Highlights
These are some achievements reached by our group since 2014:
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Contribution to a unification of the theory of Gowers norms with the theory of Host-Kra seminorms.
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Source:
[LINK] P. Candela and B. Szegedy.
Nilspace factors for general uniformity seminorms, cubic exchangeability and limits.
Mem. Amer. Math. Soc., to appear.
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Extension of the Host-Kra Ergodic Structure Theorem to actions of nilpotent groups.
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Source:
[LINK] P. Candela, D. González-Sánchez, and B. Szegedy.
On nilspace systems and their morphisms.
Ergodic Theory Dynam. Systems, 40(11):3015-3029, 2020.
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Full solution of the lattice point problem for rational paraboloids.
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Source:
[LINK] F. Chamizo and C. Pastor.
Lattice points in elliptic paraboloids.
Publ. Mat., 63(1):343-360, 2019.
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Complete characterization of the Hölder exponents and the spectra of singularities of fractional integrals of modular forms.
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Source:
[LINK] C. Pastor.
On the regularity of fractional integrals of modular forms.
Trans. Amer. Math. Soc., 372(2):829-857, 2019.
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A uniqueness result for the quasi-geostrophic equation.
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Source:
[LINK] A. Córdoba, D. Córdoba, and F. Gancedo.
Uniqueness for SQG patch solutions.
Trans. Amer. Math. Soc. Ser. B, 5:1-31, 2018.
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The translates of the volume measure of a submanifold tends to volume measure of the space in certain semisimple homogeneous spaces, under some hypotheses.
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Source:
[LINK] A. Ubis.
Effective equidistribution of translates of large submanifolds in
semisimple homogeneous spaces.
Int. Math. Res. Not. IMRN, (18):5629-5666, 2017.
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Effective finiteness of the Carmichael numbers in certain exponential sequences.
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Source:
[LINK] J. Cilleruelo, F. Luca, and A. Pizarro-Madariaga.
Carmichael numbers in the sequence (2^nk+1)_{n\geq 1}.
Math. Comp., 85(297):357-377, 2016.
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Precise bounds for the mixed norms of singular integral operators.
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Source:
[LINK] A. Córdoba.
Singular integrals, maximal functions and Fourier restriction to
spheres: the disk multiplier revisited.
Adv. Math., 290:208-235, 2016.
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Extension of the Rokhlin lemma in ergodic theory to several commuting non invertible transformations.
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Source:
[LINK] A. Avila and P. Candela.
Towers for commuting endomorphisms, and combinatorial applications.
Ann. Inst. Fourier (Grenoble), 66(4):1529-1544, 2016.
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Proof of an old conjecture by Erdös and Rényi about random graphs.
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Source:
[LINK] M. Noy, V. Ravelomanana, and J. Rué.
On the probability of planarity of a random graph near the critical
point.
Proc. Amer. Math. Soc., 143(3):925-936, 2015.
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A new simpler statement of the Kuznetsov formula.
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Source:
[LINK] F. Chamizo and D. Raboso.
On the Kuznetsov formula.
J. Funct. Anal., 268(4):869-886, 2015. |
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A pointwise inequality for the fractional calculus with applications.
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Source:
[LINK] A. Córdoba and Á. D. Martínez.
A pointwise inequality for fractional Laplacians.
Adv. Math., 280:79-85, 2015.
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Ergodic properties of certain flows at prime times.
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Source:
[LINK] P. Sarnak and A. Ubis.
The horocycle flow at prime times.
J. Math. Pures Appl. (9), 103(2):575-618, 2015.
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Proof of the multifractal nature of some special Fourier series.
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Source:
[LINK] F. Chamizo and A. Ubis.
Multifractal behavior of polynomial Fourier series.
Adv. Math., 250:1-34, 2014. |
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Construction of Sidon and B_h sequences with small growth.
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Source:
[LINK] J. Cilleruelo.
Infinite Sidon sequences.
Adv. Math., 255:474-486, 2014.
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A form of the cone multiplier theorem for lacunary directions.
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Source:
[LINK] A. Córdoba and K. M. Rogers.
Weighted estimates for conic Fourier multipliers.
Math. Z., 278(1-2):431-440, 2014.
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Q1 papers
This is a list of Q1 publications during the periods 2015-2017, 2018-2020 and 2021-2024 covered by the grants MTM2014-56350-P, MTM2017-83496-P and PID2020-113350GB-I00, respectively (updated until 2022)
- [LINK] D. Alonso-Orán, Y. Miao, and H. Tang.
Global existence, blow-up and stability for a stochastic transport
equation with non-local velocity.
J. Differential Equations, 335:244-293, 2022.
- [LINK] D. Alonso-Orán and J. J. L. Velázquez.
Boundary value problems for two dimensional steady incompressible
fluids.
J. Differential Equations, 307:211-249, 2022.
- [LINK] A. Backhausz and B. Szegedy.
Action convergence of operators and graphs.
Canad. J. Math., 74(1):72-121, 2022.
- [LINK] P. Candela and B. Szegedy.
Regularity and inverse theorems for uniformity norms on compact
abelian groups and nilmanifolds.
