Application of q-Stokes matrices to Classification and Galois Theory -

Application of q-Stokes matrices to Classification and Galois Theory

发布时间：2025年04月19日浏览次数：134 发布者: Ruixin Li

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主讲人： Jacques Sauloy(Université Paul-Sabatier)

活动时间： 从 2025-04-29 14:00 到 15:00

场地： 北京国际数学研究中心，全斋全29教室

Abstract:

In [RSZ] two (equivalent but non obviously) versions of the q-Stokes phenomenon are proposed. One is classically related to asymptotics, formal solutions and summation processes. The other version relies on the interpretation of Stokes phenomenon as a measure of how far analytic classification is from formal classification. Now, in the case of analytic q-difference equations, the relation between formal and analytic admits a very nice algebraic formulation in terms of (block-)trigonalisation vs diagonalisation (Adams’ filtration).

I will explain how Stokes matrices are defined and computed in that framework, then how they can be used for analytic classification (« q-Birkhoff-Malgrange-Sibuya theorems ») and for the description of Galois groups.

Main references :

[RSZ] Jean-Pierre Ramis, Jacques Sauloy, and Changgui Zhang, Local analytic classification of q-di erence equations, Astérisque 355 (2013) ff Jacques Sauloy, Algebraic construction of the Stokes sheaf for irregular linear q-di erence ff equations, Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I., Astérisque 296 (2004), 227–251,

Jean-Pierre Ramis and Jacques Sauloy, The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-di erence equations, Ann. Sci. Éc. Norm. Supér. (4) ff 48 (2015), no. 1, 171–226,

Jacques Sauloy, Basic Modern Theory of Linear Complex Analytic q-difference Equations, vol.xxx, Providence, RI: American Mathematical Society (AMS), 2024 (English)

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