2015 Fiscal Year Research-status Report
Random Matrix Theory and its applications
| Project/Area Number |
26800048
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| Research Institution | Kyoto University |
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Principal Investigator |
COLLINS Benoit 京都大学, 理学(系)研究科(研究院), 准教授 (20721418)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | Random Matrices / Quantum Information / MOE additivity / positive maps / Connes Problem / free probability / planar algebras |
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| Outline of Annual Research Achievements |
During the last year I completed the following projects:
(1) together with Nechita, we wrote down a review of random matrix techniques in quantum information. It was published in the special edition of Journal of Mathematical Physics
(2) together with Nechita and Hayden, we finished a preprint where we discover new families of positive maps which are positive but not completely positive. It was published in IMRN
(3) alone, I gave a new proof of the MOE non-additivity problem. This proof is the most conceptual so far, it relies on Haagerup inequality. The paper is about to be accepted.
(3) we solved a problem of Jones about the basis dual to the canonical basis of the Temperley Lieb algebra. This is work in preparation with Brannan, and possibly Jones.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
I completed many problems that I had assigned myself. On most topics, the progress is very smooth. However, on my joint work with Brannan on quantum groups and quantum information, we got slightly delayed, because we wanted to check whether our results so far have very strong applications. We expect to finish our joint paper this spring.
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| Strategy for Future Research Activity |
Apart from the above, here are my other projects:
(1) I expect to finish other lecture notes and a collaboration with Junge this spring on non-commutative Brownian motions.
(2) I expect to finish a collaboration with Nechita and Metcalfe about Riemann Hilbert techniques in quantum information theory.
(3) I intend to continue working with Klep on non commutative real algebraic geometric aspects of the Connes embedding problem.
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| Causes of Carryover |
The amount is not zero because travel expenses were lower than expected.
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| Expenditure Plan for Carryover Budget |
I plan to use this amount for travel expenses and inviting collaborators.
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| Remarks |
This Webpage contains all information about my publications, CV and research activities
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