Timeline for Category Theory and Ergodic Theory
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2012 at 22:32 | answer | added | Asaf | timeline score: 0 | |
| Jun 25, 2012 at 22:24 | comment | added | Asaf | @Lunasaurus Rex, sorry for the late reply, but the solenoid is very common in Harmonic Analysis also (from very much the same reason it appears in ergodic theory, see for example in Schmidt's book - dynamical systems of algebraic origin). | |
| Jun 25, 2012 at 22:01 | answer | added | o a | timeline score: 0 | |
| Jan 23, 2012 at 1:19 | vote | accept | Esfan Haghverdi | ||
| Jan 23, 2012 at 1:20 | |||||
| Jan 22, 2012 at 22:45 | answer | added | Ronnie Brown | timeline score: 9 | |
| Jan 21, 2012 at 16:05 | comment | added | Esfan Haghverdi | Thanks David! As a matter of fact, now that I have read some of The Two Culture pages, I must say this was exactly the idea and motivation behind my question to begin with. For some time, I have been thinking about the same problem as you eloquently mention in those posts. I finally came to the conclusion that I should perhaps take on the unification challenge via Ergodic Theory/Additive Combinatorics connection. It seems to me one might be more successful on that front, but who knows. The first goal I set myself was to understand Furstenberg correspondence categorically and hence my question! | |
| Jan 21, 2012 at 15:05 | vote | accept | Esfan Haghverdi | ||
| Jan 23, 2012 at 1:19 | |||||
| Jan 21, 2012 at 15:04 | comment | added | Esfan Haghverdi | Thanks Benjamin. I found his paper THE TOPOLOGICAL DYNAMICS OF SEMIGROUP ACTIONS in TAMS and indeed it is ready to be rewritten, at least in part, in categorical language. I will look more closely. Do you have any specific paper of his in mind? | |
| Jan 21, 2012 at 14:42 | answer | added | Tom Leinster | timeline score: 7 | |
| Jan 21, 2012 at 14:36 | vote | accept | Esfan Haghverdi | ||
| Jan 21, 2012 at 15:05 | |||||
| Jan 21, 2012 at 14:36 | history | edited | Esfan Haghverdi |
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| Jan 21, 2012 at 12:13 | comment | added | David Corfield | Try this post golem.ph.utexas.edu/category/2008/12/bridge_building.html for some category theoretic discussion of Tao's description of cohomology in dynamic systems. | |
| Jan 21, 2012 at 0:10 | comment | added | Mark | Well, some basic constructions in ergodic theory involve products, inverse limits, etc., so the categorical language is definitely there, but I'm not aware of any theorems (in ergodic theory) whose proof uses some abstract, deep facts in category theory. | |
| Jan 20, 2012 at 21:59 | answer | added | Moshe | timeline score: 2 | |
| Jan 20, 2012 at 20:53 | comment | added | Lunasaurus Rex | One thing that I have noticed is that a solenoid may be defined as an inverse limit, which is an object that is studied in dynamics. As far as results, well... | |
| Jan 20, 2012 at 19:45 | comment | added | David White | It's probably worth mentioning that similar questions have been asked before, but this one has not been answered in any thread I'm aware of: mathoverflow.net/questions/83363, mathoverflow.net/questions/83437, mathoverflow.net/questions/38752 | |
| Jan 20, 2012 at 18:51 | comment | added | Benjamin Steinberg | Look at the work of Ellis on topological dynamics using enveloping semigroups. It is not quite categorical, but in the right direction. | |
| Jan 20, 2012 at 17:54 | history | asked | Esfan Haghverdi | CC BY-SA 3.0 |