@article{14793, abstract = {Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a sin(2y) CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on the same silicon technology compatible platform.}, author = {Valentini, Marco and Sagi, Oliver and Baghumyan, Levon and de Gijsel, Thijs and Jung, Jason and Calcaterra, Stefano and Ballabio, Andrea and Aguilera Servin, Juan L and Aggarwal, Kushagra and Janik, Marian and Adletzberger, Thomas and Seoane Souto, Rubén and Leijnse, Martin and Danon, Jeroen and Schrade, Constantin and Bakkers, Erik and Chrastina, Daniel and Isella, Giovanni and Katsaros, Georgios}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium}}, doi = {10.1038/s41467-023-44114-0}, volume = {15}, year = {2024}, } @article{12312, abstract = {Let $\ell$ be a prime number. We classify the subgroups $G$ of $\operatorname{Sp}_4(\mathbb{F}_\ell)$ and $\operatorname{GSp}_4(\mathbb{F}_\ell)$ that act irreducibly on $\mathbb{F}_\ell^4$, but such that every element of $G$ fixes an $\mathbb{F}_\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\ell$ for which some abelian surface $A/\mathbb{Q}$ fails the local-global principle for isogenies of degree $\ell$.}, author = {Lombardo, Davide and Verzobio, Matteo}, issn = {1420-9020}, journal = {Selecta Mathematica}, number = {2}, publisher = {Springer Nature}, title = {{On the local-global principle for isogenies of abelian surfaces}}, doi = {10.1007/s00029-023-00908-0}, volume = {30}, year = {2024}, } @unpublished{19425, abstract = {We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by non-zero values of the %non-Abelian patch Euler class. In particular, we report on the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial quantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties. }, author = {Karle, Volker and Lemeshko, Mikhail and Bouhon, Adrien and Slager, Robert-Jan and Ünal, F. Nur}, booktitle = {arXiv}, title = {{Anomalous multi-gap topological phases in periodically driven quantum rotors}}, doi = {10.48550/arXiv.2408.16848}, year = {2024}, } @article{17127, abstract = {Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation ∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0 (for any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as N→+∞ , where f is the Steinhaus random multiplicative function.}, author = {Wang, Victor and Xu, Max Wenqiang}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {8}, pages = {2718--2726}, publisher = {London Mathematical Society}, title = {{Paucity phenomena for polynomial products}}, doi = {10.1112/blms.13095}, volume = {56}, year = {2024}, } @article{15338, abstract = {We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields.}, author = {Browning, Timothy D and Pierce, Lillian B. and Schindler, Damaris}, issn = {1475-3030}, journal = {Journal of the Institute of Mathematics of Jussieu}, number = {6}, pages = {2859--2912}, publisher = {Cambridge University Press}, title = {{Generalised quadratic forms over totally real number fields}}, doi = {10.1017/S1474748024000161}, volume = {23}, 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{18930, abstract = {We study sumsets 𝒜 + ℬ in the set of squares 𝒮 (and, more generally, in the set of kth powers 𝒮k, where k ≥2 is an integer). It is known by a result of Gyarmati that 𝒜 + ℬ ⊂ 𝒮k ∩[1,N] implies that min(|𝒜|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ| decreases, when the size of |𝒜| increases (or vice versa). In particular, if |𝒜| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with m ∼ loglogN this gives: If |𝒜| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2).}, author = {Elsholtz, Christian and Wurzinger, Lena}, issn = {1464-3847}, journal = {The Quarterly Journal of Mathematics}, number = {4}, pages = {1243--1254}, publisher = {Oxford University Press}, title = {{Sumsets in the set of squares}}, doi = {10.1093/qmath/haae044}, volume = {75}, year = {2024}, } @article{15312, abstract = {The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree.}, author = {Browning, Timothy D and Shparlinski, Igor E.}, issn = {0022-314X}, journal = {Journal of Number Theory}, pages = {220--240}, publisher = {Elsevier}, title = {{Square-free values of random polynomials}}, doi = {10.1016/j.jnt.2024.02.013}, volume = {261}, year = {2024}, } @article{19051, abstract = {This paper corrects an error in an earlier work of the author.