Differential operators, pullbacks, and families of automorphic forms

This paper has two main parts. First, we construct certain differential operators, which generalize operators studied by G. Shimura. Then, as an application of some of these differential operators, we construct certain p-adic families of automorphic forms. Building on the author's earlier work, these differential operators map automorphic forms on a unitary group of signature (n,n) to (vector-valued) automorphic forms on the product $U^\varphi\times U^{-\varphi}$ of two unitary groups, where $U^\varphi$ denotes the unitary group associated to a Hermitian form $\varphi$ of arbitrary signature on an n-dimensional vector space. These differential operators have both a p-adic and a C-infinity incarnation. In the scalar-weight, C-infinity case, these operators agree with ones studied by Shimura. In the final section of the paper, we also discuss some generalizations to other groups and settings. The results from this paper apply to the author's paper-in-preparation with J. Fintzen, E. Mantovan, and I. Varma and to her ongoing joint project with M. Harris, J. -S. Li, and C. Skinner; they also relate to her recent paper with X. Wan.Comment: Accepted for publication in special issue of Annales Mathematiques du Quebec in honor of Glenn Stevens's sixtieth birthda

Lost, Dysfunctional or Evolving? A View of Business Schools from Silicon Valley

Recent articles have rekindled discussions around the direction and relevance of US business schools. The two main viewpoints are distinct but equally critical. On one hand, business schools are considered overly focused on “scientific research” and having lost their connection to “real world” and management issues. On the other hand, schools are considered “dysfunctionally” focused on media rankings and short-term superficial marketing fixes. Our study of educational opportunities and workforce development in Silicon Valley suggests a different viewpoint. We agree that both approaches correctly identify the challenge of preparing managers in globalized world. However, we believe they misdiagnose the cause of the failure. Rather than being lost or dysfunctional, we believe business programs — like the firms and students they serve — are in the process of evolving to meet a shifting global and local environment. Our findings indicate that business schools face structural, content, and program shifts. Educationally, business programs continue to be seen as doing a good job of educating their students in core functional areas and processes. However, they do less well in teaching their graduates interpersonal skills, real-time decision-making, recognition of contexts, and integration across functional areas. These are increasingly the skills demanded by the global business environment. Even more challenging is meeting the demand for both sets of skills within very specialized fields like technology management. Structurally, new types of students and learning demands are placing stresses on traditional full-time two-year programs and their business models. Women and minority groups increasingly form the majority of the future student population, with distinct needs and demands for part-time and executive education. This shift is also evident in demands for life-long learning and engagement as opposed to a fixed, one-shot program experiences. These challenges require business schools to build upon what they do well, while innovating to serve new business and student needs.management education; Silicon Valley; globalization; technology

p-adic Differential Operators on Automorphic Forms on Unitary Groups

The goal of this paper is to study certain p-adic differential operators on automorphic forms on U(n,n). These operators are a generalization to the higher-dimensional, vector-valued situation of the p-adic differential operators constructed for Hilbert modular forms by N. Katz. They are a generalization to the p-adic case of the C^{\infty}-differential operators first studied by H. Maass and later studied extensively by M. Harris and G. Shimura. The operators should be useful in the construction of certain p-adic L-functions attached to p-adic families of automorphic forms on the unitary groups U(n) x U(n)

A BRIEF REPORT ON pp-ADIC SPIN LL-FUNCTIONS FOR GSp6_{6} (Automorphic forms, Automorphic representations, Galois representations, and its related topics)

This document summarizes the content of the author's presentation at the remote RIMS conference "Automorphic forms, Automorphic representations, Galois representations, and its related topics." In particular, we report on a paper-inpreparation (joint with S. Shah and G. Rosso) on p-adic Spin L-functions for GSp₆

George Argus’s list of Salix references

This bibliographical list, containing more than 3600 publications related to the genus Salix, was compiled by Dr. Argus during his long scientific career