Research
Research
Research
Research
3,401+ open-access research outputs.
We develop a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly i…
We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sh…
Let $\mathcal M_{r,c}$ denote the moduli space of stable bundles with rank $r$ and second Chern class $c>0$ on a Hopf surface. We prove that the subset of $\mathcal M_{r,c}$ formed by irregular bundle…
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in Euclidean space and …
Gorenstein toric contact manifolds are good toric contact manifolds with zero first Chern class that are completely determined by certain integral convex polytopes called toric diagrams. The Ehrhart p…
We establish a general result ensuring a $C^1$ a priori bound for smooth curves of Hermitian metrics. As a main application, we obtain a new regularity result for Hermitian curvature flows, and in par…
In this paper, we advance the classification of toric 2-Fano manifolds by continuing the investigation of the minimal projective bundle dimension $m(X) \in \{1,\dots,\dim(X)\}$ introduced in our previ…
Understanding the evolution of connectivity in spatiotemporal systems requires mathematical frameworks capable of encoding not only instantaneous interactions but also their cumulative causal structur…
We define and study the rational analytic syntomification $X^{\mathrm{Syn}}$ of a partially proper rigid-analytic variety $X$ over $\mathbb{Q}_p$. We establish Poincar\'e duality and a theory of first…
We study the singular central fibre arising in the Donaldson-Friedman construction for twistor spaces of connected sums, viewing it as a Ferrand pushout of two blown-up twistor spaces along the except…
We develop methods for constructing and computing conformal invariants of submanifolds, with a particular emphasis on conformal submanifold scalars and conformally invariant integrals of natural subma…
We study the hydrodynamic limit of the Chern--Simons--Higgs system, a relativistic gauge field model involving the Chern--Simons interaction. We introduce a single scaling parameter capturing both the…
Let $(M,g,J,\omega)$ be an almost K\"{a}hler manifold. For any smooth function $f$ on $M$, one can associate an automorphism $\psi\in \mbox{Aut}(TM)$ for which the K\"{a}hler form is invariant. Using …
We establish uniform diameter estimates and volume non-collapsing estimates for the Chern-Ricci flow on smooth Hermitian minimal models of general type, assuming the initial metric is K\"ahler in a ne…
We show that every Vaisman manifold with high first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold. Furthermore, its complex structure is left-invar…
We classify extended Abelian Chern-Simons theories with gauge group $U(1)^n$ as extended $(2+1)$-dimensional topological quantum field theories. For an even integral nondegenerate lattice $(\Lambda,K)…
In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem for Higgs bundles over compact complex manifolds. Let $ (E,\theta) $ be a Higgs bundle over a compact Hermitian manifold $(M,…
We compute all the Chern, Milnor and Pontryagin numbers for canonical toric manifolds associated with abstract simplicial complexes and the Stiefel-Whitney numbers for their real counterparts. Applica…
We prove a natural isomorphism between toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/\Lambda\cong U(1)^n$ and the Reshetikhin-Turaev theory associated with the finite quadratic mod…
For a half-unknotted implanted barbell $\beta$, we construct two specific pseudo-isotopies, both resulting in that barbell diffeomorphism, and compute the Hatcher-Wagoner invariants for both. We furth…
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