Research
Research
Research
Research
762+ open-access research outputs.
For any $\beta_0<1/3$ we construct divergence free vector fields in $ C_{x,t}^{\beta_0}$ and a sequence of diffusivities $\kappa_q \searrow 0$ such that, for an arbitrary initial datum from a low regu…
In \cite{HLZ2} and \cite{HHLZ}, using $E_8$ bundles, some modular forms over $SL(2,{\bf Z})$ were constructed on $12$-dimensional manifolds and the Witten-Freed-Hopkins anomaly cancellation formula wa…
Hyperbolic uniform disk graphs (HUDGs) are intersection graphs of disks with some radius $r$ in the hyperbolic plane, where $r$ may be constant or depend on the number of vertices in a family of HUDGs…
The notions of tree-like loop and Lipschitz tree-like loop were introduced by Hambly and Lyons in their 2010 Annals of Mathematics paper. They showed that the Lipschitz tree-like property determines a…
Recently, Efron and Tibshirani (Annals of Statistics, 1996) proposed a semiparametric density estimator, which works by multiplying an initial kernel type estimate with a parametric exponential type c…
All men are created equal, proclaimed Jefferson in 1776 -- but some are more equal than others, added Orwell in Animal Farm in 1945. So what's the probability that two skaters are exactly equal, to th…
We construct a fractured structure, in the sense of Lurie, on the $\infty$-topos of condensed anima. This fractured structure allows us to better comprehend various properties of condensed anima - we …
By the family index theory, we generalize some well-known $SL(2,Z)$ modular forms to the family case and obtain some new anomaly cancellation formulas for the determinant line bundle and index gerbes,…
Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuros…
Quasi-Hermitian varieties arise as higher-dimensional generalizations of non-classical unitals, including the Buekenhout--Metz (BM) and Buekenhout--Tits (BT) families. After reviewing known construc…
We propose and analyse a mechanism by which $\mathrm{CO}_2$-driven radiative forcing can increase Arctic temperature variability in a stochastic Sellers-type energy-balance model. Starting from a fast…
Consider a sequence of estimators $\hat \theta_n$ which converges almost surely to $\theta_0$ as the sample size $n$ tends to infinity. Under weak smoothness conditions, we identify the asymptotic lim…
We compare the classifying anima of two natural condensed $\infty$-categories associated to a coherent $\infty$-topos. One from our work with Barwick and Glasman on exit-path categories in algebraic g…
Using $E_8$ bundles, we construct some new modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$ and get some new anomaly cancellation formulas of characteristic forms which generalize s…
In this paper, we provide a complete list of anomaly-free hyperspherical Hamiltonian spaces for simple reductive groups, as well as their conjectural dual spaces in the sense of BZSV duality.…
We revisit the Ligon--Schaaf regularization of the Kepler problem and identify the geometric origin of the rotation appearing in their transformation. We show that this rotation is determined by the e…
Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representatio…
We study the chemical distance of supercritical Bernoulli percolation on $\mathbb{Z}^d$. Recently, Dembin [Dem22] showed that the chemical distance exhibits sublinear variance, a phenomenon now referr…
This paper aims to derive new anomaly cancellation formulas by combining modular forms with E8 and E8*E8 bundles. To this end, we systematically twist and generalize known SL(2,Z) modular forms to def…
A kind of two-variable elliptic genus for almost-complex manifolds was introduced by Ping Li and its various properties were established by him. In this paper, we define a two-variable elliptic genus …
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