Research
Research
My research is currently focused on the following areas and the interplay between them:
Including general and unrestricted partitions and overpartitions as well as other partition theoretic functions, with applications including combinatorial properties, congruences, asymptotics, and connections with modular forms.
Including modular forms, mock modular forms, and quantum modular forms, with applications including location and properties of zeros, relationships between mock modular forms and their shadows, and connections with partition theory.
Including classical, finite field versions, and p-adic interpretations, with applications to supercongruences and the geometry of hypergeometric abelian varieties.
2. Gabriel Gray, Emily Payne, Holly Swisher, and Ren Watson, Fixed perimeter analogues of some partition results, submitted.
1. Leah Sturman and Holly Swisher, Toward resolving Kang and Park's generalization of the Alder-Andrews Theorem, submitted.
35. Angelica Babei, Manami Roy, Holly Swisher, Bella Tobin, and Fang-Ting Tu, Supercongruences arising from Ramanuian-Sato series, Results in Mathematics, Vol. 80, no. 184 (2025), 1-52.
34. Gabriel Gray, David Hovey, Brandt Kronholm, Emily Payne, Holly Swisher, and Ren Watson, A generalization of Franklin's partition identity and a Beck-type companion identity, The Ramanujan Journal, Vol. 67, No. 100 (2025), 1-17.
33. Ling Chen, Isabelle Hernandez, Zain Shields, and Holly Swisher, Analogues of Alder-Type Partition Inequalities for Fixed Perimeter Partitions, Integers 24, A102 (2024), 1-17.
32. Angelica Babei, Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin, and Fang-Ting Tu, Generalized Ramanujan-Sato Series Arising from Modular Forms, Research Directions in Number Theory: Women in Numbers V (2024), 87-131.
31. Liam Armstrong, Bryan Ducasse, Thomas Meyer, and Holly Swisher, Generalized Alder-Type Partition Inequalities, The Electronic Journal of Combinatorics, Vol. 30, Issue 2, P2.36 (2023), 1-16.
30. Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu, Hypergeometric functions over finite fields, Memoirs of the American Mathematical Society, Vol. 280, no. 1382 (2022), 1-124.
29. Savana Ammons, Young Jin Kim, Laura Seaberg, and Holly Swisher, An analogue of k-marked Durfee symbols for strongly unimodal sequences, Integers 21, A35 (2021), 1-14.
28. Adriana L. Duncan, Simran Khunger, Holly Swisher, and Ryan Tamura, Generalizations of Alder's Conjecture via a Conjecture of Kang and Park, Research in Number Theory, 7, 11 (2021), 1-26.
27. Michael Allen, Nicholas Anderson, Asimina Hamakiotes, Ben Oltsik, and Holly Swisher, Eta-quotients of prime or semiprime level and elliptic curves, Involve, Vol. 13, No. 5 (2020), 879–900.
26. Ali Al-Saedi, Tamsyn Morrill, and Holly Swisher, Inequalities for the dth Residual Crank Moments of Overpartitions, International Journal of Number Theory, vol. 16, no. 7 (2020), 1599-1606.
25. Amanda Folsom, Min-Joo Jang, Sam Kimport, and Holly Swisher, Quantum modular forms and singular combinatorial series with repeated roots of unity, Acta Arithmetica, 194.4 (2020), 393-421.
24. Allison Arnold-Roksandich, Brian Diaz, Erin Ellefsen, and Holly Swisher, Extending a catalog of mock and quantum modular forms to an infinite class, Research in Number Theory, 6, 17 (2020) 1-20.
23. Amanda Folsom, Min-Joo Jang, Sam Kimport, and Holly Swisher, Quantum modular forms and singular combinatorial series with distinct roots of unity, Research Directions in Number Theory: Women in Numbers IV (2019), 173-195.
22. Chris Jennings-Shaffer and Holly Swisher, Mock Modularity of the Md-rank of overpartitions, Journal of Mathematical Analysis and Applications, 466, no. 2 (2018), 1144-1189.
21. Sharon Frechette, Holly Swisher, and Fang-Ting Tu, A Cubic Transformation Formula for Appell-Lauricella Hypergeometric Functions over Finite Fields, Research in Number Theory, 4:27 (2018), 1-27.
20. Oleg Lazarev, Matthew S. Mizuhara, Benjamin Reid, and Holly Swisher, An extension of a proof of the Ramanujan congruences for multipartitions, The Ramanujan Journal 45, issue 1, (2018), 1-20.
