From curves to tropical Jacobians and back
For a curve over an algebraically closed field that is complete with respect to a nontrivial
valuation, we study its tropical Jacobian. We first tropicalize the curve and then use the …
valuation, we study its tropical Jacobian. We first tropicalize the curve and then use the …
Schottky algorithms: classical meets tropical
We present a new perspective on the Schottky problem that links numerical computing with
tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and …
tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and …
Multiple lattice tilings in Euclidean spaces
Q Yang, C Zong - Canadian Mathematical Bulletin, 2019 - cambridge.org
In 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean
plane if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves …
plane if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves …
A friendly introduction to Fourier analysis on polytopes
S Robins - arXiv preprint arXiv:2104.06407, 2021 - arxiv.org
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones.
There is a rapidly growing number of applications of these methods, so it is appropriate to …
There is a rapidly growing number of applications of these methods, so it is appropriate to …
Voronoi conjecture for five-dimensional parallelohedra
A Garber - arXiv preprint arXiv:1906.05193, 2019 - arxiv.org
arXiv:1906.05193v5 [math.CO] 1 Jul 2023 Page 1 arXiv:1906.05193v5 [math.CO] 1 Jul 2023
VORONOI CONJECTURE FOR FIVE-DIMENSIONAL PARALLELOHEDRA ALEXEY GARBER …
VORONOI CONJECTURE FOR FIVE-DIMENSIONAL PARALLELOHEDRA ALEXEY GARBER …
Characterization of the three-dimensional multiple translative tiles
M Han, K Sriamorn, Q Yang, C Zong - Advances in Mathematics, 2022 - Elsevier
This paper proves the following statement which answers questions of Gravin, Robins and
Shiryaev: If a convex body can form a two, three or fourfold translative tiling in E 3, it must be …
Shiryaev: If a convex body can form a two, three or fourfold translative tiling in E 3, it must be …
Characterization of the two-dimensional fivefold translative tiles
Q Yang, C Zong - Bull. Soc. Math. France, 2021 - smf.emath.fr
In 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean
plane, if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves …
plane, if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves …
Voronoi's conjecture for extensions of Voronoi parallelohedra
A Magazinov - arXiv preprint arXiv:1308.6225, 2013 - arxiv.org
Let $ I $ be a segment in the $ d $-dimensional Euclidean space $\mathbb E^ d $. Let $ P $
and $ P+ I $ be parallelohedra in $\mathbb E^ d $, where"+" denotes the Minkowski sum …
and $ P+ I $ be parallelohedra in $\mathbb E^ d $, where"+" denotes the Minkowski sum …
Twofold Translative Tiles in Three-Dimensional Space
M Han, Q Yang, K Sriamorn, C Zong - arXiv preprint arXiv:2106.15388, 2021 - arxiv.org
This paper proves the following statement:{\it If a convex body can form a twofold translative
tiling in $\mathbb {E}^ 3$, it must be a parallelohedron.} In other words, it must be a …
tiling in $\mathbb {E}^ 3$, it must be a parallelohedron.} In other words, it must be a …
Characterization of the two-dimensional six-fold lattice tiles
C Zong - arXiv preprint arXiv:1904.06911, 2019 - arxiv.org
arXiv:1904.06911v1 [math.MG] 15 Apr 2019 Page 1 arXiv:1904.06911v1 [math.MG] 15 Apr
2019 Characterization of the Two-Dimensional Six-Fold Lattice Tiles Chuanming Zong …
2019 Characterization of the Two-Dimensional Six-Fold Lattice Tiles Chuanming Zong …