Sina Saleh

University of British Columbia | UBC · Department of Mathematics

We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.

We prove the Zariski dense orbit conjecture in positive characteristic for endomorphisms of GaN defined over Fp‾.

We prove the Zariski dense orbit conjecture in positive characteristic for endo-morphisms of a power of the additive group scheme defined over Fp.

We prove the Zariski dense orbit conjecture in positive characteristic for regular self-maps of split semiabelian varieties.

We provide a direct proof of the Medvedev–Scanlon’s conjecture from Medvedev and Scanlon (Ann. Math. Second Series 179 (2014), 81–177) regarding Zariski dense orbits under the action of regular self-maps on split semiabelian varieties defined over a field of characteristic $0$ . Besides obtaining significantly easier proofs than the ones previously...

Background The aim of this study was to develop a low-cost prototype near-infrared fluorescence device that enables contrast-free, real time, high-resolution intraoperative visualization of normal and pathological parathyroid glands (PG) by imaging their autofluorescence (AF). Methods A novel near-infrared parathyroid AF (NIR-PAF) imaging device w...

We prove a quantitative partial result in support of the dynamical Mordell–Lang conjecture (also known as the DML conjecture ) in positive characteristic. More precisely, we show the following: given a field K of characteristic p , a semiabelian variety X defined over a finite subfield of K and endowed with a regular self-map $\Phi :X{\longrightarr...

Given an integer $g$ and also some given integers $m$ (sufficiently large) and $c_1,\dots, c_m$, we show that the number of all non-negative integers $n\le M$ with the property that there exist non-negative integers $k_1,\dots, k_m$ such that $$n^2=\sum_{i=1}^m c_i g^{k_i}$$ is $o\left(\left(\log M \right)^{m-1/2}\right)$. We also obtain a similar...

We prove a quantitative partial result in support of the Dynamical Mordell-Lang Conjecture (also known as the DML conjecture) in positive characteristic. More precisely, we show the following: given a field $K$ of characteristic $p$, given a semiabelian variety $X$ defined over a finite subfield of $K$ and endowed with a regular self-map $\Phi:X \l...