}, author = {Browning, Timothy D}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {13}, pages = {10165--10168}, publisher = {Oxford University Press}, title = {{The polynomial sieve and equal sums of like polynomials}}, doi = {10.1093/imrn/rnae066}, volume = {2024}, year = {2024}, } @article{10018, abstract = {In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines.}, author = {Derenthal, Ulrich and Wilsch, Florian Alexander}, issn = {1475-3030 }, journal = {Journal of the Institute of Mathematics of Jussieu}, keywords = {Integral points, del Pezzo surface, universal torsor, Manin’s conjecture}, number = {3}, pages = {1259--1294}, publisher = {Cambridge University Press}, title = {{Integral points on singular del Pezzo surfaces}}, doi = {10.1017/S1474748022000482}, volume = {23}, year = {2024}, } @article{17447, abstract = {Let F be a diagonal cubic form over Z in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F in regions of diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general F.}, author = {Wang, Victor}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {3}, publisher = {Wiley}, title = {{Special cubic zeros and the dual variety}}, doi = {10.1112/jlms.12975}, volume = {110}, year = {2024}, } @article{17323, abstract = {We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences.}, author = {Browning, Timothy D and Verzobio, Matteo}, issn = {2041-7942}, journal = {Mathematika}, number = {4}, publisher = {London Mathematical Society}, title = {{Strong divisibility sequences and sieve methods}}, doi = {10.1112/mtk.12269}, volume = {70}, year = {2024}, } @article{18064, abstract = { We show that the total number of non-torsion integral points on the elliptic curves ED : y 2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N) −1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family.}, author = {Chan, Yik Tung}, issn = {1090-2082}, journal = {Advances in Mathematics}, number = {11}, publisher = {Elsevier}, title = {{The average number of integral points on the congruent number curves}}, doi = {10.1016/j.aim.2024.109946}, volume = {457}, year = {2024}, } @article{18173, abstract = {Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.}, author = {Glas, Jakob}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {4}, publisher = {London Mathematical Society}, title = {{Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)}}, doi = {10.1112/jlms.12991}, volume = {110}, year = {2024}, } @unpublished{18295, abstract = {By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d.}, author = {Glas, Jakob}, booktitle = {arXiv}, title = {{Canonical singularities on moduli spaces of rational curves via the circle method}}, doi = {10.48550/arXiv.2405.16648}, year = {2024}, } @unpublished{19013, abstract = {We study the singularities of the moduli space of degree e maps from smooth genus g curves to an arbitrary smooth hypersurface of low degree. For e large compared to g, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method.}, author = {Glas, Jakob and Hase-Liu, Matthew }, booktitle = {arXiv}, title = {{Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method}}, doi = {10.48550/arXiv.2412.14923}, year = {2024}, } @article{14687, abstract = {The short history of research on Li-O2 batteries has seen a remarkable number of mechanistic U-turns over the years. From the initial use of carbonate electrolytes, that were then found to be entirely unsuitable, to the belief that (su)peroxide was solely responsible for degradation, before the more reactive singlet oxygen was found to form, to the hypothesis that capacity depends on a competing surface/solution mechanism before a practically exclusive solution mechanism was identified. Herein, we argue for an ever-fresh look at the reported data without bias towards supposedly established explanations. We explain how the latest findings on rate and capacity limits, as well as the origin of side reactions, are connected via the disproportionation (DISP) step in the (dis)charge mechanism. Therefrom, directions emerge for the design of electrolytes and mediators on how to suppress side reactions and to enable high rate and high reversible capacity.