{"id":33,"date":"2022-08-26T11:27:01","date_gmt":"2022-08-26T11:27:01","guid":{"rendered":"https:\/\/press.math.cmu.edu\/anderson\/?page_id=33"},"modified":"2026-08-26T14:40:06","modified_gmt":"2026-08-26T14:40:06","slug":"research","status":"publish","type":"page","link":"https:\/\/faculty.math.cmu.edu\/anderson\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n

I build bridges in mathematics and beyond, with a particular eye to connecting things in new ways. My mathematical research is broad, encompassing both harmonic analysis and number theory and especially their interplay. Some recent work has been in discrete (number theoretic) tools in harmonic analysis, expanding framework in harmonic analysis, and bringing Fourier analytic methods to arithmetic statistics. I have had a large number of collaborators, including undergraduates, and am passionate about improving infrastructure, communicating science, and inspiring others to pursue STEM.<\/p>\n\n\n\n

Current Funding<\/h3>\n\n\n\n

I am funded by NSF CAREER DMS 2237937 jointly in Analysis and Number Theory.<\/p>\n\n\n\n

\n\n\n\n

Curriculum Vitae<\/h3>\n\n\n\n

Download Curriculum Vitae<\/a><\/p>\n\n\n\n

\n\n\n\n

Publications and preprints<\/h3>\n\n\n\n

Anderson, Theresa C., Chow, Sam, Dietmann, Rainer, Hokken, David, Koymans, Peter and Lemke Oliver,
Robert J. The strong form of Van der Waerden\u2019s conjecture via twisted Chowla. Preprint on
arXiv.<\/p>\n\n\n\n

Anderson, Theresa C. and O\u2019Dorney, Evan M. Galois groups of reciprocal polynomials II: Twisted reciprocal
polynomials . Submitted. Preprint on arXiv.<\/p>\n\n\n\n

Anderson, Theresa C., Asarhasa, Ufuoma V., Bertelli, Adam, O\u2019Dorney, Evan M., and Gundlach, Fabian. The structure of the double discriminant. Submitted. Preprint on arXiv.<\/p>\n\n\n\n

Anderson, Theresa C. and O\u2019Dorney, Evan M. Galois groups of random integer matrices. To appear in Mathematical Proceedings of the Cambridge Philosophical Society<\/em>.<\/p>\n\n\n\n

Anderson, Theresa C. and Lemke Oliver, Robert J. Appendix to: Kim, Elena. Characterizing the support of
semiclassical measures for higher-dimensional cat maps. To appear in Analysis and PDE<\/em>.<\/p>\n\n\n\n

Anderson, Theresa C., Phillips, David, Rudenko, Anastasiia, and You, Kevin. Infinite intersections
of doubling measures, weights, and function classes. Research in the Mathematical Sciences<\/em> (2026), no. 2,
Paper No. 29, 21 pp.<\/p>\n\n\n\n

Anderson, Theresa C., Bertelli, Adam, and O\u2019Dorney, Evan M. Galois groups of reciprocal polynomials
and the van der Waerden-Bhargava theorem. Algebra and Number Theory 20 (2026), no. 3, 602-628<\/em>.<\/p>\n\n\n\n

Anderson, Theresa C., Bellah, E., Markman, Z., Pollard, T. and Zeitlin, J. Arbitrary finite intersections of doubling measures and applications. Journal of Functional Analysis<\/em> 287 (2024), no. 9, Paper No. 110573, 35 pp.<\/p>\n\n\n\n

Anderson, Theresa C., Maldague, Dominique, Pierce, Lillian, and Yung, Po-Lam. On polynomial Carleson operators along quadratic hypersurfaces. Journal of Geometric Analysis<\/em> 34 (2024), no. 10, Paper No. 321, 47 pp.<\/p>\n\n\n\n

Anderson, Theresa C., Lehrback, Juha, Mudarra, Carlos, and Vah\u00e4kangas, Antti. Weakly porous sets and
Muckenhoupt $A_p$ distance functions. Journal of Functional Analysis<\/em> 287 (2024), no. 8, Paper No. 110558,
34 pp.<\/p>\n\n\n\n

