 Award ID(s):
 1749013
 Publication Date:
 NSFPAR ID:
 10232976
 Journal Name:
 The Quarterly Journal of Mathematics
 ISSN:
 00335606
 Sponsoring Org:
 National Science Foundation
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A bstract We revisit the proposal that the ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space — is dual to an exotic theory of gravity in three dimensions dubbed U(1) gravity. We consider flavored partition functions, where the usual genus g partition function is weighted by Wilson lines coupled to the conserved U(1) currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure these U(1) charges. This allows us to derive a SiegelWeil formula which computes the average of these flavored partition functions. The result takes the form of a “sum over geometries”, albeit with modifications relative to the unflavored case.

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Abstract Manx comets are objects on longperiod comet orbits that are inactive as they approach perihelion. They are of particular interest because they may help constrain solar system formation models. 2013 LU28 was discovered as an inactive asteroidal object on 2013 June 8 at a heliocentric distance of 21.8 au. Images and photometric data were obtained of 2013 LU28 from multiple telescopes from prediscovery data in 2010 until the present. Its spectral reflectivity is consistent with typical organicrich comet surfaces with colors of
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Abstract We investigate a covering problem in 3uniform hypergraphs (3graphs): Given a 3graph F , what is c 1 ( n , F ), the least integer d such that if G is an n vertex 3graph with minimum vertexdegree $\delta_1(G)>d$ then every vertex of G is contained in a copy of F in G ? We asymptotically determine c 1 ( n , F ) when F is the generalized triangle $K_4^{(3)}$ , and we give close to optimal bounds in the case where F is the tetrahedron $K_4^{(3)}$ (the complete 3graph on 4 vertices). This latter problem turns out to be a special instance of the following problem for graphs: Given an n vertex graph G with $m> n^2/4$ edges, what is the largest t such that some vertex in G must be contained in t triangles? We give upper bound constructions for this problem that we conjecture are asymptotically tight. We prove our conjecture for tripartite graphs, and use flag algebra computations to give some evidence of its truth in the general case.