Research Interests | Research Papers | Notes / Expository Articles

Thomas R. Shemanske

CONTACT INFORMATION

Dartmouth College | (603) 646-3179 (office) |

Department of Mathematics | (603) 646-1312 (fax) |

Hanover, NH 03755-3551 | thomas.r.shemanske@dartmouth.edu |

Ph.D. | University of Rochester | 1979 |

M.A. | University of Rochester | 1976 |

A.B. | Cornell University | 1974 |

GRANTS/ RECOGNITION

- A. W. Mellon Foundation: “A Better Calculus for Less” (Dwight Lahr, PI), ($224K approx) July 1, 2000 - June 30, 2003. [1 month of support, Summer 2003]
- AT&T Foundation: (co-PI, funded) “Development and Dissemination of a Free, Online Calculus Course for College and High School Students” (DC 5-38132), $50k, July 1, 2003 - June 30, 2006.
- Hewlett Foundation: (co-PI, proposed) “Opening Access to Quality Calculus”, $400k, July 1, 2003 - June 30, 2006.
- A. W. Mellon Foundation: “A Better Calculus for Less” (Dwight Lahr, PI), ($224K approx) July 1, 2000 - June 30, 2003. [1 month of support, Summer 2000]
- NSF Grant USE 8953908:(Co-Principal Investigator 1990-1991) “Calculus: Restructuring and Integration with Computing” (3-year grant to carry out calculus reform), ($300K approx) 1989 - 1992.
- Sloan Foundation Grant 89-10-1: “Computers and the teaching of Mathematics”, ($80K approx) November, 1989 - November 1990.
- NSF Grant USE 8814009: “Calculus: Restructuring and Integration with Computing” (planning grant for revision of calculus curriculum), ($50K approx) 1988 - 1989.

2021– | Professor Emeritus | — | Dartmouth College |

2004–2007 | Department Chair | — | Dartmouth College |

1994 (Fall) | Member | — | MSRI |

1993–2021 | Professor | — | Dartmouth College |

1987–1993 | Associate Professor | — | Dartmouth College |

1981–1987 | Assistant Professor | — | Dartmouth College |

1979–1981 | Lawton Lecturer | — | Temple University |

My research is in algebraic number theory with a particular interest in the theory of modular forms, central simple algebras, and the theory of buildings and their applications. I have done extensive work on questions of the representability of modular forms by theta series attached to quadratic forms, and have used the arithmetic of quaternion algebras to answer questions regarding the representation numbers of ternary and quaternary quadratic forms. Other work has included aspects of the theory of newforms for integral and half-integral weight modular forms of elliptic and Hilbert type as well as the study of higher rank Hecke operators and their relation to Bruhat-Tits buildings for $GL_n(K)$ and $Sp_n(K)$, $K$ a local field. Recent work has focused on the geometric and combinatorial aspects of affine buildings, as well as their application to the study of arithmetic in central simple algebras.

SUPERVISED PHD STUDENTSStudent Name | Current Affiliation | Degree Year | Thesis title |
---|---|---|---|

Angelica Babei | McMaster University | 2019 | On the Arithmetic of Tiled Orders |

Michael Wijaya | Bard HS Early College Queens | 2015 | A function-field analogue of Conway's Topograph |

Benjamin Linowitz | Oberlin College | 2012 | Selectivity in Central Simple Algebras and Isospectrality |

Alison Setyadi | Department of Defense | 2007 | The Affine Buildings of $SL_n$ and $Sp_n$: A Combinatorial Perspective |

Nathan Ryan | Bucknell University | 2005 | Calculating Satake parameters |

Susan D'Agostino | Editor/Writer/Mathematician | 2003 | Classifying Additive Codes |

Holly Rosson | Warren Wilson College | 2000 | Theta functions over function fields |

Sharon Frechette | Holy Cross | 1997 | Decomposition of Spaces of Half-Integral Weight Cusp Forms |

Tamara Veenstra | University of Redlands | 1997 | Characterizing Siegel Modular Forms |

Timothy Atwill | Former Head:Investment Strategy/Portfolio Mgr, Parametric Portfolio Assoc | 1993 | Diagonalizing Spaces of Hilbert Cusp Forms |

Lynne Walling | University of Bristol, UK | 1987 | Theta Series attached to Lattices of Arbitrary Rank |

John Wesley Young Research Instructors at Dartmouth

Name | Current Affiliation | Years |
---|---|---|

Cristina Ballantine | Holy Cross | 2000–2002 |

Anne Schwartz | U Mass, Amherst | 1989–1991 |

Jacob Nemchenok | Private Industry | 1985–1987 |

John Cremona | Warwick Mathematics Institute, UK | 1982–1984 |

- National Science Foundation
- National Security Agency
- Mathematical Reviews
- Zentralblatt für Mathematik
- Acta Arithmetica
- Glasgow Mathematical Journal
- International Journal of Number Theory
- Journal of Number Theory
- London Math Society
- Pacific Journal of Mathematics
- Ramanujan Journal
- Rocky Mountain Journal
- Transactions of the American Mathematical Society

- American Mathematical Society
- Mathematical Association of America

[Books and Monographs]

- (with H. Hijikata and A.
Pizer), The Basis Problem for Modular Forms on Gamma_0(N)
*Memoirs of the AMS*,**418**(1989), 159 pages. *Modern Cryptography and Elliptic Curves: A Beginner's Guide*, STML 83, AMS, 252 pages, 2017, ISBN: 978-1-4704-3582-0.

