{"id":20,"date":"2015-07-05T21:48:12","date_gmt":"2015-07-06T01:48:12","guid":{"rendered":"http:\/\/pages.vassar.edu\/adamlowrance\/?page_id=20"},"modified":"2026-04-10T12:17:27","modified_gmt":"2026-04-10T16:17:27","slug":"research","status":"publish","type":"page","link":"https:\/\/pages.vassar.edu\/adamlowrance\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

My research interests are in low dimensional topology, knot theory, and graph theory. Students interested in a research project under my supervision should email me.<\/p>\n

Papers and preprints. <\/strong>(<\/em>Undergraduate coauthors marked with *)<\/em><\/p>\n

    \n
  1. On the arc index and Turaev genus of a link. Joint with \u00c1lvaro Del Valle V\u00edlchez. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.<\/i>\u00a0120<\/b>, 62 (2026). arXiv:2509.21274<\/a>.<\/span><\/li>\n
  2. A characterization of adequate Turaev genus one links. Joint with Khaled Qazaqzeh and Nafaa Chbili.\u00a0arXiv:2507.18855<\/a>.<\/li>\n
  3. Average crosscap number of a 2-bridge knot. Joint with Moshe Cohen, Thomas Kindred, Patrick D. Shanahan, and Cornelia A. Van Cott. To appear in Algebr. Geom. Topol. arXiv:2501.03099<\/a>.<\/li>\n
  4. Average signature and 4-genus of 2-bridge knots. Joint with Moshe Cohen, Neal Madras, and Steven Raanes*. arXiv:2406.17738<\/a>.<\/li>\n
  5. The distribution of braid indices of 2-bridge knots. Joint with Tobias Clark* and Jeremy Frank*. To appear in\u00a0 J. Knot Theory Ramifications. arXiv:2401.08388<\/a>.<\/li>\n
  6. The distribution of genera of 2-bridge knots. Joint with Moshe Cohen, Abigail Dinardo*, Steven Raanes*, Izabella M. Rivera*, Andrew J. Steindl*, and Ella S. Wanebo*. Fund. Math. 267 <\/strong>(2024), no. 3, 195-229.\u00a0arXiv:2307.09399<\/a>.<\/li>\n
  7. Near extremal Khovanov homology of Turaev genus one links. Joint with Theo Beldin*, Mia DeStefano*, Wyatt Milgrim*, and Cecilia Villase\u00f1or*.\u00a0Topology Appl. 346<\/strong> (2024), 108861.\u00a0arXiv:2211.100009<\/a>.<\/li>\n
  8. The average genus of a 2-bridge knot is asymptotically linear. Joint with Moshe Cohen<\/a>. New York J. Math.\u00a030<\/strong> (2024), 1032-1055. arXiv:2205.06122<\/a>.<\/li>\n
  9. On Khovanov homology and related invariants. Joint with Carmen Caprau<\/a>, Nicolle Gonz\u00e1lez<\/a>,\u00a0 Christine Ruey Shan Lee<\/a>, Radmila Sazdanovi\u0107<\/a>, and Melissa Zhang<\/a>. Research Directions in Symplectic and Contact Geometry and Topology, Springer,\u00a0<\/i>2021.\u00a0\u00a0arXiv:2002.05247<\/a>.<\/li>\n
  10. The multi-region index of a knot. Joint with Sarah Goodhill*, Valeria Munoz Gonzales*, Jessica Rattray*, and Amelia Zeh*.\u00a0 J. Knot Theory Ramifications.\u00a029<\/strong> (2020), no. 4, 16pp.\u00a0arXiv:1909.11831<\/a>.<\/li>\n
  11. Torsion in thin regions of Khovanov homology. Joint with Alex Chandler<\/a>, Radmila Sazdanovi\u0107<\/a>, and Victor Summers<\/a>. Canadian Journal of Mathematics.\u00a074<\/strong>. (2022), no. 3, 630-654.\u00a0arXiv:1903.05760<\/a>.<\/li>\n
  12. Extremal Khovanov homology of Turaev genus one links. Joint with Oliver Dasbach<\/a>. Fund. Math.\u00a0250\u00a0<\/strong>(2020), 63-99.\u00a0arXiv:1812.11387<\/a>.<\/li>\n
