[geometry-ml:03113] 原田芽ぐみ氏の集中講義(12/11-15)

[Mikiya Masuda]

幾何学分科会の皆様

重複して受け取られた方，ご容赦ください．
以下の要領で，原田芽ぐみ氏（McMaster大学，大阪市大数学研究所）の集中講義 
を行います．多くの方のご参加をお待ちしています．

枡田幹也（大阪市立大学）

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期間： 12月11日（月） 14:00 -16:00
     　 12日（火）〜15日（金） 10:00-12:00, 14:00-16:00
場所： 大阪市大数学教室（杉本キャンパス）理学部Ｅ棟 大講究室（E408）
アクセス：https://www.osaka-cu.ac.jp/ja/about/university/access
題目： Khovanskii bases, tropical geometry, and toric degenerations

Brief description:
(NOTE: The plan is subject to change.)
This will be an exposition on recent developments in the theory of  
Khovanskii bases and related topics. Recent work of Kaveh and Manon give  
a necessary and sufficient condition for the existence of a Khovanskii  
basis for a finitely generated algebra in terms of the tropical geometry  
of A, thus connecting the theory of Newton-Okounkov bodies with tropical  
geometry and hence also connecting the toric degenerations arising in  
both contexts. The first part of the lectures will be an explanation of  
the background and content of the work of Kaveh and Manon. The second  
part of the lectures will be more informal and speculative, and mainly  
be a discussion of open questions which relate to Khovanskii bases and  
toric degenerations. More specifically, I intend to discuss recent  
developments on the toric degenerations of flag varieties and related  
varieties, following the expository paper of Fang-Fourier-Littelmann  
(arXiv: 1609.01166).

If time permits, I will also discuss my work in progress with Laura  
Escobar on how Kaveh-Manon's theorem leads to a ``wall-crossing''  
phenomenon for Newton-Okounkov bodies.
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