- (with H. Hijikata and A.
Pizer), The Basis Problem for Modular Forms on Gamma_0(N),
*Proc. Japan Acad.*,**56**(1980), pp. 280-284. - Cuspidal Newforms and
Character Twists,
*J. reine angew. Math.*,**328**(1981), pp. 58-71. - Primitive Newforms of
Weight 3/2,
*Acta Arith.*,**43**(1984), pp. 97-104. - Ternary Quadratic Forms and the Arithmetic of Quaternion Algebras, preprint.
- Representations of Ternary
Quadratic Forms and the Class Number of Imaginary Quadratic Fields,
*Pacific J. of Math.*,**122**(1986), pp. 223-250. - Ternary Quadratic Forms and
Quaternion Algebras,
*Journal of Number Theory***23**(1986), pp. 203-209. - (with H. Hijikata and A.
Pizer), Orders in Quaternion Algebras,
*J. reine angew. Math.***394**(1989), pp. 59-106. - (with H. Hijikata and A.
Pizer), Twists of Newforms,
*Journal of Number Theory***35**(1990), pp 287 - 324. - (with L. Walling) On the
Shimura Lift for Hilbert Modular Forms, in
*A Tribute to Emil Grosswald: Number Theory and Related Analysis*, Contemporary Mathematics, Volume**143**, Knopp and Sheingorn Editors, American Mathematical Society, March 1993, pp 561 - 569. - (with L. Walling), Twists
of Hilbert Modular Forms,
*Transactions of the AMS*,**338**, (1993), 375 - 403. - (with L. Walling),
Determining Multiplicities of Half-Integral Weight Newforms,
*Pacific Journal of Math.*,**167**, (1995), 345 - 383. - (with L. Walling), A Characterization of Simultaneous Hecke Eigenforms, preprint
- (with A. Schwartz), Maximal
Orders in Central Simple Algebras and Bruhat-Tits Buildings,
*Journal of Number Theory*,**56**, (1996), 115 - 138. - Newforms of Half-Integral
Weight,
*Nagoya Math J.***143**, (1996), 147 - 169. - (with C. Ballantine) Rolle's Theorem over Local Fields (preprint)
- (with J. Rhodes),
Rationality Theorems for Hecke Operators on GL
_{n},*J. of Number Theory***102**, (2003), 278 - 297. - (with C. Ballantine and J.
Rhodes), Hecke Operators for $GL_n$ and Buildings,
*Acta Arithmetica***112**, (2004), 131 - 140. - The Arithmetic and
Combinatorics of Buildings for $Sp_n$
*Transactions AMS***359**, (2007), 3409-3423. - Hecke Operators, Zeta Functions, and the Satake Map (preprint)
- (with N. Ryan) Inverting the Satake Map for $Sp_n$ and
applications to Hecke Operators,
*Ramanujan J.***17**(2), 2008, 219 -- 244. - (with S. Treneer, L. Walling) Constructing Simultaneous
Hecke Eigenforms,
*International J. Number Theory***6**(5), 2010, 1117 -- 1137. - Split Orders and Convex Polytopes in Buildings,
*J. Number Theory*,**30**(1), 2010, 101 -- 115. - (with B. Linowitz) Embedding Orders in Central Simple
Algebras,
*Journal de théorie des nombres de Bordeaux*, 24 no. 2 (2012), 405 -- 424. - (with B. Linowitz) Local Selectivity of Orders in Central Simple
Algebras,
*International Journal of Number Theory.*13, No. 4, pp. 853--884 (2017) - (with J. Jorgenson, L. Smajlovic) Lynne Heather Walling, a memorial article, submitted to the
*Notices of the AMS.*

- (with J. Baumgartner, et al.) Teaching Calculus with True BASIC, in Priming the Calculus Pump: Innovations and Resources, MAA Notes 17 (1990), pp 33 - 50.

- The Basis Problem for Modular Forms on Gamma_0(2^{2r}M), Ph.D. dissertation, University of Rochester (1979).
- Notes on the Shimura-Shintani Correspondence, preprint.
- WeBWorK Newbie Guide(versions 1.4, 1.5),(2000), 41 pages
- WeBWorK Newbie Guide -- version 1.7, (2002), 68 pages
- WeBWorK Installation and Course Setup Guide (local notes version 1.6), (2001), 11 pages
- WeBWorK Installation and Course Setup Guide (local notes version 1.7), (2002), 13 pages
- WeBWorK Installation and Course Setup Guide (local notes version 1.8), (2003), 15 pages
- Introduction to Mathematics Beyond Calculus