A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III)

This article was originally published in Topology 31 (1992). The present hyperTeXed redaction corrects a few typographical errors and updates the references.Comment: 8 pages, 5 figure

Gauge Invariant Formulation and Bosonisation of the Schwinger Model

The functional integral of the massless Schwinger model in $(1+1)$ dimensions is reduced to an integral in terms of local gauge invariant quantities. It turns out that this approach leads to a natural bosonisation scheme, yielding, in particular the famous `bosonisation rule'' and giving some deeper insight into the nature of the bosonisation phenomenon. As an application, the chiral anomaly is calculated within this formulation.Comment: LaTeX, 8 page

Algebraic functions and closed braids

This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive overview of the subject as it appears 21 years later.)Comment: 12 pages, 2 figure

The Role of GLI-1 in Endocrine Resistant Breast Cancer

Estrogen receptor positive (ER+) and estrogen receptor negative (ER-) are two major types of breast cancer. For women with ER+ positive breast cancer, patients are treated with the antiestrogenic compounds, tamoxifen or faslodex for five years, immediately after surgical resection of tumors. Unfortunately, 30-40% of these patients will develop resistance to endocrine therapy. Our recent study has shown that the Hedgehog (Hhg) signaling pathway plays a significant role in endocrine resistance and that the aberrantly activated transcription factor, GLI-1, is vital to the development of resistance. However, not much is known about the GLI-1 target genes that might contribute to endocrine resistance. Our goal is to determine novel target genes of GLI-1 and determine how these genes promote endocrine therapy resistance.PelotoniaA five-year embargo was granted for this item.Academic Major: Biomedical Scienc

Twisting eigensystems of Drinfeld Hecke eigenforms by characters

We address some questions posed by Goss related to the modularity of Drinfeld modules of rank 1 defined over the field of rational functions in one variable with coefficients in a finite field. For each positive characteristic valued Dirichlet character, we introduce certain projection operators on spaces of Drinfeld modular forms with character of a given weight and type such that when applied to a Hecke eigenform return a Hecke eigenform whose eigensystem has been twisted by the given Dirichlet character. Unlike the classical case, however, the effect on Goss' $u$-expansions for these eigenforms --- and even on Petrov's $A$-expansions --- is more complicated than a simple twisting of the $u-$ (or $A-$) expansion coefficients by the given character. We also introduce Eisenstein series with character for irreducible levels $\mathfrak{p}$ and show that they and their Fricke transforms are Hecke eigenforms with a new type of $A$-expansion and $A$-expansion in the sense of Petrov, respectively. We prove congruences between certain cuspforms in Petrov's special family and the Eisenstein series and their Fricke transforms introduced here, and we show that in each weight there are as many linearly independent Eisenstein series with character as there are cusps for $\Gamma_1(\mathfrak{p})$.Comment: Research funded by the Alexander von Humboldt Foundatio