Anderson, Theresa C. Having children at critical career stages and flourishing. Notices of the AMS<\/em>, August 2024.<\/p>\n\n\n\n

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. Discrete Analysis<\/em> 2024 Paper No. 19, 24 pp.<\/p>\n\n\n\n

Anderson, Theresa C. Discrete multilinear maximal functions and number theory.\u00a0 Illinois Journal of Math <\/em>67 (2023), no. 3, 443\u2013456.<\/p>\n\n\n\n

Anderson, Theresa C., Kumchev, Angel V. and Palsson, Eyvindur A.\u00a0 A framework for discrete bilinear spherical averages and applications to $\\ell^p$-improvng.\u00a0 Colloq. Math<\/em> 175 (2024), no. 1, 55\u201376.<\/p>\n\n\n\n

Anderson, Theresa C., Hu, BIngyang, Liu, Yu-Ru, and Talmage, Alan. Bounds on tenth moments of (x, x3)
for ellipsephic sets. Contemporary Mathematics, <\/em>Volume: 792; 2024; pages 125-132.<\/p>\n\n\n\n

Anderson, Theresa C. and Hu, Bingyang.  On the general dyadic grids in $R^d$.  Canadian Journal of Math<\/em> 75(2023), no.4, 1147\u20131175.<\/p>\n\n\n\n

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<\/em> 2023, no. 3, 2188-2214.<\/p>\n\n\n\n

Anderson, Theresa C. and Hu, Bingyang. A structure theorem on intersections of general doubling measures and its applications. Int. Math. Res. Not. IMRN<\/em> (2023), no.9, 7423\u20137485.<\/p>\n\n\n\n

Anderson, Theresa C., Travesset, Chiara and Veltri, Joey. A structure theorem for weight and function classes with coprime bases. Quarterly Journal of Math<\/em> 74(2023), no.2, 459\u2013470..<\/p>\n\n\n\n

Anderson, Theresa C., Kumchev, A. V. and Palsson, E.A. Discrete maximal functions over surfaces of higher codimension.  Matematica<\/em> 1 (2022), no. 2, 442\u2013479.<\/p>\n\n\n\n

Anderson, Theresa C., Cook, Brian, Hughes, Kevin, and Kumchev, Angel.  On the Ergodic Waring-Goldbach Problem.  J. Funct. Anal.<\/em> 282 (2022), no. 5, Paper No. 109334, 39 pp.<\/p>\n\n\n\n

Anderson, Theresa C. and Hu, Bingyang. Sharp Mei’s lemma for different bases. Results Math.<\/em> 77 (2022), no. 2, Paper No. 69, 18 pp.<\/p>\n\n\n\n

Anderson, Theresa C. and Hu, Bingyang. A structure theorem for measures with different bases.  J. Math. Anal. Appl.<\/em> 505 (2022), no. 1, Paper No. 125620, 11 pp.<\/p>\n\n\n\n

Anderson, Theresa C. and Palsson, E.A..  Bounds for discrete multilinear spherical maximal operators.  Collect. Math.<\/em> 73 (2022), no. 1, 75\u201387.<\/p>\n\n\n\n

Anderson, Theresa C. and Palsson, E.A..  Bounds for discrete multilinear spherical maximal operators in higher dimensions.  Bull. Lond. Math. Soc<\/em>.. 53 (2021), no. 3, 855\u2013860.<\/p>\n\n\n\n

Anderson, Theresa C., Hughes, Kevin, Roos, Joris, and Seeger, Andreas.  $L^p \\to L^q$ bounds for spherical maximal operators.  Math Zeitschrift<\/em> 297 (2021), no. 3-4, 1057\u20131074.<\/p>\n\n\n\n

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.<\/em> 145 (2021), no. 1, 1\u201328.<\/p>\n\n\n\n

Anderson, Theresa C. Hu, Bingyang, and Roos, Joris.  S<\/em>parse bounds for discrete singular Radon transforms.  Colloq. Math<\/em>. 165 (2021), no. 2, 199\u2013217<\/p>\n\n\n\n

