Overview Lines Highlights Members Publications

 

Highlights

These are some achievements reached by our group since 2014:

• Contribution to a unification of the theory of Gowers norms with the theory of Host-Kra seminorms.
Source: [LINK] P. Candela and B. Szegedy. Nilspace factors for general uniformity seminorms, cubic exchangeability and limits. Mem. Amer. Math. Soc., to appear.

• Extension of the Host-Kra Ergodic Structure Theorem to actions of nilpotent groups.
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.

• Full solution of the lattice point problem for rational paraboloids.
Source: [LINK] F. Chamizo and C. Pastor. Lattice points in elliptic paraboloids. Publ. Mat., 63(1):343-360, 2019.

• Complete characterization of the Hölder exponents and the spectra of singularities of fractional integrals of modular forms.
Source: [LINK] C. Pastor. On the regularity of fractional integrals of modular forms. Trans. Amer. Math. Soc., 372(2):829-857, 2019.

• A uniqueness result for the quasi-geostrophic equation.
Source: [LINK] A. Córdoba, D. Córdoba, and F. Gancedo. Uniqueness for SQG patch solutions. Trans. Amer. Math. Soc. Ser. B, 5:1-31, 2018.

• The translates of the volume measure of a submanifold tends to volume measure of the space in certain semisimple homogeneous spaces, under some hypotheses.
Source: [LINK] A. Ubis. Effective equidistribution of translates of large submanifolds in semisimple homogeneous spaces. Int. Math. Res. Not. IMRN, (18):5629-5666, 2017.

• Effective finiteness of the Carmichael numbers in certain exponential sequences.
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.

• Precise bounds for the mixed norms of singular integral operators.
Source: [LINK] A. Córdoba. Singular integrals, maximal functions and Fourier restriction to spheres: the disk multiplier revisited. Adv. Math., 290:208-235, 2016.

• Extension of the Rokhlin lemma in ergodic theory to several commuting non invertible transformations.
Source: [LINK] A. Avila and P. Candela. Towers for commuting endomorphisms, and combinatorial applications. Ann. Inst. Fourier (Grenoble), 66(4):1529-1544, 2016.

• Proof of an old conjecture by Erdös and Rényi about random graphs.
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.

• A new simpler statement of the Kuznetsov formula.
Source: [LINK] F. Chamizo and D. Raboso. On the Kuznetsov formula. J. Funct. Anal., 268(4):869-886, 2015.

• A pointwise inequality for the fractional calculus with applications.
Source: [LINK] A. Córdoba and Á. D. Martínez. A pointwise inequality for fractional Laplacians. Adv. Math., 280:79-85, 2015.

• Ergodic properties of certain flows at prime times.
Source: [LINK] P. Sarnak and A. Ubis. The horocycle flow at prime times. J. Math. Pures Appl. (9), 103(2):575-618, 2015.

• Proof of the multifractal nature of some special Fourier series.
Source: [LINK] F. Chamizo and A. Ubis. Multifractal behavior of polynomial Fourier series. Adv. Math., 250:1-34, 2014.

• Construction of Sidon and B_h sequences with small growth.
Source: [LINK] J. Cilleruelo. Infinite Sidon sequences. Adv. Math., 255:474-486, 2014.

• A form of the cone multiplier theorem for lacunary directions.
Source: [LINK] A. Córdoba and K. M. Rogers. Weighted estimates for conic Fourier multipliers. Math. Z., 278(1-2):431-440, 2014.

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)
  1. [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.

  2. [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.

  3. [LINK] A. Backhausz and B. Szegedy. Action convergence of operators and graphs. Canad. J. Math., 74(1):72-121, 2022.

  4. [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.

  5. [LINK] F. Chamizo and J. Jiménez-Urroz. Extendable orthogonal sets of integral vectors. Res. Math. Sci., 9(4):Paper No. 59, 13, 2022.

  6. [LINK] Á. D. Martínez and F. Torres~de Lizaur. Distribution symmetry of toral eigenfunctions. Rev. Mat. Iberoam., 38(4):1371-1382, 2022.

  7. [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.

  8. [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.

  9. [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.

  10. [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.

  11. [LINK] P. Candela, D. González-Sánchez, and B. Szegedy. On nilspace systems and their morphisms. Ergodic Theory Dynam. Systems, 40(11):3015-3029, 2020.

  12. [LINK] F. Chamizo, A. Córdoba, and A. Ubis. Fourier series in BMO with number theoretical implications. Math. Ann., 376(1-2):457-473, 2020.

  13. [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.

  14. [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.

  15. [LINK] F. Chamizo and C. Pastor. Lattice points in elliptic paraboloids. Publ. Mat., 63(1):343-360, 2019.

  16. [LINK] C. Pastor. On the regularity of fractional integrals of modular forms. Trans. Amer. Math. Soc., 372(2):829-857, 2019.

  17. [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.

  18. [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.

  19. [LINK] D. Alonso-Orán, A. Córdoba, and Á. D. Martínez. Integral representation for fractional Laplace-Beltrami operators. Adv. Math., 328:436-445, 2018.

  20. [LINK] A. Córdoba, D. Córdoba, and F. Gancedo. Uniqueness for SQG patch solutions. Trans. Amer. Math. Soc. Ser. B, 5:1-31, 2018.

  21. [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.

  22. [LINK] J. Cilleruelo. A greedy algorithm for B_h[g] sequences. J. Combin. Theory Ser. A, 150:323-327, 2017.

  23. [LINK] A. Ubis. Effective equidistribution of translates of large submanifolds in semisimple homogeneous spaces. Int. Math. Res. Not. IMRN, (18):5629-5666, 2017.

  24. [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.

  25. [LINK] A. Córdoba. Singular integrals, maximal functions and Fourier restriction to spheres: the disk multiplier revisited. Adv. Math., 290:208-235, 2016.

  26. [LINK] F. Chamizo and D. Raboso. On the Kuznetsov formula. J. Funct. Anal., 268(4):869-886, 2015.

  27. [LINK] J. Cilleruelo. On Sidon sets and asymptotic bases. Proc. Lond. Math. Soc. (3), 111(5):1206-1230, 2015.

  28. [LINK] J. Cilleruelo and R. Tesoro. Dense infinite B_h sequences. Publ. Mat., 59(1):55-73, 2015.

  29. [LINK] A. Córdoba and Á. D. Martínez. A pointwise inequality for fractional Laplacians. Adv. Math., 280:79-85, 2015.

  30. [LINK] P. Sarnak and A. Ubis. The horocycle flow at prime times. J. Math. Pures Appl. (9), 103(2):575-618, 2015.

 
nom3