TY - GEN
AB - Soon, the genetic basis of most human Mendelian diseases will be solved. The next challenge will be to leverage this information to uncover basic mechanisms of disease and develop new therapies. To understand how this transformation is already beginning to unfold, we focus on the ciliopathies, a class of multi-organ diseases caused by disruption of the primary cilium. Through a convergence of data involving mutant gene discovery, proteomics, and cell biology, more than a dozen phenotypically distinguishable conditions are now united as ciliopathies. Sitting at the interface between simple and complex genetic conditions, these diseases provide clues to the future direction of human genetics.
AU - Gaia Novarino
AU - Akizu, Naiara
AU - Gleeson, Joseph G
ID - 2312
IS - 1
T2 - Cell
TI - Modeling human disease in humans: The ciliopathies
VL - 147
ER -
TY - CONF
AB - The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Thomas, Lawrence E
ID - 2320
TI - Binding, stability, and non-binding of multi-polaron systems
ER -
TY - CONF
AB - We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger operators on the half-line with complex-valued potentials.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Robert Seiringer
ID - 2321
TI - A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials
VL - 214
ER -
TY - JOUR
AB - For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated.
AU - Timothy Browning
ID - 233
IS - 2
JF - Archiv der Mathematik
TI - Power-free values of polynomials
VL - 96
ER -
TY - JOUR
AB - We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications.
AU - Timothy Browning
ID - 234
IS - 3
JF - Journal de Theorie des Nombres de Bordeaux
TI - The divisor problem for binary cubic forms
VL - 23
ER -
TY - JOUR
AB - For given positive integers m and n, we consider the frequency of representations of m/n as a sum of unit fractions.
AU - Browning, Timothy D
AU - Elsholtz, Christian
ID - 235
IS - 2
JF - Illinois Journal of Mathematics
TI - The number of representations of rationals as a sum of unit fractions
VL - 55
ER -
TY - JOUR
AB - An asymptotic formula is established for the number of Q-rational points of bounded height on a nonsingular quartic Del Pezzo surface with a conic bundle structure.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 236
IS - 1
JF - Duke Mathematical Journal
TI - Manin's conjecture for quartic Del Pezzo surfaces with a conic fibration
VL - 160
ER -
TY - JOUR
AB - An effective search bound is established for the least non-trivial integer zero of an arbitrary cubic form C ε ℤ[X 1,...,X n], provided that n ≥ 17.
AU - Timothy Browning
AU - Dietmann, Rainer
AU - Elliott, Peter
ID - 239
IS - 3
JF - Mathematische Annalen
TI - Least zero of a cubic form
VL - 352
ER -
TY - JOUR
AB - We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>2α, that is, the ground state energy per particle has a finite limit as N→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Thomas, Lawrence E
ID - 2390
IS - 1
JF - Publications Mathematiques de l Institut des Hautes Etudes Scientifiques
TI - Stability and absence of binding for multi-polaron systems
VL - 113
ER -
TY - JOUR
AB - The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.
AU - Frank, Rupert L
AU - Lewin, Mathieu
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2391
IS - 15
JF - Physical Review Letters
TI - Energy cost to make a hole in the fermi sea
VL - 106
ER -