Anderson, Theresa C. Quantitative $l^p$ improving for discrete spherical averages along the primes.  J. Fourier Anal. Appl.<\/em> 26<\/strong> (2020), no. 2, Paper No. 32, 12 pp<\/p>\n\n\n\n

Anderson, Theresa C., Hu, Bingyang, Jiang, Liwei, Olson, Connor, and Wei, Zeyu.  O<\/em>n the translates of general dyadic systems on $\\R$.  Mathematische Annalen, 377(3), 911-933.<\/em>  <\/p>\n\n\n\n

Anderson, Theresa C. and Hu, Bingyang.  A unified method for maximal truncated Calder\u00f3n-Zygmund operators in general function spaces by sparse domination.  Proc. Edinb. Math. Soc. (2)<\/em> 63<\/strong> (2020), no. 1, 229–247.<\/p>\n\n\n\n

Anderson, Theresa C., Cook, Brian, Hughes, Kevin, and Kumchev, Angel.  Improved l^p boundedness for Integral k-Spherical Maximal Functions.  Discrete Analysis, <\/em>May 29, 2018. (pdf<\/a>)<\/p>\n\n\n\n

Anderson, Theresa C. and Weirich, David E.  A Dyadic Gehring Inequality and Applications.  New York Journal of Math, <\/em>Volume 24, 2018. (pdf<\/a>)<\/p>\n\n\n\n

Anderson, Theresa C., Cruz-Uribe OFS, David, and Moen, Kabe.  Extrapolation in the scale of generalized reverse H\u00f6lder weights. Rev. Math Complutense, 31<\/strong>, <\/em>pages 263\u2013286 (2018)<\/em>. (pdf<\/a>)<\/p>\n\n\n\n

Anderson, Theresa C., Hytonen, Tuomas and Tapiola, Olli. Weak A-infinity weights and weak reverse H\u00f6lder property in a Space of Homogeneous Type. J. Geom. Anal. 27 <\/strong>(2017), no. 1, 95–119. (pdf<\/a>)<\/p>\n\n\n\n

Anderson, Theresa C. and Dami\u00e1n, Wendol\u00edn. Calder\u00f3n-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities. Analysis Math 48 (2022), no. 4, 939\u2013959.<\/em>. <\/p>\n\n\n\n

Anderson, Theresa C.\u00a0 A framework for Calder\u00f3n-Zygmund operators on Spaces of Homogeneous Type.\u00a0 PhD thesis, Brown University, 2015.<\/p>\n\n\n\n

Anderson, Theresa C. A new sufficient two-weighted bump assumption for $L^p$ boundedness of Calder\u00f3n-Zygmund operators. Proceedings of the AMS,<\/em> Volume 143, Number 8, August 2015, Pages 3573\u20133586. <\/p>\n\n\n\n

Anderson, Theresa C., Cruz-Uribe SFO, David and Moen, Kabe. Logarithmic bump conditions for Calder\u00f3n-Zygmund Operators on spaces of homogeneous type. Publicacions Mathematiques<\/em> 59(1), 2015.<\/p>\n\n\n\n

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.<\/em> July 2014, Volume 24, Issue 3, pp 1276-1297. <\/p>\n\n\n\n

Anderson, Theresa C. and Mar\u00ed-Beffa, Gloria. A completely integrable flow of star-shaped curves on the light cone in Lorenzian $R^4$. J. Phys. A: Math.Theor.<\/strong><\/em> 44 (2011) 445203. *Featured in IOP select http:\/\/Select.iop.org. <\/p>\n\n\n\n

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<\/em>. 139 (2011) 1533-1541.<\/p>\n","protected":false},"excerpt":{"rendered":"

I build bridges in mathematics and beyond, with a particular eye to connecting things in new ways. My mathematical research is broad, encompassing both harmonic analysis and number theory and especially their interplay. Some recent work has been in discrete (number theoretic) tools in harmonic Continue Reading<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-33","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/pages\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":49,"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/pages\/33\/revisions"}],"predecessor-version":[{"id":267,"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/pages\/33\/revisions\/267"}],"wp:attachment":[{"href":"https:\/\/faculty.math.cmu.edu\/anderson\/wp-json\/wp\/v2\/media?parent=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}