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pro vyhledávání: '"Evans, Jonathan David"'
We use Luttinger surgery to show that there are no Lagrangian Klein bottles in $S^2\times S^2$ in the $\mathbb{Z}_2$-homology class of an $S^2$-factor if the symplectic area of that factor is at least twice that of the other.
Comment: 13 pages,
Comment: 13 pages,
Externí odkaz:
http://arxiv.org/abs/2410.07782
Autor:
Euler, Leonhard, Evans, Jonathan David
This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of amicable numb
Externí odkaz:
http://arxiv.org/abs/2409.08783
Publikováno v:
SIGMA 20 (2024), 109, 13 pages
Suppose you have a family of Lagrangian submanifolds $L_t$ and an auxiliary Lagrangian $K$. Suppose that $K$ intersects some of the $L_t$ more than the minimal number of times. Can you eliminate surplus intersection (surplusection) with all fibres by
Externí odkaz:
http://arxiv.org/abs/2408.14883
This paper has been written to illustrate the power of techniques from tropical geometry and mirror symmetry for studying the KSBA moduli space of surfaces on or near the Noether line. We focus on the moduli space of octic double planes ($K^2 = 2$, $
Externí odkaz:
http://arxiv.org/abs/2405.02735
Autor:
Evans, Jonathan David
This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on the case
Externí odkaz:
http://arxiv.org/abs/2403.03519
Autor:
Evans, Jonathan David, Lekili, Yanki
We compute the wrapped Fukaya category $\mathcal{W}(T^*S^1, D)$ of a cylinder relative to a divisor $D= \{p_1,\ldots, p_n\}$ of $n$ points, proving a mirror equivalence with the category of perfect complexes on a crepant resolution (over $k[t_0,\ldot
Externí odkaz:
http://arxiv.org/abs/2307.06592
Autor:
Evans, Jonathan David
This is a book aimed at graduate students and researchers in symplectic geometry, based on a course I taught in 2019. The primary message is that the base of a Lagrangian torus fibration inherits an integral affine structure, which you can use to "re
Externí odkaz:
http://arxiv.org/abs/2110.08643
Autor:
Evans, Jonathan David, Lekili, Yanki
We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution has stron
Externí odkaz:
http://arxiv.org/abs/2104.11713
Autor:
Evans, Jonathan David
Publikováno v:
Journal of Fixed Point Theory and Applications volume 24, Article number: 47 (2022) in Symplectic geometry - A Festschrift in honour of Claude Viterbo's 60th birthday
Suppose you have a nonorientable Lagrangian surface L in a symplectic 4-manifold. How far can you deform the symplectic form before the smooth isotopy class of L contains no Lagrangians? I solve this question for a particular Lagrangian Klein bottle.
Externí odkaz:
http://arxiv.org/abs/2009.01546
Autor:
Evans, Jonathan David, Mauri, Mirko
We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways. We find a Lagrangian torus fibration on the 3-fold negative vertex w
Externí odkaz:
http://arxiv.org/abs/1905.09229