Research
Research
Research
Research
499+ open-access research outputs.
Computing edge-connected components in directed and undirected graphs is a fundamental and well-studied problem in graph algorithms. In a very recent breakthrough, Korhonen [STOC 2025] showed that for…
In this work, we investigate the well-posedness of a stochastic heat equation with an arbitrary (but polynomial) nonlinearity in any dimension $d\geq 1$ perturbed by a multiplicative white noise in th…
We study the three-dimensional stochastic electron magnetohydrodynamics (EMHD) system with fractional dissipation on the torus, driven by Stratonovich transport noise acting through divergence-free fi…
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the …
In dynamical systems, invariants, i.e., constants of motion conserved along the trajectory, play important roles in characterizing the system's dynamical behavior. Recent applications of the Koopman o…
We establish existence of probabilistically strong solutions and pathwise uniqueness for a class of quasilinear stochastic evolution equations on bounded domains. Our results combine recent weak exist…
Recently Watanabe has given an algorithm to compute a bijection, that he calls (quantum) Littlewood-Richardson (LR) map (or quantum LR rule of type AII), between semi-standard Young tableaux of shape …
Motivated by an open question going back to P.Malliavin and P.-A.Meyer (and closely related to the foundational work of S.Watanabe) on whether Malliavin-Watanabe-Sobolev regularity admits a characteri…
The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand can be regarded as a multivalued function on an elliptic curve. In this paper, we stud…
In this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations among these series a…
We compute the rational homotopy groups of the classifying space $\mathrm{BDiff}_{\partial}(S^1 \times D^{d-1})$ of the topological group of diffeomorphisms of $S^1 \times D^{d-1}$ fixing the boundary…
Motivated by Osserman's problem on the number $D_g$ of omitted values of the Gauss map of a complete minimal surface with finite total curvature in $\boldsymbol{R}^3$, its totally ramified value n…
In this paper we extend existing results on the numerical approximation of one-dimensional SDEs with drift in a negative order Besov space and driven by Brownian motion. Using the Yamada-Watanabe appr…
In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-tra…
The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally s…
We present a unified operator-theoretic framework for stochastic calculus based on the factorization (Id - E)F = {\delta}_X {\Pi}_X D_X F, valid for F_T^X-measurable F in L^2({\Omega}) when the drivin…
In 2005, Watanabe and Yoshida formulated a conjecture for a lower bound of the Hilbert-Kunz multiplicity of local rings that was recently settled by Meng using analytic methods. More recently, Pak-Sha…
We study a twice-differentiable transformation applied to a CKLS-type short-rate model with linear drift and power-type diffusion. The transformation yields a new process whose diffusion component has…
We prove formally that the momentum-mixing Hatsugai-Kohmoto model (MMHK) is the Hubbard model with a twist. With this result in tow, we rely on the proof of Watanabe's that two models which differ by …
Watanabe's singular learning theory provides a framework for asymptotic analysis of Bayesian model selection for statistical models with singularities, where traditional statistical regularity assumpt…
Free open-access publishing with Google Scholar indexing.
Submission Guide →