Algebra and Number Theory Faculty
Faculty with Research Interests in Algebra and Number Theory
Research Faculty:
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Efraim Armendariz
(efraim@math.utexas.edu):
Research interests include the general structure
theory of noncommucative rings and their modules, with an emphasis
on rings satisfying a polynomial identity and von Neumann regular
rings; radical properties and torsion theories for ring and module
categories. Professional interests include issues in mathematics
education and reform mechanisms which lead to improved access for
groups not traditionally represented in the mathematical sciences.
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Frank Gerth III
(gerth@math.utexas.edu):
Research interests include Algebraic Number Theory, including class numbers, class groups,
discriminants, class field theory, density theorems, Iwasawa theory.
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Sean M. Keel
(keel@math.utexas.edu):
Research interests include Algebraic Geometry, particularly Mori's program, GIT, moduli
problems, and intersection theory.
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Stephen McAdam
(mcadam@math.utexas.edu):
Research interests include commutative
rings. His future research plans are to continue developing the theory
of asymptotic and essential prime divisors and their applications, and
to study projective equivalence.
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Alan W. Reid
(areid@math.utexas.edu):
Research interests include low-dimensional topology and
discrete groups. He is particularly interested in the geometry and topology
of hyperbolic 3-manifolds, and properties of their fundamental groups.
He is also interested in connections between hyperbolic 3-manifolds and
number theory..
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David Saltman
(saltman@math.utexas.edu):
Research interests include Brauer group theory and division algebras,
with an emphasis on invariant theory of groups acting on fields, rationality of
invariant fields, the center of the generic division algebra, and division
algebras over p-adic curves and their geometry.
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John Tate
(tate@math.utexas.edu):
Research interests include Algebraic Number Theory (local and global fields),
Class Field Theory, Galois cohomology, Galois representations, L-functions
and their special values, modular forms, elliptic curves and abelian varieties.
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Jeffrey Vaaler
(vaaler@math.utexas.edu):
Research interests include Analytic Number Theory, Diophantine
approximation and the geometry of numbers in local and global fields,
Diophantine inequalities, polynomials, effective measures of irrationality
and transcendence, applications of Fourier analysis in number theory, inequalities
and extremal problems.
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Felipe Voloch
(
):
Research interests include arithmetic of function fields. Diophantine
geometry over function fields. Geometry of algebraic curves. Arithmetic
analogues of geometric methods. Modular forms, elliptic curves and
abelian varieties. Applications to coding theory.
Post-Doctoral Faculty:
Links to Research Groups:
