scholarly journals Extremal conformal structures on projective surfaces

2020 ◽  
Vol 20 (4) ◽  
pp. 1621-1663 ◽  
Author(s):  
Thomas Mettler
Keyword(s):  
Conformal Structures ◽  
Projective Surfaces

scholarly journals Dimension rigidity in conformal structures

2017 ◽  
Vol 308 ◽  
pp. 1127-1186 ◽  
Author(s):  
Tushar Das ◽  
David Simmons ◽  
Mariusz Urbański
Keyword(s):  
Conformal Structures

scholarly journals From partitions to Hodge numbers of Hilbert schemes of surfaces

2019 ◽  
Vol 378 (2163) ◽  
pp. 20180435 ◽  
Author(s):  
Nate Gillman ◽  
Xavier Gonzalez ◽  
Ken Ono ◽  
Larry Rolen ◽  
Matthew Schoenbauer
Keyword(s):  
Partition Function ◽  
Royal Society ◽  
Asymptotic Properties ◽  
Circle Method ◽  
100Th Anniversary ◽  
Hilbert Schemes ◽  
Hodge Numbers ◽  
Projective Surfaces

We celebrate the 100th anniversary of Srinivasa Ramanujan's election as a Fellow of the Royal Society, which was largely based on his work with G. H. Hardy on the asymptotic properties of the partition function. After recalling this revolutionary work, marking the birth of the ‘circle method’, we present a contemporary example of its legacy in topology. We deduce the equidistribution of Hodge numbers for Hilbert schemes of suitable smooth projective surfaces. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

scholarly journals Rational cuspidal curves in projective surfaces. Topological versus algebraic obstructions

2017 ◽  
Vol 28 (14) ◽  
pp. 1750106
Author(s):  
Maciej Borodzik
Keyword(s):  
Floer Homology ◽  
Singular Points ◽  
The Other ◽  
Heegaard Floer Homology ◽  
Heegaard Floer ◽  
Bezout Theorem ◽  
Projective Surfaces

We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo, Melle–Hernandez and Némethi and is based on the Bézout theorem. The other one is a generalization of the result obtained by Livingston and the author and relies on Ozsváth–Szabó inequalities for [Formula: see text]-invariants in Heegaard Floer homology. We show by means of explicit calculations that the two approaches give very similar obstructions.

scholarly journals Computational wrapping: A universal method to wrap 3D-curved surfaces with nonstretchable materials for conformal devices

2020 ◽  
Vol 6 (15) ◽  
pp. eaax6212 ◽  
Author(s):  
Yu-Ki Lee ◽  
Zhonghua Xi ◽  
Young-Joo Lee ◽  
Yun-Hyeong Kim ◽  
Yue Hao ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Reliable Method ◽  
Design Method ◽  
Universal Method ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Steel Sheets ◽  
Computer Aided ◽  
Conformal Structures ◽  
Aided Design

This study starts from the counterintuitive question of how we can render conventional stiff, nonstretchable, and even brittle materials sufficiently conformable to fully wrap curved surfaces, such as spheres, without failure. Here, we extend the geometrical design method of computational origami to wrapping. Our computational wrapping approach provides a robust and reliable method for fabricating conformal devices for arbitrary curved surfaces with a computationally designed nonpolyhedral developable net. This computer-aided design transforms two-dimensional (2D)–based materials, such as Si wafers and steel sheets, into various targeted conformal structures that can fully wrap desired 3D structures without fracture or severe plastic deformation. We further demonstrate that our computational wrapping approach enables a design platform that can transform conventional nonstretchable 2D-based devices, such as electroluminescent lighting and flexible batteries, into conformal 3D curved devices.

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