{"id":20,"date":"2023-07-26T15:05:10","date_gmt":"2023-07-26T19:05:10","guid":{"rendered":"https:\/\/pages.vassar.edu\/thyde\/?page_id=20"},"modified":"2026-05-07T12:30:18","modified_gmt":"2026-05-07T16:30:18","slug":"research","status":"publish","type":"page","link":"https:\/\/pages.vassar.edu\/thyde\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n<p>My research interests include arithmetic dynamics, arithmetic statistics, geometry of configuration spaces, Galois theory, and algebraic combinatorics.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Publications<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/pages.vassar.edu\/thyde\/files\/2026\/05\/Hyde-Rational-orbits-under-correspondences.pdf\" data-type=\"attachment\" data-id=\"166\"><strong>Rational orbits under correspondences<\/strong><\/a>,<br \/>preprint (2026),<br \/><a href=\"https:\/\/arxiv.org\/abs\/2605.04391\" data-type=\"link\" data-id=\"https:\/\/arxiv.org\/abs\/2605.04391\">arXiv preprint 2605.04391<\/a>.<br \/><\/li>\n\n\n\n<li><a href=\"https:\/\/pages.vassar.edu\/thyde\/files\/2025\/04\/Adams-Hyde-Profinite-iterated-monodromy-groups-of-unicritical-polynomials.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Profinite iterated monodromy groups of unicritical polynomials<\/strong><\/a>,<br \/>with Ophelia Adams,<br \/>to appear in <em>Algebra and Number Theory<\/em> (2026).<br \/><a href=\"https:\/\/arxiv.org\/abs\/2504.13028\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv preprint 2504.13028.<\/a><br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Doyle-Hyde-Polynomials-with-many-rational-preperiodic-points.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Polynomials with many rational preperiodic points<\/a><\/strong>,<br \/>with John R. Doyle,<br \/><em>Transactions of the AMS,<\/em> Vol. 378, No. 08 (2025), 5981-6011.<br \/><a href=\"https:\/\/arxiv.org\/abs\/2201.11707\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv preprint 2201.11707<\/a>.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-Cyclotomic-factors-of-necklace-polynomials.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Cyclotomic factors of necklace polynomials<\/a><\/strong>,<br \/><em>Acta Arithmetica<\/em>, Vol. 204 (2022), 287-316.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Doyle-Fili-Hyde-Dynatomic-polynomials-necklace-operators-and-universal-relations-for-dynamical-units.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Dynatomic polynomials, necklace operators, and universal relations for dynamical units<\/a><\/strong>,<br \/>with John R. Doyle and Paul Fili,<br \/><em>New York Journal of Mathematics<\/em>, Vol. 28 (2022), 534-556.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Blum-Doyle-Hyde-Kelln-Talbott-Weinreich-Dynamical-moduli-spaces-and-polynomial-endomorphisms-of-configurations.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Dynamical moduli spaces and polynomial endomorphisms of configurations<\/a><\/strong>,<br \/>with Talia Blum, John R. Doyle, Colby Kelln, Henry Talbott, and Max Weinreich,<br \/><em>Arnold Mathematical Journal<\/em>, Vol. 8 (2022), 285-317, DOI:&nbsp;<a href=\"https:\/\/link.springer.com\/article\/10.1007\/s40598-022-00197-z\" target=\"_blank\" rel=\"noreferrer noopener\">10.1007\/s40598-022-00197-z<\/a><br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-Euler-characteristic-of-the-space-of-real-multivariate-irreducible-polynomials.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Euler characteristic of the space of real multivariate irreducible polynomials<\/a><\/strong>,<br \/><em>Proceedings of the AMS<\/em>, Vol. 150 (2022), 2331-2343.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Bell-Camero-Cho-Hyde-Lu-Miller-Thompson-Zhu-Density-of-periodic-points-for-Lattes-maps-over-finite-fields.