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Douglas Ulmer
Member of the Graduate Faculty | Department Head, Mathematics | Professor, Mathematics
Mathematics
Map Page
Research Area
algebraic geometry,
number theory,
mathematics,
group theory,
function fields,
elliptic curves,
cryptography,
abstract algebra,
curves,
field theory,
arithmetic
Grants
(2)
Arithmetic Geometry
Active
·
2020
·
$42K
·
External
Principal Investigator (PI)
algebraic geometry,
number theory,
mathematics,
commutative algebra,
cryptography
Arithmetic of Abelian Varieties over Function Fields
2017
·
$21K
·
External
Principal Investigator (PI)
algebraic geometry,
number theory,
mathematics,
function fields,
arithmetic
Publications
(54)
Recent
-torsion for unramified Artin-Schreier covers of curves
2023
algebraic geometry,
number theory,
field theory,
galois theory,
cryptography
Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces
2022
elliptic surfaces,
divisibility sequences,
geography of surfaces,
transversality of sections,
applications
Every 𝐵𝑇₁ grouscheme appears in a Jacobian
2022
algebra,
mathematics,
jacobian,
group theory,
abstract algebra
Bounding tangencies of sections on elliptic surfaces
2021
elliptic surfaces,
tangencies,
bounding,
sections,
curves
On BT1 grouschemes and Fermat curves
2021
number theory,
algebraic geometry,
cryptography,
abstract algebra,
mathematics
Every grouscheme appears in a Jacobian
2021
algebraic geometry,
mathematics,
group theory,
topology,
complex analysis
p-torsion of unramified ZZ-covers
2021
algebraic geometry,
number theory,
field theory,
algebraic topology,
group theory
On the arithmetic of a family of twisted constant elliptic curves
2020
elliptic curves,
arithmetic,
twisted curves,
family,
constant
On grouschemes and Fermat Jacobians
2020
number theory,
algebraic geometry,
abstract algebra,
cryptography,
mathematical cryptography
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
2020
number theory,
algebraic geometry,
elliptic curves,
global function fields,
arithmetic geometry
Collaborations
(9)
Hao Zhang
Mutual work: 1 Proposal
Collaboration Details
Michael Chertkov
Mutual work: 1 Proposal
Collaboration Details
Shankar Venkataramani
Mutual work: 1 Proposal
Collaboration Details
Joseph Watkins
Mutual work: 1 Proposal
Collaboration Details
Kevin Lin
Mutual work: 1 Proposal
Collaboration Details
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News
(1)
UArizona Mathematician and Cosmologist Awarded Sloan Research Fellowships
2021
8+ Collaborators
$63K / $63K Funding
50+ Publications