My interests are in both harmonic analysis and number theory and particularly their interplay. Some recent work has been in discrete (number theoretic) tools in harmonic analysis, lattice point counting on surfaces, structure theorems in harmonic analysis, and development of Fourier analytic methods in arithmetic statistics.
Current Funding
I am funded by both NSF CAREER DMS 2237937 and NSF DMS 2231990 jointly in Analysis and Number Theory.
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Publications and preprints
Anderson, Theresa C., Bertilli, Adam, and O’Dorney, Evan M. Galois groups of reciprocal polynomials
and the van der Waerden-Bhargava theorem. Preprint on arXiv.
Anderson, Theresa C., Bellah, E., Markman, Z., Pollard, T. and Zeitlin, J. Arbitrary finite intersections of doubling measures and applications. To appear in Journal of Functional Analysis.
Anderson, Theresa C., Maldague, Dominique, Pierce, Lillian, and Yung, Po-Lam. On polynomial Carleson operators along quadratic hypersurfaces. To appear in Journal of Geometric Analysis.
Anderson, Theresa C., Lehrback, Juha, Mudarra, Carlos, and Vahäkangas, Antti. Weakly porous sets and
Muckenhoupt $A_p$ distance functions. To appear in Journal of Functional Analysis.
Anderson, Theresa C. Having children at critical career stages and flourishing. To appear in Notices of the AMS.
Anderson, Theresa C., Gafni, Ayla, Hughes, Kevin, Lemke Oliver, Robert, Lowry-Duda, David, Thorne, Frank, Wang, Jiuya and Zhang, Ruixiang. Improved bounds on number fields of small degree. To appear in Discrete Analysis.
Anderson, Theresa C. Discrete multilinear maximal functions and number theory. To appear in Illinois Journal of Math.
Anderson, Theresa C., Kumchev, Angel V. and Palsson, Eyvindur A. A framework for discrete bilinear spherical averages and applications to $\ell^p$-improvng. To appear in Colloq. Math.
Anderson, Theresa C., Hu, BIngyang, Liu, Yu-Ru, and Talmage, Alan. Bounds on tenth moments of (x, x3)
for ellipsephic sets. To appear in Contemporary Mathematics.
Anderson, Theresa C. and Hu, Bingyang. On the general dyadic grids in $R^d$. Canadian Journal of Math 75(2023), no.4, 1147–1175.
Anderson, Theresa C., Gafni, Ayla, Lemke Oliver, Robert, Lowry-Duda, David, Shakan, George, and Zhang, Ruixiang. Quantitative Hilbert Irreducibility and almost prime values of polynomial discriminants. Int. Math. Res. Not. IMRN 2023, no. 3, 2188-2214.
Anderson, Theresa C. and Hu, Bingyang. A structure theorem on intersections of general doubling measures and its applications. Int. Math. Res. Not. IMRN (2023), no.9, 7423–7485.
Anderson, Theresa C., Travesset, Chiara and Veltri, Joey. A structure theorem for weight and function classes with coprime bases. Quarterly Journal of Math 74(2023), no.2, 459–470..
Anderson, Theresa C., Kumchev, A. V. and Palsson, E.A. Discrete maximal functions over surfaces of higher codimension. Matematica 1 (2022), no. 2, 442–479.
Anderson, Theresa C., Cook, Brian, Hughes, Kevin, and Kumchev, Angel. On the Ergodic Waring-Goldbach Problem. J. Funct. Anal. 282 (2022), no. 5, Paper No. 109334, 39 pp.
Anderson, Theresa C. and Hu, Bingyang. Sharp Mei’s lemma for different bases. Results Math. 77 (2022), no. 2, Paper No. 69, 18 pp.
Anderson, Theresa C. and Hu, Bingyang. A structure theorem for measures with different bases. J. Math. Anal. Appl. 505 (2022), no. 1, Paper No. 125620, 11 pp.
Anderson, Theresa C. and Palsson, E.A.. Bounds for discrete multilinear spherical maximal operators. Collect. Math. 73 (2022), no. 1, 75–87.
