Quadratic forms and systems of forms in many variables

Let $F_1,\dotsc,F_R$ be quadratic forms with integer coefficients in $n$ variables. When $n\geq 9R$ and the variety $V(F_1,\dotsc,F_R)$ is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish, which in particular implies the Hasse principle for $V(F_1,\dotsc,F_R)$. Previous work in this direction required $n$ to grow at least quadratically with $R$. We give a similar result for $R$ forms of degree $d$, conditional on an upper bound for the number of solutions to an auxiliary inequality. In principle this result may apply as soon as $n> d2^dR$. In the case that $d\geq 3$, several strategies are available to prove the necessary upper bound for the auxiliary inequality. In a forthcoming paper we use these ideas to apply the circle method to nonsingular systems of forms with real coefficients.Comment: 29 pages, in revie

Systems of cubic forms in many variables

We consider a system of $R$ cubic forms in $n$ variables, with integer coefficients, which define a smooth complete intersection in projective space. Provided $n\geq 25R$, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish. In particular we can handle systems of forms in $O(R)$ variables, previous work having required that $n \gg R^2$. One conjectures that $n \geq 6R+1$ should be sufficient. We reduce the problem to an upper bound for the number of solutions to a certain auxiliary inequality. To prove this bound we adapt a method of Davenport.Comment: 23 pages, submitte

Welcoming Workplace: Rapid Design Intervention to Determine the Office Environment Needs of Older Knowledge Workers

This book chapter details the context, methods, findings and implications of the Welcoming Workplace project (RCA, 2006–8), which was part of Phase 2 of the Designing for the 21stCentury Research Programme (AHRC-EPSRC), directed by Professor Tom Inns, University of Dundee. It describes (pp. 208–24) an interdisciplinary study to determine the office environment needs of older workers in the knowledge economy. Myerson was principal investigator on the project. The research uses a mix of architectural, anthropological and design techniques to give older workers a ‘voice’ in the workplace. At the heart of the study is a series of ‘rapid design interventions’ on sites in the UK, Japan and Australia to create temporary experiential work settings for testing and evaluation. It discusses how the research team worked with academic partners (Universities of Melbourne and Kyushu) to create these within the time and operational constraints imposed by large organisations. The study generated evidence-based design guidance on the needs of older workers and significantly advanced the idea of inclusive office design. As a result, Myerson was invited to join the Workplace Productivity Group of the British Council for Offices (BCO), the professional body responsible for writing the BCO’s Guide to Specification (2009). Findings were also submitted to the Department of Work and Pensions and incorporated into its major strategy paper on an ageing society (2009). In addition, Myerson was asked by the Royal Institute of British Architects to contribute to its Good Office Design publication (RIBA Publishing, 2009, ed. David Littlefield). Myerson led a masterclass at the British Library as part of the ‘WorkTech London 2008’ conference to launch the Welcoming Workplace study, and he accepted a number of international invitations to speak on the research: at the Office and Facility Conference Warsaw, Norwegian Design Council Oslo and Tongji University Shanghai (all 2010)

On Revenue Monotonicity in Combinatorial Auctions

Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for $m$ items and $n$ buyers in the Bayesian setting, specified by a valuation function $v$ and a set $F$ of $nm$ independent item-type distributions. Let $REV(v, F)$ denote the maximum revenue achievable under $F$ by any incentive compatible mechanism. Intuitively, one would expect that $REV(v, G)\geq REV(v, F)$ if distribution $G$ stochastically dominates $F$. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when $v$ is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions $v$, showing that $REV(v, G)\geq c\,REV(v, F)$ if $G$ stochastically dominates $F$ under $v$ where $c>0$ is a universal constant. Previously, approximate monotonicity was known only for the case $n=1$: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.Comment: 10 page

Sequential Equilibria in Bayesian Games with Communication

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games.Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium

Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori

We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.Comment: 28 page

Notes--The Times They Are A-Changin\u27: Literary Documentary Editing in an Electronic Post-Structuralist World

I began working as a literary textual editor in the summer of 1968, my second year of graduate school at Northwestern University. At that time Northwestern housed The Writings of Herman Melville and I was taken on board as a trainee. I will always remember the shining moment when I realized that I had mastered the Hinman Collator and that a great future awaited me because of it. I spent the next three years working there, and in the next decade got up to speed on my own. I served as a vettor for the Center for Editions of American Authors, which, incidentally, sealed over one hundred volumes between 1966 and 1976, which gives you an idea of how exciting things were at this time in the editorial field. Later, I began work on my own editions of Louisa May Alcott, Ralph Waldo Emerson, and Margaret Fuller. Let us now go back, briefly, to those glorious years, when there was truly a textual moment

Two Unrecorded Notices of Whitman in 1888

Identifies and prints an essay about Whitman for children, written by Charlotte French, and a poetic tribute to Whitman, written by Coates Kinney