@article{265,
abstract = {We establish the dimension and irreducibility of the moduli space of rational curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low degree. A spreading out argument reduces the problem to hypersurfaces defined over finite fields of large cardinality, which can then be tackled using a function field version of the Hardy-Littlewood circle method, in which particular care is taken to ensure uniformity in the size of the underlying finite field.},
author = {Timothy Browning and Vishe, Pankaj},
journal = {Geometric Methods in Algebra and Number Theory},
number = {7},
pages = {1657 -- 1675},
publisher = { Mathematical Sciences Publishers},
title = {{Rational curves on smooth hypersurfaces of low degree}},
doi = {10.2140/ant.2017.11.1657},
volume = {11},
year = {2017},
}
@article{266,
abstract = {We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.},
author = {Timothy Browning and Heath-Brown, Roger},
journal = {Journal of the European Mathematical Society},
number = {2},
pages = {357 -- 394},
publisher = {European Mathematical Society Publishing House},
title = {{Forms in many variables and differing degrees}},
doi = {10.4171/JEMS/668},
volume = {19},
year = {2017},
}
@article{267,
abstract = {Building on recent work of Bhargava, Elkies and Schnidman and of Kriz and Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.},
author = {Timothy Browning},
journal = {Mathematika},
number = {3},
pages = {818 -- 839},
publisher = {Cambridge University Press},
title = {{Many cubic surfaces contain rational points}},
doi = {10.1112/S0025579317000195},
volume = {63},
year = {2017},
}
@article{268,
abstract = {We show that any subset of the squares of positive relative upper density contains nontrivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish the partition regularity of any diagonal quadric in five or more variables whose coefficients sum to zero. Unlike previous approaches, which are limited to equations in seven or more variables, we employ transference technology of Green to import bounds from the linear setting.},
author = {Timothy Browning and Prendiville, Sean M},
journal = {International Mathematics Research Notices},
number = {7},
pages = {2219 -- 2248},
publisher = {Oxford University Press},
title = {{A transference approach to a Roth-type theorem in the squares}},
doi = {10.1093/imrn/rnw096},
volume = {2017},
year = {2017},
}
@article{269,
author = {Browning, Timothy D and Loughran, Daniel},
journal = {Mathematische Zeitschrift},
number = {3-4},
pages = {1249 -- 1267},
publisher = {Springer},
title = {{Varieties with too many rational points}},
doi = {10.1007/s00209-016-1746-2},
volume = {285},
year = {2017},
}
@article{270,
abstract = {Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics defined over Q.},
author = {Timothy Browning and Gorodnik, Alexander},
journal = {Proceedings of the London Mathematical Society},
number = {6},
pages = {1044 -- 1080},
publisher = {Wiley Blackwell},
title = {{Power-free values of polynomials on symmetric varieties}},
doi = {10.1112/plms.12030},
volume = {114},
year = {2017},
}
@article{271,
abstract = {We show that a non-singular integral form of degree d is soluble non-trivially over the integers if and only if it is soluble non-trivially over the reals and the p-adic numbers, provided that the form has at least (d-\sqrt{d}/2)2^d variables. This improves on a longstanding result of Birch.},
author = {Timothy Browning and Prendiville, Sean M},
journal = {Journal fur die Reine und Angewandte Mathematik},
number = {731},
pages = {203 -- 234},
publisher = {Walter de Gruyter},
title = {{Improvements in Birch's theorem on forms in many variables}},
doi = {doi.org/10.1515/crelle-2014-0122},
volume = {2017},
year = {2017},
}
@article{272,
abstract = {Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.},
author = {Timothy Browning and Matthiesen, Lilian},
journal = {Annales Scientifiques de l'Ecole Normale Superieure},
number = {6},
pages = {1383 -- 1446},
publisher = {Societe Mathematique de France},
title = {{Norm forms for arbitrary number fields as products of linear polynomials}},
doi = {10.24033/asens.2348},
volume = {50},
year = {2017},
}
@inproceedings{274,
abstract = {We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.},
author = {Kolmogorov, Vladimir},
booktitle = {Proceedings of the 31st Conference On Learning Theory},
pages = {228--249},
publisher = {PMLR},
title = {{A faster approximation algorithm for the Gibbs partition function}},
volume = {75},
year = {2017},
}
@article{796,
abstract = {We present the fabrication and characterization of an aluminum transmon qubit on a silicon-on-insulator substrate. Key to the qubit fabrication is the use of an anhydrous hydrofluoric vapor process which selectively removes the lossy silicon oxide buried underneath the silicon device layer. For a 5.6 GHz qubit measured dispersively by a 7.1 GHz resonator, we find T1 = 3.5 μs and T∗2 = 2.2 μs. This process in principle permits the co-fabrication of silicon photonic and mechanical elements, providing a route towards chip-scale integration of electro-opto-mechanical transducers for quantum networking of superconducting microwave quantum circuits. The additional processing steps are compatible with established fabrication techniques for aluminum transmon qubits on silicon.},
author = {Keller, Andrew J and Dieterle, Paul and Fang, Michael and Berger, Brett and Fink, Johannes M and Painter, Oskar},
issn = {00036951},
journal = {Applied Physics Letters},
number = {4},
publisher = {American Institute of Physics},
title = {{Al transmon qubits on silicon on insulator for quantum device integration}},
doi = {10.1063/1.4994661},
volume = {111},
year = {2017},
}