Zobrazeno 1 - 10
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pro vyhledávání: '"Hugelmeyer, Cole"'
Autor:
Hugelmeyer, Cole
We resolve the periodic square peg problem using a simple Lagrangian Floer homology argument. Inscribed squares are interpreted as intersections between two non-displaceable Lagrangian sub-manifolds of a symplectic 4-torus.
Externí odkaz:
http://arxiv.org/abs/2407.20412
Autor:
Hugelmeyer, Cole
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will demonstrate t
Externí odkaz:
http://arxiv.org/abs/2307.07661
Autor:
Hugelmeyer, Cole
We develop a connection between the inscribed square problem and the question of understanding relation avoiding paths in a complex vector space. Our main theorem is that a Jordan curve with no inscribed squares would have a seemingly impossible stru
Externí odkaz:
http://arxiv.org/abs/2301.01340
Autor:
Belopolski, Ilya, Chang, Guoqing, Cochran, Tyler A., Cheng, Zi-Jia, Yang, Xian P., Hugelmeyer, Cole, Manna, Kaustuv, Yin, Jia-Xin, Cheng, Guangming, Multer, Daniel, Litskevich, Maksim, Shumiya, Nana, Zhang, Songtian S., Shekhar, Chandra, Schröter, Niels B. M., Chikina, Alla, Polley, Craig, Thiagarajan, Balasubramanian, Leandersson, Mats, Adell, Johan, Huang, Shin-Ming, Yao, Nan, Strocov, Vladimir N., Felser, Claudia, Hasan, M. Zahid
Publikováno v:
Nature 604, 647-652 (2022)
Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter, providing t
Externí odkaz:
http://arxiv.org/abs/2112.14722
Autor:
Hugelmeyer, Cole
We prove that for every smooth Jordan curve $\gamma$, if $X$ is the set of all $r \in [0,1]$ so that there is an inscribed rectangle in $\gamma$ of aspect ratio $\tan(r\cdot \pi/4)$, then the Lebesgue measure of $X$ is at least $1/3$. To do this, we
Externí odkaz:
http://arxiv.org/abs/1911.07336
Autor:
Hugelmeyer, Cole
We provide a way to produce knots in $S^3$ from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental theorem of finite type invariants. We also provide moves for the diagram
Externí odkaz:
http://arxiv.org/abs/1806.11201
Autor:
Hugelmeyer, Cole
Let $K$ be a knot type for which the quadratic term of the Conway polynomial is nontrivial, and let $\gamma: \mathbb{R}\to \mathbb{R}^3$ be an analytic $\mathbb{Z}$-periodic function with non-vanishing derivative which parameterizes a knot of type $K
Externí odkaz:
http://arxiv.org/abs/1804.09818
Autor:
Hugelmeyer, Cole
We use Batson's lower bound on the nonorientable slice genus of $(2n,2n-1)$-torus knots to prove that for any $n \geq 2$, every smooth Jordan curve has an inscribed rectangle of of aspect ratio $\tan(\frac{\pi k}{2n})$ for some $k\in \{1,...,n-1\}$.
Externí odkaz:
http://arxiv.org/abs/1803.07417
Autor:
Hugelmeyer, Cole
We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain complexes with homologously trivial operad algebra structures, thus expos
Externí odkaz:
http://arxiv.org/abs/1508.03568
Autor:
Hugelmeyer, Cole
Publikováno v:
IMRN: International Mathematics Research Notices; May2024, Vol. 2024 Issue 9, p7445-7465, 21p