In this paper we introduce a new “observable” in the dictionary between (a protected sector of) four-dimensional N=2 superconformal field theories and two-dimensional chiral algebras. On the four-dimensional side, the observable is given by the lens…

We study the supersymmetric partition function on $S^1 \times L(r, 1)$, or the lens space index of four-dimensional $\mathcal{N}=2$ superconformal fi…

Any Haken 3--manifold (possibly with boundary consisting of tori) can be transformed into a $\mathrm{surface}\times S^1$ by a series of splitting and…

In this section we present two protocols. Our protocols are based on pairwise independent generators and unbalanced expanders with near-optimal expansion. Here different rounds use different random bits. In contrast to O(nlogn) random bits per round…

We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network. We present the …

The method of exchangeable pairs can also be used to analyze nonlinear matrix-valued functions of random variables. In this section, we explain how to analyze matrix functions that satisfy a self-reproducing property.

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis r…

We give a different geometric interpretation of the deletion–contraction relation proved in the previous section, which views the graph hypersurface of Γ as a Milnor fiber for hypersurfaces related to Γ∖e and Γ/e. An advantage of this point of view …

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendiec…

For n≥0, let Kn=Q(α1,…,αn) be the field of rational functions in α1,…,αn over the set of rational numbers. We will admit that K0=Q. For k≥m≥1 and n≥0, define

We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the ge…

Cuprate superconductors have many different atoms per unit cell. A large fraction of cells (5-25%) must be modified ("doped") before the material sup…

The author especially thanks Sergei Gukov for collaboration during the early stages of this project and various interesting and helpful discussions along the way. We would also like to thank Ibrahima Bah, Chris Beem, and James Sparks for insightful …

In this paper, we initiate the study of holographic renormalization group flows acting on the metric of four-manifolds. In particular, we derive a se…

While PSR J2129−0429 clearly meets the observational criteria for identification as a redback system—it is an eclipsing MSP with a nondegenerate companion of a few tenths of a solar mass—its extreme parameters relative to other systems in that popul…

PSR J2129-0429 is a "redback" eclipsing millisecond pulsar binary with an unusually long 15.2 hour orbit. It was discovered by the Green Bank Telesco…

We study the supergravity dual of four-dimensional ${\mathcal{N}=1}$ superconformal field theories arising from wrapping M5-branes on a K\"ahler two-…

Motivated by a greedy approach for generating {\it{information stable}} processes, we prove a universal maximum likelihood (ML) upper bound on the ca…

The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achieva…

The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-f…

Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum com…

We present the design, fabrication, and characterization of a planar silicon photonic crystal cavity in which large position-squared optomechanical c…

The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as po…

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstra…

Binary black holes are the primary endpoint of massive stellar evolution. Their properties provide a unique opportunity to constrain binary evolution…

Theorem 4.2.4 implies that the mod p differential operators from Section 3 map Hecke eigenforms to Hecke eigenforms. When there are Galois representations arising from the corresponding systems of Hecke eigenvalues, it is natural to ask how our diff…

The main goal of this paper is to describe the effect of certain differential operators on mod $p$ Galois representations associated to automorphic f…

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle o…

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