2018 academic year

No. 4

Date: February 6 (Wed) 16:00 - 17:30

Place: B707, Fac. Sci., Hiroshima University

Speaker: Davide GUZZETTI (SISSA, Italy)

Title: Non-generic isomonodromy deformations at an irregular singularity and Frobenius manifolds

Abstract:

Some of the main results of [1] and [5] (see also [4] for a synthetic exposition with examples), concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are discussed. The results are the analytic part of a joint work with G. Cotti and B. Dubrovin. We were motivated by the problem of extending to coalescent structures the analytic theory of Frobenius manifolds, in view of the computation of the monodromy data of the quantum cohomology of Grassmannians [2], [3], [6]. Analytically, this problem translates to the problem of extending the isomonodromic deformation theory of Jimbo-Miwa-Ueno to certain non generic cases.

References

[1] G. Cotti, B. Dubrovin. D. Guzzetti: Isomonodromy Deformations at an Ir-regular Singularity with Coalescing Eigenvalues. arXiv:1706.04808 (2017). To appear in Duke Math. J.

[2] G. Cotti, B. Dubrovin. D. Guzzetti: Local Moduli of Semisimple Frobenius Coalescent Structures. arXiv:1712.08575 (2017).

[3] G. Cotti, D. Guzzetti: Analytic geometry of semisimple coalescent Frobenius structures. Random Matrices Theory Appl. 6 (2017), no. 4, 1740004, 36 pp.

[4] G. Cotti, D. Guzzetti: Results on the Extension of Isomonodromy Deformations to the case of a Resonant Irregular Singularity. Random Matrices Theory Appl. (2018)

[5] D. Guzzetti: Notes on non-generic Isomonodromy Deformations. SIGMA 14 (2018), 087, 34 pages

[6] G. Cotti, B. Dubrovin, D. Guzzetti. Helix Structures in Quantum Cohomology of Fano Varieties. arXiv:1811.09235 (2018)

No. 2

Date: June 8 (Fri) 16:30 - 18:00

Place: B707, Fac. Sci., Hiroshima University

Speaker: Kouki HIROTA (RITSUMEIKAN University)

Title:

Abstract:

No. 1

Date: May 7 (Mon) 16:30 - 18:00

Place: B707, Fac. Sci., Hiroshima University

Speaker: Yusaku TIBA (Ochanomizu University)

Title: The extension of holomorphic functions on a non-pluriharmonic locus

Abstract:

    Let n ≥ 4 and let Ω be a bounded hyperconvex domain in Cⁿ. Let φ be a negative exhaustive smooth plurisubharmonic function on Ω. We show that any holomorphic function defined on a connected open neighborhood of the support of (i∂∂φ)^n-3 can be extended to the holomorphic function on Ω.

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Organizers

Shingo KAMIMOTO (Graduate School of Science, Hiroshima University)
Yoshikatsu SASAKI (Faculty of Engineering, Kindai University)
Tetsu SHIMOMURA (Graduate School of Education, Hiroshima University)
Kazuhiro TAKIMOTO (Graduate School of Science, Hiroshima University)
Kentaro HIRATA (Graduate School of Science, Hiroshima University)
Yoshihiro MIZUTA (Faculty of Engineering, Hiroshima Institute of Technology)
Masafumi YOSHINO (Graduate School of Science, Hiroshima University)

Contact

Kenji KUROGI kj-kurogi@hiroshima-u.ac.jp

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Last update: April 27, 2018

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