Theresa C. Anderson

Assistant Professor of Mathematics, Purdue

Research

I will be moving to Carnegie Mellon as of July 1!  New contact info listed.

My interests are in both harmonic analysis and number theory and particularly their interplay. Some recent work has been in discrete variants of objects and tools from harmonic analysis, lattice point counting including distribution of prime vectors on surfaces, structure theorems in harmonic analysis, and development of Fourier analytic methods in arithmetic statistics.

Funding:

I am funded by NSF DMS 1954407, funded jointly by Analysis DMS and by Algebra and Number Theory DMS (50 percent funding by each group) (2020-2023).  Previously I had NSF DMS 1502464 (2015-2019).


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Publications and preprints:

Anderson, Theresa C., Bhargava, Manjul and Thorne, Frank.  Field counting via Fourier Analysis.  Preprint.

Anderson, Theresa C., Gafni, Ayla, Lemke Oliver, Robert, Lowry-Duda, David, Shakan, George, and Zhang, Ruixiang. Quantitative Hilbert Irreducility and almost prime values of polynomial discriminants. To appear in Int. Math. Res. Not. IMRN.

Anderson, Theresa C., Travesset, Chiara and Veltri, Joey. A structure theorem for weight and function classes with coprime bases. To appear in Quarterly Journal of Math.

Anderson, Theresa C. Discrete multilinear maximal functions and number theory.  Submitted.

Anderson, Theresa C. and Hu, Bingyang. A structure theorem for measures with different bases.  To appear in Jounral of Mathematical Analysis and Applications.

Anderson, Theresa C. and Hu, Bingyang. Sharp Mei's lemma for different bases. To appear in Results in Mathematics.

Anderson, Theresa C. and Hu, Bingyang. Dyadic analysis meets number theory. To appear in IMRN.

Anderson, Theresa C., Kumchev, A. V. and Palsson, E.A. Discrete maximal functions over surfaces of higher codimension.  To appear in La Matematica (Journal of the AWM).

Anderson, Theresa C. and Hu, Bingyang.  On the general dyadic grids in R^d.  Submitted.  Preprint available on arXiv.

Anderson, Theresa C. Hu, Bingyang, and Roos, Joris.  Sparse bounds for discrete singular Radon transforms.  Submitted.  Colloq. Math. 165 (2021), no. 2, 199–217

Anderson, Theresa C. and Palsson, E.A..  Bounds for discrete multilinear spherical maximal operators in higher dimensionsBull. Lond. Math. Soc.. 53 (2021), no. 3, 855–860.

Anderson, Theresa C. and Palsson, E.A..  Bounds for discrete multilinear spherical maximal operators.  Submitted.  To appear in Collectanea Mathematica.

Anderson, Theresa C., Hughes, Kevin, Roos, Joris, and Seeger, Andreas.  $L^p \to L^q$ bounds for spherical maximal operatorsMath Zeitschrift 297 (2021), no. 3-4, 1057–1074.

Anderson, Theresa C. Quantitative $l^p$ improving for discrete spherical averages along the primesJ. 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 Calder\'on-Zygmund operators in general function spaces by sparse domination.  Proc. Edinb. Math. Soc. (2) 63 (2020), no. 1, 229--247.

Anderson, Theresa C., Cladek, Laura, Pramanik, Malabika, and Seeger, Andreas.  Spherical means on the Heisenberg group: stability of a maximal function estimate.  To appear in J. d'Analyse Math.

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., Cook, Brian, Hughes, Kevin, and Kumchev, Angel.  On the Ergodic Waring-Goldbach Problem.  Journal of Functional Analysis, Volume 282, Issue 5, 1 March 2022, 109334.

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, 31pages 263286 (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. To appear in Analysis Matematica(pdf)

Anderson, Theresa C.  A framework for Calder\'on-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.  (pdf)

Anderson, Theresa C., Cruz-Uribe SFO, David and Moen, Kabe. Logarithmic bump conditions for Calderón-Zygmund Operators on spaces of homogeneous typePublicacions Mathematiques 59(1), 2015. (pdf)

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.(pdf)

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. (pdf)

Anderson, Theresa C., Rolen, Larry, and Stoehr, Ruth E., Benford's Law for Coefficients of Modular Forms and Partition FunctionsProceedings of the American Mathematical Society. 139 (2011) 1533-1541. (pdf)