  13. The 2-factor polynomial detects even perfect matchings. Joint with Scott Baldridge<\/a> and Ben McCarty<\/a>.\u00a0Electron. J. Combin.\u00a027\u00a0<\/b>(2020), no. 2, Paper No. 2.27, 16 pp.\u00a0arXiv:1812.10346<\/a>.<\/li>\n
  14. Alternating distances of knots. Encyclopedia of Knot Theory<\/a>. CRC Press, 2021.<\/li>\n
  15. The Jones polynomial of an almost alternating link. Joint with Dean Spyropoulos*. New York J. Math. 23<\/strong>\u00a0(2017), 1611-1639.\u00a0arXiv:1707.05443<\/a>.<\/li>\n
  16. The Turaev genus of torus knots. Joint with Kaitian Jin*, Eli Polston*, and Yanjie Zheng*.\u00a0 J. Knot Theory Ramifications.\u00a026\u00a0<\/strong>(2017),\u00a0no. 14, 1750095, 28 pp.\u00a0arXiv:1703.02506<\/a>.<\/li>\n
  17. Chromatic homology, Khovanov homology, and torsion. Joint with Radmila Sazdanovi\u0107<\/a>. Topology Appl. 222<\/strong> (2017), 77-99.\u00a0arXiv:1609.03585<\/a>.<\/li>\n
  18. Invariants for Turaev genus one links. Joint with Oliver Dasbach<\/a>. Comm. Anal. Geom. 25\u00a0<\/strong>(2018), no. 5, 1103-1126.\u00a0arXiv:1604.03501<\/a>.<\/li>\n
  19. Turaev genus and alternating decompositions. Joint with Cody Armond<\/a>. Algebr. Geom. Topol. 17<\/strong> (2017), 793-830.\u00a0arXiv:1507.02771<\/a>.<\/li>\n
  20. Alternating distances of knots and links. Topology Appl.\u00a0182\u00a0<\/strong>(2015), 53-70. arXiv:1406.7039<\/a>.<\/li>\n
  21. A Turaev surface approach to Khovanov homology. Joint with Oliver Dasbach<\/a>. Quantum Topol.\u00a05\u00a0<\/strong>(2014), no. 4, 425-486. arXiv:1107.2344<\/a>.<\/li>\n
  22. Turaev genus, knot signature, and the knot homology concordance invariants. Joint with Oliver Dasbach<\/a>. Proc. Amer. Math. Soc.\u00a0139<\/strong>\u00a0(2011), no. 7, 2631-2645. arXiv:1002.0898<\/a>.<\/li>\n
  23. The Khovanov width of twisted links and closed 3-braids. Comment. Math. Helv. 86\u00a0<\/strong>(2011), no. 3, 675-706. arXiv:0901.2196<\/a>.<\/li>\n
  24. Cube diagrams and 3-dimensional Reidemeister-like moves for knots. Joint with Scott Baldridge<\/a>. J. Knot Theory Ramifications\u00a021\u00a0<\/strong>(2012), no. 5, 125033, 39 pp. arXiv:0811.0225<\/a>.<\/li>\n
  25. On knot Floer width and Turaev genus. Algebr. Geom. Topol.\u00a08\u00a0<\/strong>(2008), no. 2, 1141-1162. arXiv:0709.0720<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    My research interests are in low dimensional topology, knot theory, and graph theory. Students interested in a research project under my supervision should email me. Papers and preprints. (Undergraduate coauthors marked with *) On the arc index and Turaev genus of a link. Joint with \u00c1lvaro Del Valle V\u00edlchez. Rev. Real Acad. Cienc. Exactas Fis. […]<\/p>\n","protected":false},"author":4796,"featured_media":0,"parent":0,"menu_order":2,"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\/adamlowrance\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/users\/4796"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":52,"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":283,"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/pages\/20\/revisions\/283"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/adamlowrance\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}