@article{18705,
  abstract     = {Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t].},
  author       = {Glas, Jakob and Hochfilzer, Leonhard},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  pages        = {5485--5533},
  publisher    = {Springer Nature},
  title        = {{On a question of Davenport and diagonal cubic forms over Fq(t)}},
  doi          = {10.1007/s00208-024-03035-z},
  volume       = {391},
  year         = {2025},
}

@article{20367,
  abstract     = {We prove upper and lower bounds on the number of pairs of commuting n x n matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis and leads to an analysis of exponential sums involving matrices over finite fields. These are bounded by combining a stratification result of Fouvry and Katz with a new result about the flatness of the commutator Lie bracket.},
  author       = {Browning, Timothy D and Sawin, Will and Wang, Victor},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  pages        = {1863–1880},
  publisher    = {Springer Nature},
  title        = {{Pairs of commuting integer matrices}},
  doi          = {10.1007/s00208-025-03285-5},
  volume       = {393},
  year         = {2025},
}

@article{13318,
  abstract     = {Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.},
  author       = {Volberg, Alexander and Zhang, Haonan},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  pages        = {1657--1676},
  publisher    = {Springer Nature},
  title        = {{Noncommutative Bohnenblust–Hille inequalities}},
  doi          = {10.1007/s00208-023-02680-0},
  volume       = {389},
  year         = {2024},
}

@article{15098,
  abstract     = {The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere–ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force.},
  author       = {Agresti, Antonio and Luongo, Eliseo},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  pages        = {2727--2766},
  publisher    = {Springer Nature},
  title        = {{Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions}},
  doi          = {10.1007/s00208-024-02812-0},
  volume       = {390},
  year         = {2024},
}

@article{15337,
  abstract     = {We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2).},
  author       = {Bonolis, Dante and Browning, Timothy D and Huang, Zhizhong},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  pages        = {4123--4207},
  publisher    = {Springer Nature},
  title        = {{Density of rational points on some quadric bundle threefolds}},
  doi          = {10.1007/s00208-024-02854-4},
  volume       = {390},
  year         = {2024},
}

@article{19487,
  abstract     = {Fix a non-square integer 𝑘≠0. We show that the number of curves 𝐸𝐵:𝑦^2=𝑥^3+𝑘𝐵^2 containing an integral point, where B ranges over positive integers less than N, is bounded by ≪𝑘𝑁(log𝑁)−1/2+𝜖. In particular, this implies that the number of positive integers 𝐵≤𝑁 such that −3𝑘𝐵^2 is the discriminant of an elliptic curve over 𝑄 is o(N). The proof involves a discriminant-lowering procedure on integral binary cubic forms.},
  author       = {Chan, Yik Tung},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  number       = {3},
  pages        = {2275--2288},
  publisher    = {Springer Nature},
  title        = {{Integral points on cubic twists of Mordell curves}},
  doi          = {10.1007/s00208-023-02578-x},
  volume       = {388},
  year         = {2023},
}

@article{10588,
  abstract     = {We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.},
  author       = {Dello Schiavo, Lorenzo and Suzuki, Kohei},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  keywords     = {quasi curvature-dimension condition, sub-riemannian geometry, Sobolev-to-Lipschitz property, Varadhan short-time asymptotics},
  pages        = {1815--1832},
  publisher    = {Springer Nature},
  title        = {{Sobolev-to-Lipschitz property on QCD- spaces and applications}},
  doi          = {10.1007/s00208-021-02331-2},
  volume       = {384},
  year         = {2022},
}

@article{20619,
  abstract     = {The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds with some symmetry, in particular confirming Alcolado’s prediction for P^3 and extending it to other spaces. These relations reduce the computation of Welschinger’s invariants of many real symplectic sixfolds to invariants in small degrees and provide lower bounds for counts of real rational curves with positive-dimensional insertions in some cases. In the case of P^3, our lower bounds fit perfectly with Kollár’s vanishing results.},
  author       = {Chen, Xujia and Zinger, Aleksey},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  number       = {3-4},
  pages        = {1231--1313},
  publisher    = {Springer Nature},
  title        = {{WDVV-type relations for disk Gromov–Witten invariants in dimension 6}},
  doi          = {10.1007/s00208-020-02130-1},
  volume       = {379},
  year         = {2021},
}