People

Dan Yasaki

Professor
Director of Student Success

Office: Petty 126
Email: d_yasaki@uncg.edu
Personal Website: http://www.uncg.edu/~d_yasaki/
Starting year at UNCG: 2008
Office Hours: MW 12:00 noon - 1:00 p.m., T: 10:00 - 11:00 a.m., and by appointment

Education

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

Teaching

Fall 2023

• MAT-196 LEC (Calculus A), MTWF 12:00-12:00, PETT 223
• MAT-727 LEC (Linear Algebra), MWF 11:00-11:50, PETT 217
• MAT-196 LEC (Calculus A), MTWF 2:00-2:50, PETT 219
• MAT-701 SEM (Sel Topics Computational Math)

Research

Member of the Research Group(s): Number Theory
Former Students: 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

• with Avner Ash, Paul E. Gunnells, and Mark McConnell, On the growth of torsion in the cohomology of arithmetic groups, Journal of the Institute of Mathematics of Jussieu (2018), 1-33. (PDF)
• Perfect forms over CM quartic fields (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 3/2016, Lattices and Applications in Number Theory. (PDF)
• 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)
• 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)
• 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, to appear in Journal of Homotopy and Related Structures. (PDF)
• 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)
• Integral cohomology of certain Picard modular surfaces, J. Number Theory 134 (2014) 13-28. (PDF)
• Perfect unary forms over real quadratic fields, J. Théor Nombres Bordeaux 25 (2013), no. 3, 759-775. (PDF)
• 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)
• Computing modular forms for GL_2 over certain number fields, Computations with Modular Forms, Contributions in Mathematical and Computational Sciences 6 (2014), 363-377.
• with Farshid Hajir and Paul E. Gunnells, Modular forms and elliptic curves over the field of fifth roots of unity, Exp. Math. 22 (2013), no. 2, 203-216. (PDF)
• Computing modular forms using Voronoi polyhedra (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 35/2011, Explicit Methods in Number Theory. (PDF)
• On modular forms and elliptic curves over \(\mathbb{Q}(\zeta_5)\), RIMS Automorphic forms, trace formulas, and zeta functions (2011), Proceedings. (PDF)
• with Adriano Bruno, The arithmetic of planar binary trees, Involve 4 (2011), no. 1, 1-11. (PDF)
• Hyperbolic tessellations associated to Bianchi groups, 6197 (2010), 385-396, 9th International Symposium, Nancy, France, ANTS-IX, July 19-23, 2010, Proceedings. (PDF)
• Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), 4132-4142. (PDF)
• Computing Hecke operators on Bianchi forms, Tech. Report, Magma computational group: University of Sydney, 2009. (PDF)
• Modular forms over imaginary quadratic fields, package available in Magma V2.16, 2009.
• 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)
• Elliptic points of the Picard modular group, Monatsh. Math. (2009), no. 156, 391-396. (PDF)
• An explicit spine for the Picard modular group over the Gaussian integers, J. Number Theory 128 (2008), no. 1, 207-234. (PDF)
• On the existence of spines for \(\mathbb{Q}\)-rank 1 groups, Selecta Math. (N.S.) 12 (2006), no.3-4, 541-564. (PDF)
• On the existence of spines for \(\mathbb{Q}\)-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.