[geometry-ml:04676] Leschke 氏と Pedit 氏による minicourses のご案内

[ONO, Kaoru]

幾何学分科会メーリングリストの皆様

数理解析研究所に滞在中の Katrin Leschke 氏と Franz Pedit 氏による minicourses を
以下のように計画しました。　

Prof. Katrin Leschke　 Integrable system methods in smooth and discrete surface theory
Prof. Franz Pedit         Higgs bundles, harmonic maps, and differential geometry of surfaces

5月6日                                       13:30-15:00   Leschke   15:30-17:00   Pedit 
5月7日   10:00-11:30  Leschke  13:30-15:00   Pedit        15:30-17:00   Leschke 
5月8日   10:00-11:30  Pedit 

興味のある方は、以下のページから登録 (5月3日締め切り) をお願いします。

https://docs.google.com/forms/d/e/1FAIpQLSem8yi_2UEoZBgWuYCkRstkg-5K56jbzDNDyZF-IPiTXKjBqw/viewform?usp=sf_link <https://docs.google.com/forms/d/e/1FAIpQLSem8yi_2UEoZBgWuYCkRstkg-5K56jbzDNDyZF-IPiTXKjBqw/viewform?usp=sf_link>

前日までに登録された email address に zoom meeting の情報を送ります。

大仁田義裕 (OCAMI) 
小野　薫    (RIMS)


=="Integrable system methods in smooth and discrete surface theory” by Prof. Leschke==
Abstract:  
In this lecture series we will explore how integrable system methods can be applied 
in smooth and discrete surface theory. A core ingredient for this discussion is 
the associated family of at connections. For example, for surfaces with constant
non-vanishing mean curvature (CMC), the Gauss map is harmonic by the Ruh-Vilms
theorem: this is equivalent to the flatness of a complex family of connections. We will
discuss how an integrable structure gives rise to a variety of transformations given by
parallel sections of the associated family, e.g., the so-called associated family of surfaces,
the simple factor dressing and the Darboux transformation. In particular, we will discuss
the interplay between three distinct integrable systems associated to a CMC surface and
global properties of the transforms.
As an application, we will discuss the Darboux transforms of Delaunay surfaces, that
is, CMC surfaces of revolution. We obtain new CMC cylinder as well as same-lobed
CMC multibubbletons.
If time permits, we will discuss how the smooth approaches can be discretised in
the example of a discrete polarised curve. We will introduce a discrete equivalent to
the associated family of at connections and discuss closing conditions of its Darboux
transforms.  

=="Higgs bundles, harmonic maps, and differential geometry of surfaces” by Prof. Franz Pedit==
Abstract: 
Higgs bundles arise in a number of ways: as a 2-dimensional reduction of 
the 4-dimensional self-dual Yang-Mills equations; as the equations for harmonic maps 
into a symmetric space; as a zero curvature equation for a suitable connection; 
as a representation of the fundamental group of a compact surface. These different 
incarnations relate aspects of mathematical physics, PDEs, differential/complex/symplectic 
geometry and topology. I will attempt to explain some of these connections and how they 
can be used to understand problems arising in differential geometry. In addition to providing 
a more overarching picture, I will also discuss some examples. 



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