Timeline for Contemporary mathematical themes
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Aug 9, 2013 at 16:23 | comment | added | Jon Bannon | Thanks, Ian, it was clear from your answer what you meant and I think your answer is very solid just as it stands. Alexandre's comment suggests another answer to this question distinct from yours may be "exploration of random structures". If this is understood to mean "study of probability distributions" then I agree, it is certainly not a modern theme. | |
| Aug 9, 2013 at 16:16 | comment | added | Ian Agol | @AlexandreEremenko and Jon Bannon: Of course, the study of probability distributions is a long tradition in mathematics, so certainly not modern (although the specific distributions of random objects being studied in contemporary mathematics has changed as you point out; I would add e.g. SLE). The point of my answer is that probability is being used as a tool to prove existence results where the answer says nothing about the probability distribution (1 and 4) or gives one an idea of how common certain structures are (2 and 3), which I think is a modern trend. | |
| Aug 9, 2013 at 15:46 | comment | added | Piyush Grover | Mumford's "Age of stochasticity" is relevant here:stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf | |
| Aug 9, 2013 at 15:22 | comment | added | Jon Bannon | @Alexandre: I was thinking the same thing. What came to mind for me is Voiculescu's free probability providing a solid tie between freeness and large random matrices. It's interesting that physics (I'm probably oversimplifying) seems to support the other "dichotomy" answer as well, since Wigner seemed to consider random matrices as occurring as high energy "random blocks" occurring in a block decomposition around the lower energy "stable" states. | |
| Aug 9, 2013 at 15:14 | comment | added | Alexandre Eremenko | The study of random objects is of great interest in itself, not only as a tool for existence proofs. Random matrices, random polynomials, random Taylor and Fourier series are all interesting and some of these objects are relevant for physics. | |
| S Aug 9, 2013 at 4:22 | history | answered | Ian Agol | CC BY-SA 3.0 | |
| S Aug 9, 2013 at 4:22 | history | made wiki | Post Made Community Wiki by Ian Agol |