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Density of periodic points for Latt\u00e8s maps over finite fields<\/a><\/strong>,<br \/>with Zo\u00eb Bell, Jasmine Camero, Karina Cho, Chieh-Mi Lu, Rebecca Miller, Bianca Thompson, and Eric Zhu,<br \/><em>Journal of Number Theory<\/em>, Vol. 238 (2022), 951-966, DOI:<a href=\"https:\/\/doi.org\/10.1016\/j.jnt.2021.10.009\" target=\"_blank\" rel=\"noreferrer noopener\">10.1016\/j.jnt.2021.10.009<\/a><br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-Polynomial-factorization-statistics-and-point-configurations-in-R%5E3.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Polynomial factorization statistics and point configurations in R^3<\/a><\/strong>,<br \/><em>International Mathematical Research Notices<\/em> (2018), DOI:&nbsp;<a href=\"https:\/\/doi.org\/10.1093\/imrn\/rny271\" target=\"_blank\" rel=\"noreferrer noopener\">10.1093\/imrn\/rny271<\/a>.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-Liminal-reciprocity-and-factorization-statistics.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Liminal reciprocity and factorization statistics<\/a><\/strong>,<br \/><em>Algebraic Combinatorics<\/em>, Vol. 2, No. 4 (2019), 521-539.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-FPSAC-extended-abstract.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Factorization statistics and the twisted Grothendieck-Lefschetz formula<\/a><\/strong>,<br \/>extended abstract,&nbsp;<em>Proceedings of 30th Conference on Formal Power Series and Algebraic Combinatorics<\/em> (2018).<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-Lagarias-Polynomial-splitting-measures-and-cohomology-of-the-pure-braid-group.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Polynomial splitting measures and cohomology of the pure braid group<\/a><\/strong>,<br \/>with&nbsp;<a href=\"http:\/\/www.math.lsa.umich.edu\/~lagarias\/\" target=\"_blank\" rel=\"noreferrer noopener\">Jeffrey C. Lagarias<\/a>.<br \/><em>Arnold Mathematical Journal<\/em>, Vol. 3, No. 2 (2017), 219-249, DOI:&nbsp;<a href=\"https:\/\/link.springer.com\/article\/10.1007\/s40598-017-0064-z\" target=\"_blank\" rel=\"noreferrer noopener\">10.1007\/s40598-017-0064-z<\/a>.<br \/><\/li>\n\n\n\n<li><strong><a href=\"https:\/\/stephangarcia.sites.pomona.edu\/PAPERS\/GHMFC2S.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Gauss&#8217; hidden menagerie: from cyclotomy to supercharacters<\/a><\/strong>,<br \/>with&nbsp;<a href=\"http:\/\/pages.pomona.edu\/~sg064747\/\" target=\"_blank\" rel=\"noreferrer noopener\">Stephan Ramon Garcia<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/sites.lsa.umich.edu\/boblutz\/\" target=\"_blank\" rel=\"noreferrer noopener\">Bob Lutz<\/a>.<br \/><em>Notices Amer. Math. Soc.<\/em>, Vol. 62, No. 8 (2015), 878-888.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Cox-Hyde-The-Galois-theory-of-the-lemniscate.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Galois theory of the lemniscate<\/a><\/strong>,<br \/>with&nbsp;<a href=\"http:\/\/www3.amherst.edu\/~dacox\/\" target=\"_blank\" rel=\"noreferrer noopener\">David A. Cox<\/a>,&nbsp;<br \/><em>The Journal of Number Theory<\/em>, Vol. 135 (2014), 43-59.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Benedetto-Chen-Hyde-Kovacheva-White-Small-dynamical-heights-for-quadratic-polynomials-and-rational-functions.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Small dynamical heights for quadratic polynomials and rational functions<\/a><\/strong>,<br \/>with&nbsp;<a href=\"http:\/\/www3.amherst.edu\/~rlbenedetto\/\" target=\"_blank\" rel=\"noreferrer noopener\">Rob Benedetto<\/a>, Ruqian Chen, Yordanka Kovacheva, and&nbsp;<a href=\"http:\/\/www.cs.cmu.edu\/~crwhite\/\" target=\"_blank\" rel=\"noreferrer noopener\">Colin White<\/a>.<br \/><em>Experimental Mathematics<\/em>, Vol. 23 (2014), 433-447.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-A-Wallis-product-on-clovers.