Zariski orbit dense conjecture on birational automorphisms of projective threefolds

Under the framework of dynamics on projective varieties by Kawamata, Nakayama and Zhang \cite{Kawamata85,Nakayama10,NZ10,Zhang16}, Hu and the author \cite{HL21}, we may reduce the Zariski dense orbit conjecture for automorphisms $f$ on projective threefolds $X$ with either trivial canonical divisor or negative Kodaira dimension to the following three cases: (i) weak Calabi-Yau threefolds and $f$ is primitive (ii) rationally connected threefolds and (iii) uniruled threefolds admitting a special MRC fibration over an elliptic curve. And we prove the Zariski dense orbit conjecture is true for either (1) birational automorphisms of normal projective varieties $X$ with the irregularity $q(X)\ge\mathrm{dim} X-1$, or (2) automorphisms $f$ on projective varieties $X$ such that $f^*D\equiv D$ for some big $\mathbb R$-divisors $D$ and the periodic points of $f$ are Zariski dense.Comment: 13 pages, Comments are welcome

Bounded negativity and bounding cohomology on a smooth projective surface with Picard number two

A conjecture of the bounding cohomology on a smooth projective surface $X$ asserts that there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. When the Picard number $\rho(X)=2$, we prove that if the Kodaira dimension $\kappa(X)=-\infty$ and $X$ has a negative curve, then this conjecture holds for $X$.Comment: 6 pages, Comments are welcome. arXiv admin note: text overlap with arXiv:2007.1285

Kawaguchi-Silverman conjecture on automorphisms of projective threefolds

Under the framework of dynamics on projective varieties by Kawamata, Nakayama and Zhang \cite{Kawamata85,Nakayama10, NZ10,Zhang16}, Hu and the author \cite{HL21}, we may reduce Kawaguchi-Silverman conjecture for automorphisms $f$ on normal projective threefolds $X$ with either trivial canonical divisor or negative Kodaira dimension to the following three cases: (i) weak Calabi-Yau threefolds and $f$ is primitive (ii) rationally connected threefolds and (iii) uniruled threefolds admitting a special MRC fibration over an elliptic curve. And we prove Kawaguchi-Silverman conecture is true for birational morphisms of normal projective varieties $X$ with the irregularity $q(X)\ge\dim X-1$. Finally, we discuss Kawaguchi-Silverman conjecture on projective varieties with Picard number two.Comment: 15 pages, revised a few mistakes and added related remarks 1.7 and 3.5. Comments are welcome! arXiv admin note: text overlap with arXiv:2208.0261

Review of Time Series Forecasting Methods and Their Applications to Particle Accelerators

Particle accelerators are complex facilities that produce large amounts of structured data and have clear optimization goals as well as precisely defined control requirements. As such they are naturally amenable to data-driven research methodologies. The data from sensors and monitors inside the accelerator form multivariate time series. With fast pre-emptive approaches being highly preferred in accelerator control and diagnostics, the application of data-driven time series forecasting methods is particularly promising. This review formulates the time series forecasting problem and summarizes existing models with applications in various scientific areas. Several current and future attempts in the field of particle accelerators are introduced. The application of time series forecasting to particle accelerators has shown encouraging results and the promise for broader use, and existing problems such as data consistency and compatibility have started to be addressed.Comment: 13 pages, 11 figure