C. NEAL TATE

C. Schnell TWO LECTURES ABOUT MUMFORD-TATE GROUPS

We define Hodge structures as representations, and introduce the Mumford–Tate group MT(H) of a rational Hodge structure. We give a characterization of MT(H) based on properties of reductive groups, and study it for elliptic curves and their powers. We define what it means for a Hodge structure to arise from an abelian variety (as is the case for K3 surfaces), and then focus on cases in which th...

Case Study : William Neal Moore

William Neal Moore was indicted by a grand jury in Jefferson County, Georgia, for the April 2, 1974 malice murder and armed robbery of Fredger Stapleton, an elderly black man and the uncle of an acquaintance of Mr. Moore. At a hearing conducted before Judge Walter C. McMillan, Jr. in the Superior Court of Jefferson County on June 4, 1974, Mr. Moore waived trial by jury with respect to both guil...

Uniform Generalized Steinhaus Graphs Neal

In [1] it is shown that the rst order theory of almost all generalized Steinhaus graphs is identical to the rst order theory of almost all graphs where each generalized Steinhaus graph is given the same probability. A natural probability measure on generalized Steinhaus graphs is obtained by independently assigning a probability o f p for each entry in the generating string of the graph. With t...

NEAL LOWSON McGOWAN

MAHSHID ATAPOUR and NEAL MADRAS

For a fixed permutation τ, let S N (τ) be the set of permutations on N elements that avoid the pattern τ. Madras and Liu (2010) conjectured that lim N→∞ |S N+1 (τ)| |S N (τ)| exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the 720 permutations of length 6). We also c...