- Award ID(s):
- 1749013
- Publication Date:
- NSF-PAR ID:
- 10232976
- Journal Name:
- The Quarterly Journal of Mathematics
- ISSN:
- 0033-5606
- Sponsoring Org:
- National Science Foundation
More Like this
-
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 Siegel-Weil 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.
-
We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus 2 2 curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holds for the subalgebra of cohomology generated by even tautological classes. Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted by the P=W conjecture. In combination with recent work of Mellit, this reduces the full conjecture to the multiplicativity of the perverse filtration. Our main technique is to study the Hitchin fibration as a degeneration of the Hilbert–Chow morphism associated with the moduli space of certain torsion sheaves on an abelian surface, where the symmetries induced by Markman’s monodromy operators play a crucial role.
-
In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the q-hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.
-
Abstract Manx comets are objects on long-period 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 pre-discovery data in 2010 until the present. Its spectral reflectivity is consistent with typical organic-rich comet surfaces with colors of
= 0.97 ± 0.02, = 0.43 ± 0.02, and = 0.65 ± 0.03, corresponding to a spectral reflectivity slope of 30 ± 3%/100 nm. There is no obvious indication of dust coma in deep stacked images. We estimate the nucleus radius to be ∼55.7 ± 0.3 km assuming an albedo of 4%. This is much smaller than the 1σ upper limits on the nucleus size of 79.9 km from the NEOWISE survey assuming the same albedo, since the NEOWISE survey is not very sensitive to objects this small at this distance. The heliocentric light curve suggests possible activity betweenr ∼ 17 and 13 au where 2013 LU28more » -
Abstract We investigate a covering problem in 3-uniform hypergraphs (3-graphs): Given a 3-graph F , what is c 1 ( n , F ), the least integer d such that if G is an n -vertex 3-graph with minimum vertex-degree $\delta_1(G)>d$ 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 3-graph 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.