Something

The list of something Tanaka wrote (or is writing or is considering):

1.  A proper generating functional on a Podle\'{s} sphere. This thesis was called `Some remarks on the quantum $SL(2,\mathbb{R})$'. This thesis was revised and uploaded to arXiv.  I constructed a generating functional which corresponds to our cocycle in the second paper and I proved that thhis generating functional is proper in some sense. And I proved some properties of the quantum $SL(2,\mathbb{R})$. Now I'm considering a classification of Drinfeld double coideals up to Morita equivalences.  And based on the second paper and this paper, I'm considering something about approximation propertie of Drinfeld double coideals.

2.  An extended Matsumura's commutative algebra. This is based on H. Watanabe's private note. Maybe, this will be uploaded to arXiv if I finished writing. To finish this work, I need a long  time.

3. $SL_q(2,\mathbb{R})$上の1-cocycleの話 (Something about 1-cocycles on the quantum $SL(2,\mathbb{R})$). This was written for the Proceedings of the conference the MathSci Freshman Seminar. The link is here.

4. coidealの上の1-cocycleの話(Something about 1-cocycles on coideals).  This was written for the Proceedings of the Mathematics Conference for Young Researchers (19th). The link is here. 

5. Some properties of the quantum $SL(2, \mathbb{R})$. This was written for the Proceedings of the conference Algebraic Lie Theory and Representation Theory (ALTReT).

6. A cocycle on the quantum deformation of the special linear group. This  was written for the Proceedings of Autumn Meeting of the Mathematical Society of Japan.

7. Some observations of finite quantum groups. This thesis was revised and uploaded to arXiv. Now the title is `Examples of solvable and nilpotent  finite quantum groups'. This is a  joint work with my good friends M. Hattori and G. Glowacki.  We considered examples of nilpotent (in the sense of Cohen--Westreich) finite quantum groups which don't arise from genuine groups. We classified solvable series for Kac--Paljutkin's 8-dimensional finite quantum group whose length are maximal. We proved that Kac--Paljutkin's 8-dimensional finite quantum group and Sekine quantum groups are nilpotent.  We gave a direct computation of the universal R-matrices for Kac--Paljutkin's 8-dimensional finite quantum group. (Of course this result was already found by Dr. Suzuki, Dr. Wakui and many other mathematicians.) We used Mathematica to check our computation. For the code, see QuantumGroups/check at master · guunterr/QuantumGroups (github.com). Now we are considering categorical aspects of some finite quantum groups (We use Mathematica or something else for this purpose).

8. Solvability and nilpotency for finite quantum groups. This was written for the Proceedings of the Mathematics Conference for Young Researchers (20th).

9. Examples of solvable and nilpotent algebraic quantum groups. (This is a tentative title). 

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Teaching: 

1. Super teaching assistant at Kyoto University, 2021/4/1~2022/3/31

2. Teaching assistant (for Exercises in Basic Analysis) at Kyoto University, 2021 Autumn

3. Super teaching assistant at Kyoto University, 2022/4/1~2023/3/31

4. Teaching assistant (for Exercises in Basic Analysis) at Kyoto University, 2022 Autumn

5. Super teaching assistant (for the supplementary class) at Nagoya University, 2023 Spring

Professional positions :

1. Nagoya University Interdisciplinary Frontier Fellowships (supported by Nagoya University and JST) at Graduate School of mathematics, Nagoya University (2023/4/1~2024/3/31)

2. FY2024 DC2 Research Fellowships (JSPS Fellowships) at Graduate School of mathematics, Nagoya University (2024/4/1~2026/3/31)

Fundings :

1.  Nagoya University Interdisciplinary Frontier Fellowships (supported by Nagoya University and JST) at Graduate School of mathematics, Nagoya University (`representation theory of the quantum $SL(n,\mathbb{R} ) and stochastic processes on the quantum $SL(2,mathbb{R})$', 250,000yen/year, 2023/4/1~2024/3/31)

2.  Super teaching assistant (for the supplementary class) at Nagoya University, 2023 Spring, (`representation theory of the quantum $SL(n,\mathbb{R} ) and stochastic processes on the quantum $SL(2,mathbb{R})$', 150,000yen/year, 2023/4/1~2024/3/31)

3. FY2024 DC2 Research Fellowships (JSPS Fellowships) at Graduate School of mathematics, Nagoya University (`representation theory of the quantized locally compact Lie groups and stochastic processes on the qyuantized locally compact Lie groups, yen/year, 2024/4/1~2026/3/31)

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