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">A Wallis product on clovers<\/a><\/strong>,<br \/><em>The American Mathematical Monthly<\/em>, Vol. 121, No. 3 (2014), 237-243.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hutz-Hyde-Krause-Pre-images-in-quadratic-dynamical-systems.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Pre-images in quadratic dynamical systems<\/a><\/strong>,<br \/>with&nbsp;<a href=\"http:\/\/my.fit.edu\/~bhutz\/\" target=\"_blank\" rel=\"noreferrer noopener\">Ben Hutz<\/a>&nbsp;and&nbsp;<a href=\"http:\/\/www.math.ucla.edu\/~benkrause23\/\" target=\"_blank\" rel=\"noreferrer noopener\">Ben Krause<\/a>.<br \/><em>Involve<\/em>, Vol. 4, No. 4 (2011), 343-363.<br \/><\/li>\n\n\n\n<li><strong><a href=\"http:\/\/pages.vassar.edu\/thyde\/files\/2023\/08\/Hyde-On-the-number-of-rational-iterated-pre-images-of-1-under-quadratic-dynamical-systems.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">On the number of rational iterated pre-images of -1 under quadratic dynamical systems<\/a><\/strong>,<br \/><em>American Journal of Undergraduate Research<\/em>, Vol. 9, No. 1 (2010), 19-26.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Doctoral Thesis<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><a href=\"https:\/\/math.uchicago.edu\/~tghyde\/Hyde%20--%20Thesis.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Polynomial statistics, necklace polynomials, and the arithmetic dynamical Mordell-Lang conjecture<\/a><\/strong><br \/>(Complete thesis.)<\/li>\n\n\n\n<li><strong><a href=\"https:\/\/pages.vassar.edu\/thyde\/files\/2025\/11\/Hyde-Thesis-ADML.pdf\" data-type=\"attachment\" data-id=\"159\" target=\"_blank\" rel=\"noreferrer noopener\">Chapters 5 and 6 on the arithmetic dynamical Mordell-Lang conjecture<\/a><\/strong><br \/>(Joint work with Mike Zieve.)<\/li>\n\n\n\n<li><strong><a href=\"https:\/\/math.uchicago.edu\/~tghyde\/Hyde%20--%20Thesis%20Defense.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Slides from the defense<\/a><\/strong>.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Awards and Grants<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In 2022 I received the <strong><a href=\"https:\/\/news.uchicago.edu\/story\/uchicago-instructors-grad-students-honored-2022-exceptional-teaching#swogger\">Glen and Claire Swogger Award for Exemplary Classroom Teaching<\/a><\/strong> from the University of Chicago.<\/li>\n\n\n\n<li>In 2020 I received the&nbsp;<strong>NSF Mathematical Sciences Postdoctoral Research Fellowship<\/strong>.<\/li>\n\n\n\n<li>In 2019 I received the&nbsp;<strong>Wirt and Mary Cornwell Prize<\/strong>&nbsp;in mathematics from the University of Michigan.<\/li>\n\n\n\n<li>In 2018 I received the&nbsp;<a href=\"http:\/\/www.rackham.umich.edu\/funding\/predoctoral-fellowship\"><strong>Rackham Predoctoral Fellowship<\/strong><\/a>&nbsp;from the University of Michigan.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Invited Talks<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Academia Sinica, Taiwan<\/strong><br \/>Algebra\/Number Theory Seminar, May 2026<\/li>\n\n\n\n<li><strong>National Central University, Taiwan<\/strong><br \/>Algebra\/Number Theory Seminar, May 2026<\/li>\n\n\n\n<li><strong>Boston College<\/strong><br \/>AMS Sectional Meeting, March 2026<\/li>\n\n\n\n<li><strong>Amherst College<\/strong><br \/>Colloquium, March 2026<\/li>\n\n\n\n<li><strong>AG@PUI Seminar<\/strong><br \/>March 2026<\/li>\n\n\n\n<li><strong>American Institute of Mathematics<\/strong><br \/>Dynamics of Multiple Maps Workshop, November 2025<\/li>\n\n\n\n<li><strong>University of Rochester<\/strong><br \/>Algebra\/Number Theory Seminar, March 2025<\/li>\n\n\n\n<li><strong>Florida State University<\/strong><br \/>Algebra Seminar, February 2025<\/li>\n\n\n\n<li><strong>Joint Math Meetings<\/strong><br \/>Arithmetic