}, author = {Jethwa, Rajesh B and Mondal, Soumyadip and Pant, Bhargavi and Freunberger, Stefan Alexander}, issn = {1521-3773}, journal = {Angewandte Chemie International Edition}, keywords = {General Chemistry, Catalysis}, number = {28}, publisher = {Wiley}, title = {{To DISP or not? The far‐reaching reaction mechanisms underpinning Lithium‐air batteries}}, doi = {10.1002/anie.202316476}, volume = {63}, year = {2024}, } @article{13044, abstract = {Singlet oxygen (1O2) formation is now recognised as a key aspect of non-aqueous oxygen redox chemistry. For identifying 1O2, chemical trapping via 9,10-dimethylanthracene (DMA) to form the endoperoxide (DMA-O2) has become the mainstay method due to its sensitivity, selectivity, and ease of use. While DMA has been shown to be selective for 1O2, rather than forming DMA-O2 with a wide variety of potentially reactive O-containing species, false positives might hypothetically be obtained in the presence of previously overlooked species. Here, we first give unequivocal direct spectroscopic proof by the 1O2-specific near infrared (NIR) emission at 1270 nm for the previously proposed 1O2 formation pathways, which centre around superoxide disproportionation. We then show that peroxocarbonates, common intermediates in metal-O2 and metal carbonate electrochemistry, do not produce false-positive DMA-O2. Moreover, we identify a previously unreported 1O2-forming pathway through the reaction of CO2 with superoxide. Overall, we give unequivocal proof for 1O2 formation in non-aqueous oxygen redox and show that chemical trapping with DMA is a reliable method to assess 1O2 formation.}, author = {Mondal, Soumyadip and Jethwa, Rajesh B and Pant, Bhargavi and Hauschild, Robert and Freunberger, Stefan Alexander}, issn = {1364-5498}, journal = {Faraday Discussions}, keywords = {Physical and Theoretical Chemistry}, pages = {175--189}, publisher = {Royal Society of Chemistry}, title = {{Singlet oxygen in non-aqueous oxygen redox: Direct spectroscopic evidence for formation pathways and reliability of chemical probes}}, doi = {10.1039/d3fd00088e}, volume = {248}, year = {2024}, } @unpublished{20071, abstract = {Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over linearly ordered fields in Lean 4. Furthermore, we extend duality theory to the case when some coefficients are allowed to take "infinite values".}, author = {Dvorak, Martin and Kolmogorov, Vladimir}, booktitle = {arXiv}, keywords = {Farkas lemma, linear programming, extended reals, calculus of inductive constructions}, title = {{Duality theory in linear optimization and its extensions -- formally verified}}, doi = {10.48550/arXiv.2409.08119}, year = {2024}, } @article{18307, abstract = {Vaccination is the most effective tool to control infectious diseases. However, the evolution of vaccine resistance, exemplified by vaccine resistance in SARS-CoV-2, remains a concern. Here, we model complex vaccination strategies against a pathogen with multiple epitopes—molecules targeted by the vaccine. We found that a vaccine targeting one epitope was ineffective in preventing vaccine escape. Vaccine resistance in highly infectious pathogens was prevented by the full-epitope vaccine, that is, one targeting all available epitopes, but only when the rate of pathogen evolution was low. Strikingly, a bet-hedging strategy of random administration of vaccines targeting different epitopes was the most effective in preventing vaccine resistance in pathogens with the low rate of infection and high rate of evolution. Thus, complex vaccination strategies, when biologically feasible, may be preferable to the currently used single-vaccine approaches for long-term control of disease outbreaks, especially when applied to livestock with near 100% vaccination rates.}, author = {Rella, Simon and Kulikova, Yuliya A. and Minnegalieva, Aygul and Kondrashov, Fyodor}, issn = {1558-5646}, journal = {Evolution: International journal of organic evolution}, number = {10}, pages = {1722--1738}, publisher = {Oxford University Press}, title = {{Complex vaccination strategies prevent the emergence of vaccine resistance}}, doi = {10.1093/evolut/qpae106}, volume = {78}, year = {2024}, }