Research
Research
Research
Research
243+ open-access research outputs.
Solutions to the Schr\"{o}dinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the d…
This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning …
The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another b…
For the double of a quiver, the works of Ginzburg, Bocklandt-Le Bruyn and Schedler show that its closed paths, called the necklaces, have a natural Lie bialgebra structure. Schedler also constructed,i…
We prove the weak relative Kawamata-Morrison movable cone conjecture for K-trivial fibrations whose very general fibre is a quotient, by a finite group of automorphisms acting freely in codimension on…
We show that the It\^o solutions of the nonlinear stochastic heat equation $$ \partial_t u^\varepsilon- \Delta u^\varepsilon =\varepsilon^{3/4} g (u^\varepsilon) \nabla \xi_\varepsilon, $$ where $ \xi…
Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and bat…
Linear viscoelastic materials are commonly described by continuous relaxation spectra, yet practical measurements and simulations employ discrete Prony series. In the Laplace frequency domain, the dis…
Let $A$ be an abelian compact Lie group and let $E$ be an oriented $A$-spectrum. We compute the $E$-homology of tom Dieck's homotopical $A$-equivariant complex bordism spectrum $MU_A$ in two ways, cor…
We study the generalized conditional gradient (GCG) method for time-dependent second-order mean field games (MFG) with local coupling terms. While explicit convergence rates of the GCG method were pre…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov s…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be no…
Explicit irrotational solutions, obtained via the Cole-Hopf transform from the multi-d heat equation, give examples of non-uniqueness for the Cauchy problem in supercritical $L^p$, $W^{1,p}$, and …
We introduce Nevanlinna--Pick norms associated with finite families of characters in a commutative semisimple Banach algebra $A$, and study the class $NP_\infty$ of algebras for which every such norm …
This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first estab…
In this paper, we investigate the optimal large-time behavior of the global solution to a singular chemotaxis system in the whole space $\mathbb{R}^d$ with $d=2,3$. Assuming that the initial data is s…
A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The proposed SBP formul…
We analyze a variant of the Noisy $K$-Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a large number of offspri…
We develop and study an asymptotic-preserving (AP) numerical scheme for a linear kinetic equation in a large deviation regime. After applying a Hopf-Cole transform to the distribution function, the sy…
Consider an unknot $c$ in $S^3$ and a knot $K$ in ${S^3-N(c)}$. Twisting the knot $K$ along $c$, or equivalently applying $\frac{1}{m}$-surgery on $c$, produces a family of knots $\{K_m\}_{m \in \math…
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