19. Soon-Yi Kang and Holly Swisher, Mock Theta Functions of Order 2 and their Shadow Computations, Bull. Korean Math. Soc. 54 (2017), No. 6, 2155-2163.
18. Ethan Alwaise, Elena Iannuzzi, Holly Swisher A proof of some conjectures of Mao on partition rank inequalities, The Ramanujan Journal, 43, issue 3, (2017), 633-648.
17. Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Holly Swisher, and Stephanie Treneer, Quantum mock modular forms arising from eta-theta functions, Research in Number Theory 2:14 (2016), 1-41.
16. Ling Long, Robert Osburn, and Holly Swisher, On a conjecture of Kimoto and Wakayama, Proceedings of the American Mathematical Society, 144, no. 10 (2016), 4319-4327.
15. Matthew S. Mizuhara, James A. Sellers, and Holly Swisher, A periodic approach to plane partition congruences, Integers 16, A16 (2016), 1-13.
14. Alyson Deines, Jenny G. Fuselier, Ling Long, Holly Swisher, and Fang-Ting Tu, Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions, Directions in Number Theory: Proceedings of the 2014 WIN3 (2016), 125-160.
13. Alyson Deines, Jenny G. Fuselier, Ling Long, Holly Swisher, and Fang-Ting Tu, Generalized Legendre curves and Quaternionic Multiplication, Journal of Number Theory, Sp. Vol. in honor of Wen-Ching Winnie Li, 161, April (2016), 175-203.
12. Holly Swisher, On the supercongruence conjectures of van Hamme, Research in the Mathematical Sciences, 2:18, December (2015), 1-21.
11. Acadia Larsen, Alexa Rust, and Holly Swisher, Inequalities for positive rank and crank moments of overpartitions, International Journal of Number Theory, 10, no. 8 (2014), 2115-2133.
10. Christopher Jennings-Shaffer and Holly Swisher, A note on the transcendence of zeros of a certain family of weakly holomorphic forms, International Journal of Number Theory, 10, no. 2 (2014), 309-317.
9. Sarah Chisholm, Alyson Deines, and Holly Swisher, Recent Advances for Ramanujan Type Supercongruences, Women in Numbers 2: research directions in number theory, Contemporary Mathematics 606, American Mathematical Society, Providence, RI (2013), 189-206.
8. Sarah Chisholm, Alyson Deines, Ling Long, Gabriele Nebe, and Holly Swisher, p-adic Analogs of Ramanujan Type Formulas for 1/pi, Mathematics 1 (2013), 9-30.
7. Oleg Lazarev and Holly Swisher, A combinatorial proof of a recursive formula for multipartitions, Integers 11, A52 (2011), 1-13.
6. Sharon Garthwaite, Ling Long, Holly Swisher, and Stephanie Treneer, Zeros of classical Eisenstein series and recent developments, WIN—Women in Numbers, Fields Institute Communications, 60, American Mathematical Society, Providence, RI (2011), 251-263.
5. Holly Swisher, The Andrews-Stanley partition function and p(n): congruences, Proceedings of the American Mathematical Society, 139, no. 4 (2011), 1175-1185.
4. Sharon Garthwaite, Ling Long, Holly Swisher, and Stephanie Treneer, Zeros of some level 2 Eisenstein series, Proceedings of the American Mathematical Society, 138, no. 2 (2010), 467-480.
3. Kathrin Bringmann and Holly Swisher, On a conjecture of Koike on identities between Thompson series and Rogers-Ramanujan Functions, Proceedings of the American Mathematical Society, 135, no. 8 (2007), 2317-2326. Corrigendum, Proceedings of the American Mathematical Society, Volume 136, no. 4 (2008), 1501.
2. Holly Swisher, A remark on Hecke operators and a theorem of Dwork and Koike, Illinois Journal of Mathematics, 48, no. 1 (2004), 353-356.
1. Scott Chapman, Victor DeLorenzo, and Holly Swisher, On the asymptotic behavior of irreducibles in block semigroups, Semigroup Forum, 63, no. 1 (2001), 34-48.
2. Sharon Frechette, Holly Swisher, Fang-Ting Tu Appell–Lauricella hypergeometric functions over finite fields, and a new cubic transformation formula, 2017 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Volume 2, Springer, 417-422.
1. Jenny Fuselier, Ling Long, Ravi Ramakrishna, Holly Swisher, Fang-Ting Tu Hypergeometric functions over finite fields, 2017 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Volume 2, Springer, 461-466.