Dynamics Special Session, January 2025<\/li>\n\n\n\n<li><strong>Penn State University<\/strong><br \/>Algebra Seminar, November 2024<\/li>\n\n\n\n<li><strong>Oklahoma State University<\/strong><br \/>Number Theory Seminar, April 2023<\/li>\n\n\n\n<li><strong>Oregon State University<\/strong><br \/>Number Theory Seminar, April 2023<\/li>\n\n\n\n<li><strong>Vassar College<\/strong><br \/>Colloquium, February 2023<\/li>\n\n\n\n<li><strong>Baruch College<\/strong><br \/>Colloquium, February 2023<\/li>\n\n\n\n<li><strong>Joint Math Meetings<\/strong><br \/>Arithmetic Dynamics Special Session, January 2023<\/li>\n\n\n\n<li><strong>AMS Sectional Meeting<\/strong><br \/>Arithmetic Dynamics Special Session, October 2022<\/li>\n\n\n\n<li><strong>Arithmetic Dynamics International Online Seminar (ADIOS)<\/strong><br \/>February 2022<\/li>\n\n\n\n<li><strong>Harvard University<\/strong><br \/>Algebraic Dynamics Seminar, February 2022<\/li>\n\n\n\n<li><strong>Oklahoma State University<\/strong><br \/>Number Theory Seminar, March 2021<br \/><a href=\"https:\/\/www.youtube.com\/watch?v=bshTIIxQr9Q\">Video<\/a><\/li>\n\n\n\n<li><strong>University of Washington<\/strong><br \/>Algebraic Geometry Seminar, February 2021<\/li>\n\n\n\n<li><strong>University of Connecticut<\/strong><br \/>Math Club, October 2020<\/li>\n\n\n\n<li><strong>Joint Math Meetings<\/strong><br \/>Arithmetic Dynamics Special Session, January 2020<\/li>\n\n\n\n<li><strong>CUNY Graduate Center<\/strong><br \/>Combinatorial and Additive Number Theory Workshop, May 2019<\/li>\n\n\n\n<li><strong>University of Chicago<\/strong><br \/>Midwest Representation Stability Research Meeting, April 2019<\/li>\n\n\n\n<li><strong>AMS Western Sectional Meeting<\/strong><br \/>Emerging Connections in Number Theory, March 2019<\/li>\n\n\n\n<li><strong>University of Michigan<\/strong><br \/>Graduate Recruitment Symposium, March 2019<\/li>\n\n\n\n<li><strong>University of Michigan<\/strong><br \/>Complex Analysis, Dynamics, and Geometry Seminar, March 2019<\/li>\n\n\n\n<li><strong>University of Michigan<\/strong><br \/>Combinatorics Seminar, February 2019<\/li>\n\n\n\n<li><strong>Wayne State University<\/strong><br \/>Algebra Seminar, January 2019<\/li>\n\n\n\n<li><strong>University of California, Berkeley<\/strong><br \/>Combinatorics Seminar, November 2018<\/li>\n\n\n\n<li><strong>University of Chicago<\/strong><br \/>Geometry\/Topology Seminar, November 2018<\/li>\n\n\n\n<li><strong>Dartmouth College<\/strong><br \/>Formal Power Series and Algebraic Combinatorics Conference, July 2018<\/li>\n\n\n\n<li><strong>CUNY Graduate Center<\/strong><br \/>Combinatorial and Additive Number Theory Workshop, May 2018<\/li>\n\n\n\n<li><strong>AMS Eastern Sectional Meeting<\/strong><br \/>Arithmetic Dynamics Special Session, April 2018<\/li>\n\n\n\n<li><strong>Joint Math Meetings<\/strong><br \/>Arithmetic Dynamics Special Session, January 2018<\/li>\n\n\n\n<li><strong>Fields Institute<\/strong><br \/>Workshop on Interactions between Model Theory and Arithmetic Dynamics, July 2016<\/li>\n\n\n\n<li><strong>Amherst College<\/strong><br \/>Colloquium, April 2013<\/li>\n\n\n\n<li><strong>University of Connecticut<\/strong><br \/>Pi Day Colloquium, March 2013<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My research interests include arithmetic dynamics, arithmetic statistics, geometry of configuration spaces, Galois theory, and algebraic combinatorics. Publications Doctoral Thesis Awards and Grants Invited Talks<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-20","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":26,"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":174,"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/pages\/20\/revisions\/174"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/thyde\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}