KEY PUBLICATIONS IN 2023
- Bárány I, Frankl P: Cells in the box and a hyperplane, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 25:7 pp. 2863-2877. 15 p. (2023)
https://real.mtak.hu/162573/
- Révész SzGy: Oscillation of the Remainder Term in the Prime Number Theorem of Beurling, "Caused by a Given zeta-Zero", INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2023:14 pp. 11752-11790. 39 p. (2023)
https://real.mtak.hu/191438/
- Manolescu C, Marengon M, Sarkar S, Willis M: A generalization of Rasmussen’s invariant, with applications to surfaces in some four-manifolds, DUKE MATHEMATICAL JOURNAL 172:2 pp. 231-311. 81 p. (2023)
https://real.mtak.hu/163239/
- Abért M, Bergeron N, Biringer I, Gelander T: Convergence of normalized Betti numbers in nonpositive curvature, DUKE MATHEMATICAL JOURNAL 172:4 pp. 633-700. 68 p. (2023)
https://real.mtak.hu/163252/
- Fox J, Pach J, Suk A: Sunflowers in set systems of bounded dimension, COMBINATORICA 43 pp. 187-202. 16 p. (2023)
https://real.mtak.hu/163240/
- Berdysheva EE, Révész SzGy: Delsarte’s extremal problem and packing on locally compact Abelian groups, ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 24:2 pp. 1007-1052. 45 p. (2023)
https://real.mtak.hu/191440/
- Napoli L, Sekara V, García-Herranz M, Karsai M: Socioeconomic reorganization of communication and mobility networks in response to external shocks, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 120:50 Paper: 2305285120, 7 p. (2023)
https://real.mtak.hu/191155/
- Ivanov G, Naszódi M: Functional John and Löwner Conditions for Pairs of Log-Concave Functions, INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2023:23 pp. 20613-20669. 57 p. (2023)
https://real.mtak.hu/191949/
- Gerbner D: The profile polytope of nontrivial intersecting families, SIAM JOURNAL ON DISCRETE MATHEMATICS 37:4 pp. 2265-2275. 11 p. (2023)
https://real.mtak.hu/191869/
- Ambrus G, Bárány I, Frankl P, Varga D: Piercing the chessboard, SIAM JOURNAL ON DISCRETE MATHEMATICS 37:3 pp. 1457-1471. 15 p. (2023)
https://real.mtak.hu/134436/
- Benjamini I, Fraczyk M, Kun G: Expander spanning subgraphs with large girth, ISRAEL JOURNAL OF MATHEMATICS 251:1 pp. 156-172. 17 p. (2023)
https://real.mtak.hu/150425/
- Domokos M: Separating monomials for diagonalizable actions, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 55:1 pp. 205-223. 19 p. (2023)
https://real.mtak.hu/191051/
- Bencs F, Borbényi M, Csikvári P: Random Cluster Model on Regular Graphs, COMMUNICATIONS IN MATHEMATICAL PHYSICS 399 pp. 203-248. 46 p. (2023)
https://real.mtak.hu/191052/
- Juhász I, van Mill J, Soukup L, Szentmiklóssy Z: The double density spectrum of a topological space, ISRAEL JOURNAL OF MATHEMATICS 255 pp. 383-400. 18 p. (2023)
https://real.mtak.hu/191921/
- Cavallo A, Stipsicz AI: Traces of links and simply connected 4-manifolds, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 55:1 pp. 321-337. 17 p. (2023)
https://real.mtak.hu/191926/
- Grósz D, Methuku A, Tompkins C: Ramsey numbers of Boolean lattices, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 55:2 pp. 914-932. 19 p. (2023)
https://real.mtak.hu/162654/
- Bárány I, Kalai G, Pór A: Universal sequences of lines in Rd, ISRAEL JOURNAL OF MATHEMATICS 256 pp. 35-60. 26 p. (2023)
https://real.mtak.hu/162686/
- Zhu X, Győri E, He Z, Lv Z, Salia N, Xiao C: Stability version of Dirac's theorem and its applications for generalized Turán problems, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 55:4 pp. 1857-1873. 17 p. (2023)
https://real.mtak.hu/162689/
- Gong S, Marengon M: Nonorientable link cobordisms and torsion order in Floer homologies, ALGEBRAIC AND GEOMETRIC TOPOLOGY 23 pp. 2627-2672. 46 p. (2023)
https://real.mtak.hu/163243/
- Alon N, Gujgiczer A, Körner J, Milojević A, Simonyi G: Structured Codes of Graphs, SIAM JOURNAL ON DISCRETE MATHEMATICS 37:1 pp. 379-403. 25 p. (2023)
https://real.mtak.hu/191871/
- Berkes I, Borda B: Random walks on the circle and Diophantine approximation, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY 108:2 pp. 409-440. 32 p. (2023)
https://real.mtak.hu/191456/
OUTSTANDING ACHIEVEMENTS IN 2023
Unbiased phase estimation and improved quantum tomography
Quantum algorithms are known to provide modest speedups for a wide range of optimization problems, and one of the original motivations for the paper was to improve the running time of interior-point-method-based quantum optimization algorithms that are applicable to a variety of linear, semidefinite and convex programs. The improvements are obtained by revisiting and improving a fundamental quantum primitive known as quantum phase estimation, which is at the core of many quantum algorithms including Shor's quantum algorithm for factorization, that breaks much of modern cryptography. The devised improvement in phase estimation is to make the estimator continuous, unbiased, and symmetrically distributed around the phase to be estimated (see green line on figure 1) – this is in contrast to vanilla phase estimation where the distribution is discrete, non-symmetric, and typically slightly biased (see red dots on the figure 1). More generally the paper develops several improved quantum algorithmic techniques for phase, state, and expectation value estimation tasks. Such tasks are central in problems where quantum algorithms offer speedups, because quantum computers naturally and natively operate with quantum states. On a high level this work is part of a wider research direction incentivizing the native processing of quantum information by avoiding quantum-classical conversions as much as possible and thereby removing unnecessary overheads in quantum information processing.
Figure 1: Estimating the (unknown) phase pi/12 using conventional quantum phase estimation with 3 (qu)bits of precision and the resulting discrete distribution (red dots) vs. using the new continuous, unbiased and symmetric estimation method (continuous green line).
A generalization of Rasmussen's invariant, with applications to surfaces
in some four-manifolds
The objects we see every day have three fundamentally distinct, or "independent", directions we call them width, height, and depth. At first it sounds unnatural and confusing to consider four dimensions, after Einstein’s work it became clear that the "space-time" in which we live is intrinsically a 4-dimensional object, whose shape we do not fully understand. Many questions about 4-dimensional shapes are still far from a complete answer: for example, it is still unknown if the simplest 4-dimensional shape (called the 4-sphere) has any "exotic" siblings, that is shapes that look very similar to it, but which are in reality subtly different.
With the goal of constructing exotic 4-spheres, Gluck introduced in 1962 a technique known as "Gluck twist": this produced a large family of 4-dimensional shapes that look like the 4-sphere. In certain cases, it is known that Gluck's construction produces the standard 4-sphere, but in all other cases we simply don't know if the Gluck twist produces an exotic 4-sphere.
In 2009 researchers Freedman, Gompf, Morrison, and Walker proposed a possible method which could tell one of those examples apart from the standard 4-sphere. Their method is based on knot theory: to any potentially exotic 4-sphere one can associate a knot, like the one in the figure 2. In turn, given any knot, one can associate a number to it, known as its s invariant, which can be found using a computer. Freedman, Gompf, Morrison, and Walker noted that if the s invariant of such a knot is non-zero, then the 4-dimensional shape must be a truly exotic 4-sphere! They tried this approach on two examples of Gluck’s construction, but the s invariant they got was always zero, so nothing could be concluded.
In the paper “A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds”, Manolescu, Marengon, Sarkar, and Willis provide a conceptual reason for the failure of this approach: they show that if a potentially exotic 4-sphere is constructed using Gluck’s method, then its associated knot will always have vanishing s invariant. This implies that in order to detect an exotic 4-sphere we must either use a different construction from Gluck’s one, or use a strategy different from the one proposed by Freedman, Gompf, Morrison, and Walker to detect exotic spheres.
Figure 2: The figure shows a complicated knot from Freedman-Gompf-Morrison-Walker’s paper. If its s invariant were non-zero, then it would yield an exotic 4-sphere. However, the paper of Manolescu, Marengon, Sarkar, and Willis gives a conceptual reason why its s invariant (along with that of many other examples) cannot work.