J. Reine Angew. Math., 789:1-42, 2022.
- [LINK] F. Chamizo and J. Jiménez-Urroz.
Extendable orthogonal sets of integral vectors.
Res. Math. Sci., 9(4):Paper No. 59, 13, 2022.
- [LINK] Á. D. Martínez and F. Torres~de Lizaur.
Distribution symmetry of toral eigenfunctions.
Rev. Mat. Iberoam., 38(4):1371-1382, 2022.
- [LINK] D. Alonso-Orán, C. Rohde, and H. Tang.
A local-in-time theory for singular SDEs with applications to
fluid models with transport noise.
J. Nonlinear Sci., 31(6):Paper No. 98, 55, 2021.
- [LINK] A. Farina and J. Ocáriz.
Splitting theorems on complete Riemannian manifolds with
nonnegative Ricci curvature.
Discrete Contin. Dyn. Syst., 41(4):1929-1937, 2021.
- [LINK] Á. D. Martínez and D. Spector.
An improvement to the John-Nirenberg inequality for functions in
critical Sobolev spaces.
Adv. Nonlinear Anal., 10(1):877-894, 2021.
- [LINK] D. Alonso-Orán, A. Bethencourt de León, D. D. Holm, and S. Takao.
Modelling the climate and weather of a 2D Lagrangian-averaged
Euler-Boussinesq equation with transport noise.
J. Stat. Phys., 179(5-6):1267-1303, 2020.
- [LINK] P. Candela, D. González-Sánchez, and B. Szegedy.
On nilspace systems and their morphisms.
Ergodic Theory Dynam. Systems, 40(11):3015-3029, 2020.
- [LINK] F. Chamizo, A. Córdoba, and A. Ubis.
Fourier series in BMO with number theoretical implications.
Math. Ann., 376(1-2):457-473, 2020.
- [LINK] F. Chamizo, E. A. Gallardo-Gutiérrez, M. Monsalve-López, and A. Ubis.
Invariant subspaces for Bishop operators and beyond.
Adv. Math., 375:107365, 25, 2020.
- [LINK] D. Alonso-Orán and A. Bethencourt de León.
Stability, well-posedness and blow-up criterion for the
incompressible slice model.
Phys. D, 392:99-118, 2019.
- [LINK] F. Chamizo and C. Pastor.
Lattice points in elliptic paraboloids.
Publ. Mat., 63(1):343-360, 2019.
- [LINK] C. Pastor.
On the regularity of fractional integrals of modular forms.
Trans. Amer. Math. Soc., 372(2):829-857, 2019.
- [LINK] D. Alonso-Orán, A. Córdoba, and Á. D. Martínez.
Continuity of weak solutions of the critical surface quasigeostrophic
equation on S^2.
Adv. Math., 328:264-299, 2018.
- [LINK] D. Alonso-Orán, A. Córdoba, and Á. D. Martínez.
Global well-posedness of critical surface quasigeostrophic equation
on the sphere.
Adv. Math., 328:248-263, 2018.
- [LINK] D. Alonso-Orán, A. Córdoba, and Á. D. Martínez.
Integral representation for fractional Laplace-Beltrami
operators.
Adv. Math., 328:436-445, 2018.
- [LINK] A. Córdoba, D. Córdoba, and F. Gancedo.
Uniqueness for SQG patch solutions.
Trans. Amer. Math. Soc. Ser. B, 5:1-31, 2018.
- [LINK] F. Chamizo and A. González-Arroyo.
Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and
its connection to number theory.
J. Phys. A, 50(26):265401, 17, 2017.
- [LINK] J. Cilleruelo.
A greedy algorithm for B_h[g] sequences.
J. Combin. Theory Ser. A, 150:323-327, 2017.
- [LINK] A. Ubis.
Effective equidistribution of translates of large submanifolds in
semisimple homogeneous spaces.
Int. Math. Res. Not. IMRN, (18):5629-5666, 2017.
- [LINK] J. Cilleruelo, F. Luca, and A. Pizarro-Madariaga.
Carmichael numbers in the sequence (2^nk+1)_{n\geq 1}.
Math. Comp., 85(297):357-377, 2016.
- [LINK] A. Córdoba.
Singular integrals, maximal functions and Fourier restriction to
spheres: the disk multiplier revisited.
Adv. Math., 290:208-235, 2016.
- [LINK] F. Chamizo and D. Raboso.
On the Kuznetsov formula.
J. Funct. Anal., 268(4):869-886, 2015.
- [LINK] J. Cilleruelo.
On Sidon sets and asymptotic bases.
Proc. Lond. Math. Soc. (3), 111(5):1206-1230, 2015.
- [LINK] J. Cilleruelo and R. Tesoro.
Dense infinite B_h sequences.
Publ. Mat., 59(1):55-73, 2015.
- [LINK] A. Córdoba and Á. D. Martínez.
A pointwise inequality for fractional Laplacians.
Adv. Math., 280:79-85, 2015.
- [LINK] P. Sarnak and A. Ubis.
The horocycle flow at prime times.
J. Math. Pures Appl. (9), 103(2):575-618, 2015.