Research
Research
Research
Research
2,866+ open-access research outputs.
We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete $\mathbb{G}_m$-variety with finite fixed locus. Our results include novel characterizations of when the Bialy…
We define a torus $U \subset T = (\mathbb{C}^\times)^K$ which acts on the $\Delta$-Springer varieties $Y_{n,\lambda,s}$ defined by Griffin-Levinson-Woo and give a Borel-style presentation for the equi…
Let $P\subset\mathbb R^n$ be a convex polytope and let $\ell$ be a linear functional which is nonconstant on every edge of $P$. The induced acyclic orientation determines positive and negative Bia{\l}…
We compute a presentation for the integral Chow rings of the moduli stacks of degree $2$ maps from smooth rational curves to projective space $\mathbb{P}^r$, as a quotient of a three-variable polynomi…
We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems…
We study the polynomial coefficients of lightning self-attention as coordinates of an algebraic variety. We identify linear and nonlinear families of algebraic invariants, including Chow-type, low-ran…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are…
Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic $K$-theory, and Levine--Morel's algebraic cobordism are all instances of…
We prove a lower bound on the Calabi functional for degenerations of polarized varieties, involving the difference of CM degrees between generically isomorphic families. This may be viewed as a discre…
We show for $\kappa \in (4,8)$ that the canonical conformally covariant measure on the conformal loop ensemble (CLE$_\kappa$) gasket, previously constructed indirectly by the first co-author and Schou…
We consider the Dirichlet problem for the complex Monge--Amp\`ere equation on strongly pseudoconvex K\"ahler manifolds when the right-hand side is decreasing in the solution. Using flow-based argument…
We present a conjecture for the Chow ring of the universal moduli stack of bundles over hyperelliptic curves and prove it for rank and genus two. Consequently, we obtain explicit generators and relati…
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…
Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P…
We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity t…
We develop dual approaches for continuous-time stochastic control problems, enabling the computation of robust dual bounds in high-dimensional state and control spaces. Building on the dual formulatio…
We prove that every ordinal $\alpha<\omega_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive…
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the s…
Well-known conjectures of Charney--Davis, Gal, and Nevo--Petersen predict increasingly strong positivity phenomena for the h-vectors of flag simplicial spheres. In this paper, we formulate and prove m…
In this paper we initiate the study of higher Chow cycles on holomorphic symplectic manifolds. Our concrete central result is construction of explicit indecomposable (2,1)- and (4,1)-cycles on the Fan…
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