Hilbert-Samuel sequences of homogeneous finite type

This paper deals with the problem of the classification of the local graded Artinian quotients $\mathbb{K}[x,y]/I$ where $\mathbb{K}$ is an algebraically closed field of characteristic $0$. They have a natural invariant called Hilbert-Samuel sequence. We say that a Hilbert-Samuel sequence is of homogeneous finite type, if it is the Hilbert-Samuel sequence of a finite number of isomorphism classes of graded local algebras. We give the list of all the Hilbert-Samuel sequences of homogeneous finite type in the case of algebras generated by $2$ elements of degree $1$

Interpolating Between Hilbert-Samuel and Hilbert-Kunz Multiplicity

We define a function, called s-multiplicity, that interpolates between Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value is equal to Hilbert-Samuel multiplicity for small values of s and is equal to Hilbert-Kunz multiplicity for large values of s. We prove that it has an Associativity Formula generalizing the Associativity Formulas for Hilbert-Samuel and Hilbert-Kunz multiplicity. We also define a family of closures such that if two ideals have the same s-closure then they have the same s-multiplicity, and the converse holds under mild conditions. We describe the s-multiplicity of monomial ideals in toric rings as a certain volume in real spaceComment: 19 page

Lust

2 Samuel 11:2-5, Matthew 5:27-3

Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

It is a well-known fact, that the greatest ambit for a topological group $G$ is the Samuel compactification of $G$ with respect to the right uniformity on $G.$ We apply the original destription by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using Fra\"iss\'e theory and Ramsey theory. This work generalizes some of the known results about countable structures.Comment: 12 page

Concerto Competition Finals, March 6, 2012

This is the concert program of the Concerto Competition Finals performance on Tuesday, March 6, 2012 at 6:30 p.m., at the Boston University Concert Hall, 855 Commonwealth Avenue, Boston, Massachusetts. Works performed were Concerto no. 3 in d minor, op. 30 by Sergei Rachmaninoff, Concert Piece for Four Horns and Orchestra by Robert Schumann, Four Last Songs by Richard Strauss, Violin Concert, op. 14 by Samuel Barber, Concerto in A major, K. 622 by Wolfgang Amadeus Mozart, Incantation, Threne, et Danse by Alfred Desenclos, Concerto no. 1 in b-flat minor, op. 23 by Peter Tchaikovsky, Knoxville: Summer of 1915 by Samuel Barber, Concerto in D major, op. 19 by Sergei Prokofiev, Concerto no. 3 in c minor, op. 31 by Ludwig van Beethoven, and Concerto in a minor, op. 22 by Samuel Barber. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund