| Dartmouth College | (603) 646-3179 (office) | |
| Department of Mathematics | (603) 646-1312 (fax) | |
| Hanover, NH 03755-3551 | thomas.r.shemanske@dartmouth.edu |
EDUCATION
| 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.
TEACHING AND PROFESSIONAL EXPERIENCE
| 2004--2007 | Department Chair | --- | Dartmouth College |
| 1994 Fall | Member | --- | MSRI |
| 1993--present | Professor | --- | Dartmouth College |
| 1987--1993 | Associate Professor | --- | Dartmouth College |
| 1981--1987 | Assistant Professor | --- | Dartmouth College |
| 1979--1981 | Lawton Lecturer | --- | Temple University |
RESEARCH
My research is in algebraic number theory with a particular interest in the theory of modular forms. I have done an extensive amount of work on questions of the representability of modular forms by theta series attached to quadratic forms, and I have used the arithmetic of quaternion algebras to answer questions regarding the representation numbers of 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 GLn(K) and SPn(K), K a local field. Current work concerns Hecke operators and auxilliary operators for Siegel modular forms.
SUPERVISED PhD STUDENTS
| Student Name | Current Affiliation | Degree Year | Thesis title |
|---|---|---|---|
| Benjamin Linowitz | Dartmouth College | 2011/12 | |
| Alison Setyadi | College of Mount St. Vincent | 2007 | The Affine Buildings of SL_n and Sp_n: A Combinatorial Perspective |
| Nathan Ryan | Bucknell | 2005 | Calculating Satake parameters |
| Susan D'Agostino | Portsmouth, NH | 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 | Russell Investments | 1993 | Diagonalizing Spaces of Hilbert Cusp Forms |
| Lynne Walling | University of Colorado (Boulder) | 1987 | Theta Series attached to Lattices of Arbitrary Rank |
SPONSORED POSTDOCTORAL FELLOWS
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 | University of Nottingham, UK | 1982--1984 |
RECENT INVITED TALKS
REFEREE/REVIEWER
PROFESSIONAL SOCIETIES
PUBLICATIONS
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.
Research Articles
(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 GLn, J. of Number Theory 102, (2003), 278 - 297.
(with C. Ballantine and J. Rhodes), Hecke Operators for GLn and Buildings, Acta Arithmetica 112, (2004), 131 - 140.
The Arithmetic and Combinatorics of Buildings for Spn 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 (to appear Ramanujan Journal)
(with S. Treneer, L. Walling) Constructing Simultaneous Hecke Eigenforms, submitted.
Split Orders and Convex Polytopes in Buildings, submitted.
(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.
Other Manuscripts
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