Anderson, Theresa C. and Palsson, E.A.. Bounds for discrete multilinear spherical maximal operators in higher dimensions. Bull. Lond. Math. Soc.. 53 (2021), no. 3, 855–860.
Anderson, Theresa C., Hughes, Kevin, Roos, Joris, and Seeger, Andreas. $L^p \to L^q$ bounds for spherical maximal operators. Math Zeitschrift 297 (2021), no. 3-4, 1057–1074.
Anderson, Theresa C., Cladek, Laura, Pramanik, Malabika, and Seeger, Andreas. Spherical means on the Heisenberg group: stability of a maximal function estimate. J. Anal. Math. 145 (2021), no. 1, 1–28.
Anderson, Theresa C. Hu, Bingyang, and Roos, Joris. Sparse bounds for discrete singular Radon transforms. Colloq. Math. 165 (2021), no. 2, 199–217
Anderson, Theresa C. Quantitative $l^p$ improving for discrete spherical averages along the primes. J. Fourier Anal. Appl. 26 (2020), no. 2, Paper No. 32, 12 pp
Anderson, Theresa C., Hu, Bingyang, Jiang, Liwei, Olson, Connor, and Wei, Zeyu. On the translates of general dyadic systems on $\R$. Mathematische Annalen, 377(3), 911-933.
Anderson, Theresa C. and Hu, Bingyang. A unified method for maximal truncated Calderón-Zygmund operators in general function spaces by sparse domination. Proc. Edinb. Math. Soc. (2) 63 (2020), no. 1, 229–247.
Anderson, Theresa C., Cook, Brian, Hughes, Kevin, and Kumchev, Angel. Improved l^p boundedness for Integral k-Spherical Maximal Functions. Discrete Analysis, May 29, 2018. (pdf)
Anderson, Theresa C. and Weirich, David E. A Dyadic Gehring Inequality and Applications. New York Journal of Math, Volume 24, 2018. (pdf)
Anderson, Theresa C., Cruz-Uribe OFS, David, and Moen, Kabe. Extrapolation in the scale of generalized reverse Hölder weights. Rev. Math Complutense, 31, pages 263–286 (2018). (pdf)
Anderson, Theresa C., Hytonen, Tuomas and Tapiola, Olli. Weak A-infinity weights and weak reverse Hölder property in a Space of Homogeneous Type. J. Geom. Anal. 27 (2017), no. 1, 95–119. (pdf)
Anderson, Theresa C. and Damián, Wendolín. Calderón-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities. Analysis Math 48 (2022), no. 4, 939–959..
Anderson, Theresa C. A framework for Calderón-Zygmund operators on Spaces of Homogeneous Type. PhD thesis, Brown University, 2015. See above for a copy.
Anderson, Theresa C. A new sufficient two-weighted bump assumption for $L^p$ boundedness of Calderón-Zygmund operators. Proceedings of the AMS, Volume 143, Number 8, August 2015, Pages 3573–3586.
Anderson, Theresa C., Cruz-Uribe SFO, David and Moen, Kabe. Logarithmic bump conditions for Calderón-Zygmund Operators on spaces of homogeneous type. Publicacions Mathematiques 59(1), 2015.
Anderson, Theresa C. and Vagharshakyan, Armen. A simple proof of the sharp weighted estimate for Calderon-Zygmund operators on homogeneous spaces. Journal of Geometric Analysis. July 2014, Volume 24, Issue 3, pp 1276-1297.
Anderson, Theresa C. and Marí-Beffa, Gloria. A completely integrable flow of star-shaped curves on the light cone in Lorenzian $R^4$. J. Phys. A: Math.Theor. 44 (2011) 445203. *Featured in IOP select http://Select.iop.org.
Anderson, Theresa C., Rolen, Larry, and Stoehr, Ruth E., Benford’s Law for Coefficients of Modular Forms and Partition Functions. Proceedings of the American Mathematical Society. 139 (2011) 1533-1541.