
Graduate Materials
Open Source
Abbreviated Vitæ
Photo Gallery

Research Interests
Research Papers
Expository Papers
Undergrad Materials
Thomas R. Shemanske
CONTACT INFORMATION
Dartmouth College  (603) 6463179 (office)  
Department of Mathematics  (603) 6461312 (fax)  
Hanover, NH 037553551  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: (coPI, funded) ``Development and Dissemination of a Free, Online Calculus Course for College and High School Students'' (DC 538132), $50k, July 1, 2003  June 30, 2006.
Hewlett Foundation: (coPI, 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:(CoPrincipal Investigator 19901991) ``Calculus: Restructuring and Integration with Computing" (3year grant to carry out calculus reform), ($300K approx) 1989  1992.
Sloan Foundation Grant 89101: ``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
20042007  Department Chair    Dartmouth College 
1994 Fall  Member    MSRI 
1993present  Professor    Dartmouth College 
19871993  Associate Professor    Dartmouth College 
19811987  Assistant Professor    Dartmouth College 
19791981  Lawton Lecturer    Temple University 
RESEARCH
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 halfintegral weight modular forms of elliptic and Hilbert type as well as the study of higher rank Hecke operators and their relation to BruhatTits 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 STUDENTS
Student Name  Current Affiliation  Degree Year  Thesis title 

Michael Wijaya  Dartmouth College  2015  A functionfield analogue of Conway's Topograph 
Benjamin Linowitz  U of Michigan  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  2005  Calculating Satake parameters 
Susan D'Agostino  Southern NH Univ  2003  Classifying Additive Codes 
Holly Rosson  Warren Wilson College  2000  Theta functions over function fields 
Sharon Frechette  Holy Cross  1997  Decomposition of Spaces of HalfIntegral Weight Cusp Forms 
Tamara Veenstra  University of Redlands  1997  Characterizing Siegel Modular Forms 
Timothy Atwill  Parametric  1993  Diagonalizing Spaces of Hilbert Cusp Forms 
Lynne Walling  University of Bristol, UK  1987  Theta Series attached to Lattices of Arbitrary Rank 
SPONSORED POSTDOCTORAL FELLOWS
John Wesley Young Research Instructors at DartmouthName  Current Affiliation  Years 

Cristina Ballantine  Holy Cross  20002002 
Anne Schwartz  U Mass, Amherst  19891991 
Jacob Nemchenok  Private Industry  19851987 
John Cremona  Warwick Mathematics Institute, UK  19821984 
REFEREE/REVIEWER
 National Science Foundation
 Mathematical Reviews
 Zentralblatt für Mathematik
 Acta Arithmetica
 Glasgow Mathematical Journal
 Journal of Number Theory
 London math Society
 Pacific Journal of Mathematics
 Ramanujan Journal
 Rocky Mountain Journal
 Transactions of the American Mathematical Society
PROFESSIONAL SOCIETIES
 American Mathematical Society
 Mathematical Association of America
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.

(underr development) Working title: From Calculus to Applications of Elliptic Curves, 138 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. 280284.
Cuspidal Newforms and Character Twists, J. reine angew. Math., 328 (1981), pp. 5871.
Primitive Newforms of Weight 3/2, Acta Arith., 43 (1984), pp. 97104.
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. 223250.
Ternary Quadratic Forms and Quaternion Algebras, Journal of Number Theory 23 (1986), pp. 203209.
(with H. Hijikata and A. Pizer), Orders in Quaternion Algebras, J. reine angew. Math. 394 (1989), pp. 59106.
(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 HalfIntegral 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 BruhatTits Buildings, Journal of Number Theory, 56, (1996), 115  138.
Newforms of HalfIntegral 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), 34093423.
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, arXiv, to appear, International Journal of Number Theory.
(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 ShimuraShintani 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
Back to the homepage
Last modified on April 10, 2016