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A Fruitful Interaction Between Algebra, Geometry, and Topology: Varieties Through the Lens of Group Actions

Rubí E. Rodríguez and Anita M. Rojas

We discuss how the knowledge about group algebras and representation theory has proved fruitful in understanding fundamental questions about complex abelian varieties, compact Riemann surfaces, and their moduli spaces.
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Classical Values of Zeta, as Simple as Possible But Not Simpler

Olga Holtz

The goal of this article is to present two simple ways to obtain all classical values of 𝜁.
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From the Random Geometry of Conformally Invariant Systems to the Kähler Geometry of Universal Teichmüller Space

Yilin Wang

We explain how a fundamental functional on the space of Jordan curves arising from SLE—Loewner energy—is connected to a seemingly far apart subject: the Kähler geometry of universal Teichmüller space.
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Isometric Immersions and Applications

Qing Han and Marta Lewicka

We review several important aspects of isometric embeddings and immersions of Riemannian manifolds in the Euclidean space.
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The Isoperimetric Inequality

Simon Brendle and Michael Eichmair

The isoperimetric problem is one of the oldest and most famous problems in geometry.
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Tumbling Downhill Along a Given Curve

Jean-Pierre Eckmann, Yaroslav I. Sobolev and Tsvi Tlusty

For which curves drawn on the inclined plane can one carve a shape that will roll downhill following precisely this prescribed curve and its translationally repeated copies?
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