianized higher-rank sector on smooth projective toric threefolds $X$ . Nonzero first Chern classes are enco…

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 $G$ -Higgs bu…

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 $g : Y \to X$ be a divisorial contraction betwe…

q-fin.PM2026

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…

math.OC2026

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…

math.OC2026

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…

Hodge rigidity of Chern classes

Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau

In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component…

Microlocal index theorems and analytic torsion invariants in the geometric theory of partial differential equations

Jacob Kryczka, Vladimir Rubtsov, Artan Sheshmani +1

We develop a microlocal and derived-geometric framework for index theory and analytic torsion of nonlinear PDEs. By integrating Spencer hypercohomology, microlocal sheaf theory, an…

Non-commutative crepant resolutions for (almost) simplicial toric algebras

Aimeric Malter, Artan Sheshmani

Given a rational convex polyhedral Gorenstein cone constructed as cone over a lattice polytope P, we establish that toric non-commutative crepant resolutions (NCCRs) of its associa…

Sheaf stable pairs on projective surfaces and birational geometry

Caucher Birkar, Jia Jia, Artan Sheshmani +1

We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth…

Tyurin Degenerations, Derived Lagrangians and Categorification of DT Invariants

Jacob Kryczka, Artan Sheshmani

We consider the moduli space of rigidified perfect complexes with support on a general complete intersection Calabi-Yau threefold $X$ and its Tyurin degeneration $X\rightsquigarrow…

Tropicalization of super Gromov-Witten invariants

Artan Sheshmani, Shing-Tung Yau, Benjamin Zhou

We show that genus-0, $n$ Neveu-Schwarz marked, super Gromov-Witten invariants of a convex, toric variety $X$ can be defined and computed using tropical geometry. When $X$ is a poi…

Towards non-commutative crepant resolutions of affine toric Gorenstein varieties

Aimeric Malter, Artan Sheshmani

In this paper we prove a common generalisation of results by Špenko-Van den Bergh and Iyama-Wemyss that can be used to generate non-commutative crepant resolutions (NCCRs) of some…

The $D$ -Geometric Hilbert Scheme -- Part I: Involutivity and Stability

Jacob Kryczka, Artan Sheshmani

We construct a moduli space of formally integrable and involutive ideal sheaves arising from systems of partial differential equations (PDEs) in the algebro-geometric setting, by i…

Geography of Landau-Ginzburg models and threefold syzygies

Yang He, Artan Sheshmani

We study the behavior of toric Landau-Ginzburg models under extremal contraction and minimal model program. We also establish a relation between the moduli space of toric Landau-Gi…

On the normality of commuting scheme for general linear Lie algebra

Artan Sheshmani, Xiaopeng Xia, Beihui Yuan

The commuting scheme $C_{g}^{d}$ for reductive Lie algebra $g$ over an algebraically closed field $K$ is the subscheme of $\mathfrak{g}^{d…

The $D$ -Geometric Hilbert Scheme -- Part II: Hilbert and Quot DG-Schemes

Jacob Kryczka, Artan Sheshmani

This is the second in a series of two papers developing a moduli-theoretic framework for differential ideal sheaves associated with formally integrable, involutive systems of algeb…

Multi-rigidity of Schubert classes in partial flag varieties

Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau

In this paper, we study the multi-rigidity problem in rational homogeneous spaces. A Schubert class is called multi-rigid if every multiple of it can only be represented by a union…

Relative Monoidal Bondal-Orlov

Artan Sheshmani, Angel Toledo

In this article we study a relative monoidal version of the Bondal-Orlov reconstruction theorem. We establish an uniqueness result for tensor triangulated category structures $(\bo…

Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism

Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau

This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement…

Sheaf stable pairs, Quot-schemes, and birational geometry

Caucher Birkar, Jia Jia, Artan Sheshmani

In this paper we build bridges between moduli theory of sheaf stable pairs on one hand and birational geometry on the other hand. We will in particular treat moduli of sheaf stable…

cond-mat.dis-nn2024

Renormalization Group flow, Optimal Transport and Diffusion-based Generative Model

Artan Sheshmani, Yi-Zhuang You, Baturalp Buyukates +2

Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can…