University COVID-19 update

The University of Waterloo is constantly updating our most Frequently Asked Questions.

Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

Valuative Tree SeminarExport this event to calendar

Monday, September 23, 2019 — 2:30 PM EDT

**Note time and room change**

Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo

"Introduction to the valuative tree"

If $X$ is a variety and $\varphi:X\rightarrow X$ is a morphism, we can ask some basic questions about the orbit $\{x,\varphi(x),\varphi^2(x),\ldots\}$. For example: when is it possible for an orbit to be Zariski-dense? Or how often does an orbit intersect a proper subvariety of $X$? These dynamical problems can be approached by analyzing the induced map $\varphi^*$ on the space of valuations on the coordinate ring $R=K[X]$ --- this space is called the Berkovich analytification $X^{\mathrm{an}}$. In the case $X=\mathbb{A}^2$ and $R=K[x,y]$, Xie proved the above two conjectures by studying certain $\varphi^*$-invariant subspaces of $X^{\mathrm{an}}$. This will be a recap of the three lectures we had in August.

MC 5413

S M T W T F S
29
30
31
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
  1. 2020 (64)
    1. March (16)
    2. February (26)
    3. January (22)
  2. 2019 (199)
    1. December (7)
    2. November (26)
    3. October (19)
    4. September (13)
    5. August (7)
    6. July (12)
    7. June (18)
    8. May (22)
    9. April (11)
    10. March (25)
    11. February (17)
    12. January (22)
  3. 2018 (219)
  4. 2017 (281)
  5. 2016 (335)
  6. 2015 (209)
  7. 2014 (235)
  8. 2013 (251)
  9. 2012 (135)