# Helen G. Grundman

- Ph.D. University of California, Berkeley, CA 1989
- B.S. University of Michigan, Ann Arbor, MI 1979

Office: 334 Park Science Bldg

Phone: (610)526-5347

E-mail: hgrundma@brynmawr.edu
### Research Interests: Algebra and Number Theory

My mathematical research interests span a wide range of topics in the
areas of algebra and number theory. My primary work is in the areas of
algebraic number theory and computational algebraic geometry.
Specifically, my research involves exploiting the connections between
Hilbert modular varieties and certain algebraic number fields,
studying the fields to determine classifications of the varieties.
Additional research topics include:
- Galois realizability and embedding of small 2-groups, Q-adequacy..
- Various areas of elementary number theory, including Niven numbers
and happy numbers.
- Multiplier systems of functions similar to modular functions,
arising from considerations of modular equations.
- Solving diophantine equations over number rings using algebraic
number theory and computational methods.

My teaching philosophies are too numerous to list here. My goals in
teaching include giving students the tools to enable them to teach
themselves and challenging them sufficiently that they are likely to
achieve much more than they thought they could. These goals guide
me whether I'm teaching students who are afraid of mathematics or
graduate students working towards a Ph.D. in Mathematics.
### Recent publications:

"Multipliers of a family of almost modular functions,"
with A. Schwartz, The Ramanujan Journal, to appear.
"Heights of happy numbers and cubic happy numbers,"
with E. A. Teeple, The Fibonacci Quarterly, to appear.

"Realizability of non-split group extensions of
C_{2}
by
(C_{2})^{r}
×
(C_{4})^{s}
×
(D_{4})^{t},"
with G. Stewart, Journal of Algebra, to appear.

"Hilbert modular fourfolds of arithmetic genus one,"
with L. E. Lippincott, High Primes and Misdemeanours:
lectures in honour of the 60th birthday of Hugh Cowie Williams,
Fields Institute Communications Series, to appear.

"**Q**-adequacy of Galois 2-extensions,"
with D. B. Leep and T. L. Smith, The Israel Journal of Mathematics,
130 (2002), 11-19.

"Hilbert modular threefolds of arithmetic genus one,"
with L. E. Lippincott, The Journal of Number Theory,
95 (2002), 72-76.

"**Q**-adequate bicyclic bicubic fields,"
with T. L. Smith, Valuation Theory and its Applications,
Fields Institute Communications, 32 (2002), 163-173.

"Generalized happy numbers," with E. A. Teeple,
The Fibonacci Quarterly, 39 (2001), 462-466.

"An analysis of n-riven numbers,"
The Fibonacci Quarterly, 39 (2001), 253-255.

"Nonrational Hilbert modular threefolds,"
The Journal of Number Theory, 83 (2000), 50-58.

"Explicit resolutions of cubic cusp singularities,"
Mathematics of Computation, 69 (2000), 815-825.