Grant, David R

Research

research overview

Grant's research is in the area of number theory related to algebraic geometry, known as arithmetic geometry. He also applies this research to the construction of codes used for reliable digital communications. From time to time he is involved in mathematical education research into equitable mathematical education practices.

keywords

number theory, arithmetic geometry, coding theory

Publications

selected publications

chapter
- All-in University: Changing Everything at Once 2021
- Culture and Equity 2021
- Sustaining Active Learning 2021
- Space-time codes and non-associative division algebras arising from elliptic curves. Contemporary Mathematics. 29-44. 2008
- Theta functions and singular torsion on elliptic curves. 111-126. 2002
- A public key cryptosystem based on sparse polynomials. 114-121. 2000
- Formal groups of twisted multiplicative groups and $L$-series. 89-102. 1995
journal article
- Differential codes on higher dimensional varieties via Grothendieck's residue symbol. Journal of Pure and Applied Algebra. 2024
- On the universal p-adic sigma and Weierstrass zeta functions. Journal of Number Theory. 348-376. 2023
- Modeling human health behavior with a new index that measures connectivity. Preventive Medicine Reports. 102172-102172. 2023
- A higher-order generalization of Jacobi's derivative formula and its algebraic geometric analogue. Journal de Theorie des Nombres de Bordeaux. 361-386. 2021
- A generalization of Jacobi's derivative formula to dimension two, II. Acta Arithmetica. 403-420. 2019
- Feasibility of Single-Beam Interference Alignment in Multi-Carrier Interference Channels. IEEE Transactions on Information Theory. 7352-7357. 2017
- HIGHER GENUS UNIVERSALLY DECODABLE MATRICES (UDMG). Advances in Mathematics of Communications. 257-270. 2014
- The Quadratic Gauss Sum Redux. American Mathematical Monthly. 145-149. 2014
- Integral division points on curves. Compositio Mathematica. 2011-2035. 2013
- On an analogue of the Lutz-Nagell Theorem for hyperelliptic curves. Journal of Number Theory. 963-969. 2013
- Integral division points on curves. 2011-2035. 2013
- One-parameter families of elliptic curves over Q with maximal Galois representations. Proceedings of the London Mathematical Society. 654-675. 2011
- On the classification of 3-dimensional non-associative division algebras over p-adic fields. Journal de Theorie des Nombres de Bordeaux. 329-346. 2011
- The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications. 131-145. 2008
- Duality theory for space-time codes over finite fields. Advances in Mathematics of Communications. 35-54. 2008
- Some remarks on almost rational torsion points. Journal de Theorie des Nombres de Bordeaux. 13-28. 2006
- Geometric proofs of reciprocity laws. Journal für die Reine und Angewandte Mathematik. 91-124. 2005
- Torsion on theta divisors of hyperelliptic Fermat Jacobians. Compositio Mathematica. 1432-1438. 2004
- The cuspidal torsion packet on hyperelliptic Fermat quotients. Journal de Theorie des Nombres de Bordeaux. 577-585. 2004
- Singular torsion points on elliptic curves. Mathematical Research Letters. 847-866. 2003
- On Gunning's prime form in genus 2. Canadian Mathematical Bulletin. 89-96. 2002
- Some product formulas for theta functions in one and two variables. Acta Arithmetica. 223-238. 2002
- 5-torsion points on curves of genus 2. Journal of the London Mathematical Society. 29-43. 2001
- An explicit theorem of the square for hyperelliptic Jacobians. Michigan Mathematical Journal. 485-492. 2001
- A formula for the number of elliptic curves with exceptional primes. Compositio Mathematica. 151-164. 2000
- Examples of torsion points on genus two curves. Transactions of the American Mathematical Society. 4533-4555. 2000
- Units from 5-torsion on the Jacobian of y(2)=x(5)+1/4 and the conjectures of Stark and Rubin. Journal of Number Theory. 227-251. 1999
- Sequences of fields with many solutions to the unit equation. Rocky Mountain Journal of Mathematics. 1017-1029. 1996
- A proof of quintic reciprocity using the arithmetic of y(2)=x(5)+1/4. Acta Arithmetica. 321-337. 1996
- UNITS FROM 3-TORSION AND 4-TORSION ON JACOBIANS OF CURVES OF GENUS-2. Compositio Mathematica. 311-320. 1994
- A CURVE FOR WHICH COLEMAN EFFECTIVE CHABAUTY BOUND IS SHARP. Proceedings of the American Mathematical Society. 317-319. 1994
- INTEGER POINTS ON CURVES OF GENUS-2 AND THEIR JACOBIANS. Transactions of the American Mathematical Society. 79-100. 1994
- COMPUTING THE MORDELL-WEIL RANK OF JACOBIANS OF CURVES OF GENUS-2. Transactions of the American Mathematical Society. 807-824. 1993
- SMALL SOLUTIONS TO A GIVEN QUADRATIC FORM WITH A VARIABLE MODULUS. Journal of Number Theory. 57-60. 1992
- A GENERALIZATION OF A FORMULA OF EISENSTEIN. Proceedings of the London Mathematical Society. 121-132. 1991
- FORMAL GROUPS IN GENUS 2. Journal für die Reine und Angewandte Mathematik. 96-121. 1990
- On Heterogeneous Spaces. Journal of the London Mathematical Society. 385-397. 1989
- A GENERALIZATION OF JACOBI DERIVATIVE FORMULA TO DIMENSION-2. Journal für die Reine und Angewandte Mathematik. 125-136. 1988
- COATES-WILES TOWERS IN DIMENSION-2. Mathematische Annalen. 645-666. 1988

Background

education and training

Ph.D., Massachusetts Institute of Technology 1985
B.A., Princeton University 1981

awards and honors

President's Teaching Scholar, conferred by University of Colorado President, 2018
BFA Award for Excellence in Teaching and Pedagogy, conferred by Boulder Faculty Assembly, 1991

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Research

research overview

keywords

Publications

selected publications

chapter

journal article

Background

education and training

awards and honors

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