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

p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups

We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic imaginary field split at p. When r=2, we show that the constant term of the Klingen Eisenstein family is divisible by a certain p-adic L-function.Comment: Accepted for publication in the Journal of the Institute of Mathematics of Jussie

A p-adic Eisenstein measure for vector-weight automorphic forms

We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms, including Eisenstein series, as their weights vary. We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz's p-adic families of Eisenstein series for Hilbert modular forms.Comment: Accepted for publication in Algebra & Number Theor

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

A p-adic Eisenstein measure for unitary groups

We construct a p-adic Eisenstein measure with values in the space of p-adic automorphic forms on certain unitary groups. Using this measure, we p-adically interpolate certain special values of both holomorphic and non-holomorphic Eisenstein series, as both the archimedean and the p-adic weights of the Eisenstein series vary.Comment: Accepted for publication in the Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal

Mdm2 Is Required for Survival and Growth of p53-Deficient Cancer Cells.

p53 deletion prevents the embryonic lethality of normal tissues lacking Mdm2, suggesting that cells can survive without Mdm2 if p53 is also absent. Here we report evidence challenging this view, with implications for therapeutically targeting Mdm2. Deletion of Mdm2 in T-cell lymphomas or sarcomas lacking p53 induced apoptosis and G2 cell-cycle arrest, prolonging survival of mice with these tumors. p53-/- fibroblasts showed similar results, indicating that the effects of Mdm2 loss extend to pre-malignant cells. Mdm2 deletion in p53-/- cells upregulated p53 transcriptional target genes that induce apoptosis and cell-cycle arrest. Mdm2 deletion also increased levels of p73, a p53 family member. RNAi-mediated attenuation of p73 rescued the transcriptional and biological effects of Mdm2 loss, indicating that p73 mediates the consequences of Mdm2 deletion. In addition, Mdm2 deletion differed from blocking Mdm2 interaction with p53 family members, as Nutlin-3 induced G1 arrest but did not activate apoptosis in p53-/- sarcoma cells. Our results indicate that, in contrast to current dogma, Mdm2 expression is required for cell survival even in the absence of p53. Moreover, our results suggest that p73 compensates for loss of p53 and that targeting Mdm2 in p53-deficient cancers has therapeutic potential. ©2017 AACR

Haploinsufficiency of the Myc regulator Mtbp extends survival and delays tumor development in aging mice.

Alterations of specific genes can modulate aging. Myc, a transcription factor that regulates the expression of many genes involved in critical cellular functions was shown to have a role in controlling longevity. Decreased expression of Myc inhibited many of the deleterious effects of aging and increased lifespan in mice. Without altering Myc expression, reduced levels of Mtbp, a recently identified regulator of Myc, limit Myc transcriptional activity and proliferation, while increased levels promote Myc-mediated effects. To determine the contribution of Mtbp to the effects of Myc on aging, we studied a large cohort of Mtbp heterozygous mice and littermate matched wild-type controls. Mtbp haploinsufficiency significantly increased longevity and maximal survival in mice. Reduced levels of Mtbp did not alter locomotor activity, litter size, or body size, but Mtbp heterozygous mice did exhibit elevated markers of metabolism, particularly in the liver. Mtbp(+/-) mice also had a significant delay in spontaneous cancer development, which was most prominent in the hematopoietic system, and an altered tumor spectrum compared to Mtbp(+/+) mice. Therefore, the data suggest Mtbp is a regulator of longevity in mice that mimics some, but not all, of the properties of Myc in aging