People

Dan Yasaki

Dan Yasaki

Professor
Director of Student Success

  • Recipient of 2023 Board of Governors Alumni Teaching Award

Office: Petty 126
Email: d_yasaki@uncg.edu
Personal Website: https://mathstats.uncg.edu/yasaki/
Starting year at UNCG: 2008
Office Hours: T 9:00 - 10:30 p.m., W: 11:00 - 12:30 p.m., and by appointment

Education

Degree(s): M.A. in Mathematics, Duke University (2000), Ph.D. in Mathematics, Duke University (2005)

Teaching

Fall 2024
  • MAT-311 LEC (Intro to Abstract Algebra), MWF 10:00-10:50, PETT 007
  • MAT-727 LEC (Linear Algebra), MWF 2:00-2:50, NSCI 202

Research

Member of the Research Group(s): Number Theory
Former Students: Zachary Parker , Kristen Scheckelhoff (M.A.), Debbie White (M.A.), Paula Hamby (M.A.), Nathan Fontes (M.A.), Kalani Thalagoda (Ph.D.)

Research Interests: I study arithmetic quotients of symmetric spaces. These locally symmetric spaces stand at the intersection of various topics in number theory, geometry, and topology. In particular they are closely related to the theory of automorphic forms. I use explicit reduction theory coming from quadratic forms over number fields in order to construct polyhedral tessellations that can be used to compute cohomological modular forms.

Selected Publications

  1. with Avner Ash, Cohomology of congruence subgroups of SL3(ℤ), Steinberg modules, and real quadratic fields. J. Number Theory 246 (2023), 49–86.
  2. with Greg Bell, Austin Lawson, and Neil Pritchard, An exploration of g-adic representations of integers, Involve 15 (2022), no. 5, 727-738. (PDF)
  3. with Greg Bell, Austin Lawson, and Neil Pritchard, The space of persistence diagrams fails to have Yu’s Property A, Topology Proc. 58 (2021), 279-288. (PDF)
  4. with David Burns, Rob de Jeu, Herbert Gangl, and Alexander D. Rahm, Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields, Forum of Mathematics, Forum Math. Sigma 9 (2021), Paper No. e40, 47 pp. (PDF)
  5. with Avner Ash, Steinberg homology, modular forms, and real quadratic fields, Journal of Number Theory 224 (2021), 323-367. (PDF)
  6. with Kristen Scheckelhoff and Kalani Thalagoda, Perfect forms over imaginary quadratic fields, Tbilisi Math. J. special volume on Cohomology, Geometry, Explicit Number Theory (2021), 1–12. (PDF)
  7. with Jeremy Miller, Peter Patzt, and Jennifer C. H. Wilson, Non-integrality of some Steinberg Modules, Journal of Topology 13 (2020), no. 2, 441-459. (PDF)
  8. with Avner Ash, Paul E. Gunnells, and Mark McConnell, On the growth of torsion in the cohomology of arithmetic groups, J. Inst. Math. Jussieu 19 (2020), no. 2, 537–569. (PDF)
  9. with Paul E. Gunnells, and Mark McConnell, On the cohomology of congruence subgroups of GL_3 over the Eisenstein integers, Experimental Mathematics 30 (2021), no. 4, 4990512. (PDF)
  10. with Mathieu Dutour Sikirić, Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, and Achill Schürmann, On the topological computation of K4 of the Gaussian and Eisenstein integers, J. Homotopy Relat. Struct. 14 (2019), no. 1, 281-291. (PDF)
  11. with Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, and John Voight, A database of genus 2 curves over the rational numbers, LMS J. Comput. Math. 19 (2016), no. suppl. A, 235–254. (PDF)
  12. Computation of certain modular forms using Voronoi polytopes, Computations in the Cohomology of Arithmetic Groups, Mathematisches Forschungsinstitut Oberwolfach, no. 52, 2016, extended abstract, pp. 27–30. (PDF)
  13. Perfect forms over CM quartic fields (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 3/2016, Lattices and Applications in Number Theory. (PDF)
  14. with Mathieu Dutour Sikirić, Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, and Achill Schürmann, On the cohomology of linear groups over imaginary quadratic fields, Journal of Pure and Applied Algebra 220, Issue 7, July 2016, 2564–2589. (PDF)
  15. with Steve Donnelly, Paul E. Gunnells, and Ariah Klages-Mundt, A table of elliptic curves over the cubic field of discriminant -23, Experimental Mathematics, 24:4 (2015), 375-390. (PDF)
  16. Computing modular forms for GL_2 over certain number fields, Computations with Modular Forms, Contributions in Mathematical and Computational Sciences 6 (2014), 363-377.
  17. Integral cohomology of certain Picard modular surfaces, J. Number Theory 134 (2014) 13-28. (PDF)
  18. Perfect unary forms over real quadratic fields, J. Théor Nombres Bordeaux 25 (2013), no. 3, 759-775. (PDF)
  19. with Paul E. Gunnells, Modular forms and elliptic curves over the cubic field of discriminant −23, Int. J. Number Theory 9 (2013), no. 1, 53-76. (PDF)
  20. with Farshid Hajir and Paul E. Gunnells, Modular forms and elliptic curves over the field of fifth roots of unity, Experimental Mathematics 22 (2013), no. 2, 203-216. (PDF)
  21. Computing modular forms using Voronoi polyhedra (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 35/2011, Explicit Methods in Number Theory. (PDF)
  22. with Adriano Bruno, The arithmetic of planar binary trees, Involve 4 (2011), no. 1, 1-11. (PDF)
  23. On modular forms and elliptic curves over \(\mathbb{Q}(\zeta_5)\), RIMS Automorphic forms, trace formulas, and zeta functions (2011), Proceedings. (PDF)
  24. Hyperbolic tessellations associated to Bianchi groups, 6197 (2010), 385-396, 9th International Symposium, Nancy, France, ANTS-IX, July 19-23, 2010, Proceedings. (PDF)
  25. Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), 4132-4142. (PDF)
  26. Elliptic points of the Picard modular group, Monatsh. Math. (2009), no. 156, 391-396. (PDF)
  27. Modular forms over imaginary quadratic fields, package available in Magma V2.16, 2009.
  28. Computing Hecke operators on Bianchi forms, Tech. Report, Magma computational group: University of Sydney, 2009. (PDF)
  29. with Paul E. Gunnells, Hecke operators and Hilbert modular forms, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 5011, Springer, Berlin, 2008, pp. 387-401. (PDF)
  30. An explicit spine for the Picard modular group over the Gaussian integers, J. Number Theory 128 (2008), no. 1, 207-234. (PDF)
  31. On the existence of spines for ℚ-rank 1 groups, Selecta Math. (N.S.) 12 (2006), no.3-4, 541-564. (PDF)
  32. On the existence of spines for ℚ-rank 1 groups, Ph.D. Thesis, Duke University, 2005.

Brief Biography

Dr. Yasaki has an M.A. (2000) and Ph.D. (2005) from Duke University under the supervision of L. Saper. After a three year post-doc at the University of Massachusetts working with P. Gunnells, he has been part of the UNCG faculty since 2008. His research interests are in the area of modular forms, particularly the connection between explicit reduction theory of quadratic forms and the computation of Hecke data for automorphic forms. Recent work has focused on producing new examples of cusp forms over number fields of small degree. Reprints and preprints of publications can be found on his personal webpage.