|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
On the dynamical Mordell-Lang conjecture
If you have a question about this talk, please contact Bob Hough.
Let $V$ be a variety, and let $\phi : V \to V$ be a morphism. If an (infinite) forward orbit of a point intersects a subvariaty $W$ infinitely many times, what can be said about $W$? The dynamical Mordell-Lang conjecture asserts that this can only happen for “the obvious reason”, namely that $W$ is $\phi$-preperiodic. We will give a brief background on the conjecture, and using a $p$-adic analytic approach, prove it for certain coordinatewise actions. Assuming certain “random map assumptions”, the approach should work for more general maps if the mod $p$ periodic part of orbit avoids the ramification locus of $\phi$. However, in sufficiently high dimensions the approach breaks down due to the periods being too long. We will discuss this in more detail, and present numerical evidence for the validity of the random map assumption in various dimensions.
This talk is part of the Discrete Analysis Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCambridge eScience Centre Quantum Matter Journal Club Conference on the Birch and Swinnerton-Dyer conjecture
Other talksBiomedical photoacoustic imaging for the clinical and life sciences Contractibility of spaces of stability conditions Chinese sentence final particles and their behaviour in L2 Chinese Scanning Electron Microscopes ESEM) - A Nanometre Scale Perspective Festival of Ideas: The Gathering Sound High-content microscopy: big-data biology goes spatio-temporal