@article{10772,
  abstract     = {We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule in Lagrangian Floer theory for the elliptic curve. We then prove a correspondence theorem equating counts of tropical corals to punctured log Gromov–Witten invariants of the Tate curve. This implies that the homogeneous coordinate ring of the mirror to the Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming a prediction of homological mirror symmetry.},
  author       = {Arguez, Nuroemuer Huelya},
  issn         = {1469-7750},
  journal      = {Journal of the London Mathematical Society},
  number       = {1},
  pages        = {343--411},
  publisher    = {London Mathematical Society},
  title        = {{Mirror symmetry for the Tate curve via tropical and log corals}},
  doi          = {10.1112/jlms.12515},
  volume       = {105},
  year         = {2022},
}

@article{12214,
  abstract     = {Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. },
  author       = {Gehér, György Pál and Titkos, Tamás and Virosztek, Daniel},
  issn         = {1469-7750},
  journal      = {Journal of the London Mathematical Society},
  keywords     = {General Mathematics},
  number       = {4},
  pages        = {3865--3894},
  publisher    = {Wiley},
  title        = {{The isometry group of Wasserstein spaces: The Hilbertian case}},
  doi          = {10.1112/jlms.12676},
  volume       = {106},
  year         = {2022},
}

@article{9977,
  abstract     = {For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the
WRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections.},
  author       = {Mistegaard, William and Andersen, Jørgen Ellegaard},
  issn         = {1469-7750},
  journal      = {Journal of the London Mathematical Society},
  number       = {2},
  pages        = {709--764},
  publisher    = {Wiley},
  title        = {{Resurgence analysis of quantum invariants of Seifert fibered homology spheres}},
  doi          = {10.1112/jlms.12506},
  volume       = {105},
  year         = {2022},
}

@article{9586,
  abstract     = {Consider integers  𝑘,ℓ  such that  0⩽ℓ⩽(𝑘2) . Given a large graph  𝐺 , what is the fraction of  𝑘 -vertex subsets of  𝐺  which span exactly  ℓ  edges? When  𝐺  is empty or complete, and  ℓ  is zero or  (𝑘2) , this fraction can be exactly 1. On the other hand, if  ℓ  is far from these extreme values, one might expect that this fraction is substantially smaller than 1. This was recently proved by Alon, Hefetz, Krivelevich, and Tyomkyn who initiated the systematic study of this question and proposed several natural conjectures.
Let  ℓ∗=min{ℓ,(𝑘2)−ℓ} . Our main result is that for any  𝑘  and  ℓ , the fraction of  𝑘 -vertex subsets that span  ℓ  edges is at most  log𝑂(1)(ℓ∗/𝑘)√ 𝑘/ℓ∗, which is best-possible up to the logarithmic factor. This improves on multiple results of Alon, Hefetz, Krivelevich, and Tyomkyn, and resolves one of their conjectures. In addition, we also make some first steps towards some analogous questions for hypergraphs.
Our proofs involve some Ramsey-type arguments, and a number of different probabilistic tools, such as polynomial anticoncentration inequalities, hypercontractivity, and a coupling trick for random variables defined on a ‘slice’ of the Boolean hypercube.},
  author       = {Kwan, Matthew Alan and Sudakov, Benny and Tran, Tuan},
  issn         = {1469-7750},
  journal      = {Journal of the London Mathematical Society},
  number       = {3},
  pages        = {757--777},
  publisher    = {Wiley},
  title        = {{Anticoncentration for subgraph statistics}},
  doi          = {10.1112/jlms.12192},
  volume       = {99},
  year         = {2019},
}