Jordan S. Ellenberg

Learn More
CONTEXT The cause of Parkinson disease (PD) is unknown. Genetic linkages have been identified in families with PD, but whether most PD is inherited has not been determined. OBJECTIVE To assess genetic inheritance of PD by studying monozygotic (MZ) and dizygotic (DZ) twin pairs. DESIGN Twin study comparing concordance rates of PD in MZ and DZ twin pairs.(More)
We introduce a new method to bound -torsion in class groups, combining analytic ideas with reflection principles. This gives, in particular, new bounds for the 3-torsion part of class groups in quadratic, cubic and quartic number fields, as well as bounds for certain families of higher degree fields and for higher . Conditionally on GRH, we obtain a(More)
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: • the cohomology of the configuration space of n distinct ordered points on an arbitrary manifold; • the diagonal coinvariant algebra on r sets of n variables; • the cohomology and tautological ring of the moduli space of n-pointed curves; •(More)
We prove that the equation A+B = C has no solutions in coprime positive integers when p ≥ 211. The main step is to show that, for all sufficiently large primes p, every Q-curve over an imaginary quadratic field K with a prime of bad reduction greater than 6 has a surjective mod p Galois representation. The bound on p depends on K and the degree of the(More)
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: • the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold; • the diagonal coinvariant algebra on r sets of n variables; • the cohomology and tautological ring of the moduli space of(More)
We consider two families Xn of varieties on which the symmetric group Sn acts: the configuration space of n points in C and the space of n linearly independent lines in C. Given an irreducible Sn-representation V , one can ask how the multiplicity of V in the cohomology groups H(Xn;Q) varies with n. We explain how the Grothendieck–Lefschetz Fixed Point(More)
This is a preliminary report of an ongoing study of the relationship between unexplained infertility and depressive illness conducted by a team of two specialists: a gynecologist and a psychiatrist. Over a 3-year period, 16 cases of unexplained infertility and depressive illness were treated by the team. Nine of the cases received psychiatric treatment,(More)
A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet [17] asked whether every Q-curve is modular, and he showed that a positive answer would follow from J.-P. Serre’s conjecture on mod p Galois representations. We answer Ribet’s question in the affirmative, subject to certain local(More)