A5067743265- Advanced Algebra and Geometry
- Algebraic Geometry and Number Theory
- Algebraic structures and combinatorial models
- Advanced Topics in Algebra
- Finite Group Theory Research
- Gene Regulatory Network Analysis
- History and Theory of Mathematics
- Homotopy and Cohomology in Algebraic Topology
- Single-cell and spatial transcriptomics
- Molecular spectroscopy and chirality
- Gene expression and cancer classification
- Advanced Combinatorial Mathematics
- Advanced Mathematical Identities
- Bioinformatics and Genomic Networks
- Urinary Bladder and Prostate Research
- Advanced Topology and Set Theory
- Advanced Numerical Analysis Techniques
- Algebraic and Geometric Analysis
- Genomics and Chromatin Dynamics
- advanced mathematical theories
- Philosophy, Science, and History
- Pelvic floor disorders treatments
- Polynomial and algebraic computation
- Rings, Modules, and Algebras
- Cell Image Analysis Techniques
University of California, Santa Cruz
2008-2024
Yale-NUS College
2014-2015
University of Utah
2011
Radboud University Nijmegen
2011
Vrije Universiteit Amsterdam
2011
University of Amsterdam
2011
Harvard University
2003
University of California, Berkeley
2003
Children's Hospital Colorado
1970
University of Colorado Denver
1970
Cell types can be classified according to shared patterns of transcription. Non-genetic variability among individual cells the same type has been ascribed stochastic transcriptional bursting and transient cell states. Using high-coverage single-cell RNA profiling, we asked whether long-term, heritable differences in gene expression impart diversity within type. Studying clonal human lymphocytes mouse brain cells, uncovered a vast different clones vivo. We combined chromatin accessibility...
We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. work with all that arise from extensions by $\mathbf{K}_2$ -- class studied Brylinski and Deligne. use this parameterize genuine irreducible representations in many contexts, including split tori, unramified representations, discrete series for double semisimple over $\mathbb R$. An appendix surveys torsors gerbes on etale site, as they are used construction L-group.
Abstract Cell types can be classified based on shared patterns of transcription. Variability in gene expression between individual cells the same type has been ascribed to stochastic transcriptional bursting and transient cell states. We asked whether long-term, heritable differences transcription impart diversity within a type. Studying clonal human lymphocytes mouse brain cells, we uncover vast states among different clones vivo. In show that this is coupled clone specific chromatin...
Abstract We adapt the conjectural local Langlands parameterization to split metaplectic groups over fields. When G ˜ is a central extension of connected reductive group field (arising from framework Brylinski and Deligne), we construct dual <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mover accent="true"> <m:mi>𝐆</m:mi> <m:mo>˜</m:mo> </m:mover> <m:mo>∨</m:mo> </m:msup> </m:math> $\tilde{\mathbf {G}}^{\vee }$ an L-group <m:mrow> <m:mspace width="0.166667em" /> </m:mrow>...
We study the “Fourier-Jacobi” functor on smooth representations of split, simple, simply-laced <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic groups. This has been extensively studied symplectic group, where it provides representation-theoretic analogue Fourier-Jacobi expansion...
Smooth irreducible representations of tori over local fields have been parameterized by Langlands, using class field theory and Galois cohomology.This paper extends this parameterization to some central extensions such tori, which arise naturally in the setting nonlinear covers reductive groups.
In this joint introduction to an Asterisque volume, we give a short discussion of the historical developments in study nonlinear covering groups, touching on their structure theory, representation theory and automorphic forms. This serves as motivation sets scene for papers volume. Our is necessarily subjective will undoubtedly leave out contributions many authors, whom apologize earnest.
In this paper, we study modular forms on two simply connected groups of type D 4 over Q. One group, G s , is a globally split group viewed as the isotopies rational octonions. The other, c isotopy (nonsplit) We automorphic in analogy to work Gross, Gan, and Savin 2 ; namely whose component at infinity corresponds quaternionic discrete series representation. using Gross's formalism "algebraic forms." Finally, follow Savin, Rallis, others, an exceptional theta correspondence connecting . This...
Given a reductive group $\mathbf {G}$ over base scheme $S$, Brylinski and Deligne studied the central extensions of by {K}_2$, viewing both as sheaves groups on big Zariski site $S$. Their work classified these three invariants, for $S$ spectrum field. We expand upon their to study âintegral modelsâ such extensions, obtaining similar results sufficiently nice ring, e.g., DVR with finite residue field or containing Milder are obtained Dedekind domain, often conditional Gerstenâs conjecture.
Langlands has described the irreducible admissible representations of $T$, when $T$ is group points an algebraic torus over a local field. Also, automorphic $T_{\Bbb{A}}$ adelic global field $F$. We describe (in setting) and $\epsilon$-genuine for ``covers'' tori, also known as ``metaplectic tori,'' which arise from framework Brylinski Deligne. In particular, our results include description spherical Hecke algebras in unramified setting, multiplicity estimate covers split tori. For we prove...
We study the dimension of space Whittaker functionals for depth zero representations unramified covering groups. In particular, we determine such dimensions arbitrary Brylinski–Deligne coverings general linear group. The results in article are motivated by and compatible with work Howard second author, earlier Blondel.
We generalize the methods of Moy–Prasad in order to define and study genuine depth-zero representations some nonlinear covers reductive groups over p-adic local fields. In particular, we construct all supercuspidal metaplectic group Mp2n a field odd residue characteristic.
No AccessJournal of Urology1 Dec 1970Bender Gestalt Test and the Urodynamics Enuresis William A. Campbell, Martin Weissman, Jane Lupp CampbellWilliam Campbell More articles by this author , WeissmanMartin Weissman LuppJane View All Author Informationhttps://doi.org/10.1016/S0022-5347(17)61870-6AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail © 1970 The American Urological Association Education Research,...
Abstract The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of G 2 over a p -adic field, one can associate either PGSp 6 or PGL 3 . We prove this conjectural dichotomy, demonstrating precise correspondence between certain representations and other This arises from theta correspondences in E 7 , analysis Shalika functionals, spin L-functions. Our main result reduces the parameterization single conjecture about for
We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. work with all that arise from extensions by $\mathbf{K}_2$ -- class studied Brylinski and Deligne. use this parameterize genuine irreducible representations in many contexts, including split tori, unramified representations, discrete series for double semisimple over $\mathbb R$. An appendix surveys torsors gerbes on \'etale site, as they are used construction L-group.
The space of elliptic modular forms fixed weight and level can be identfied with a intertwining operators, from holomorphic discrete series representation SL2(R) to automorphic forms. Moreover, multiplying corresponds branching problem involving tensor products representations. In this paper, we explicitly connect the ring structure on spaces problems in theory real semisimple Lie groups. Furthermore, construct family operators representations into other This collection provides well-known...
When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves $E_{\mathbb C}$, smooth with respect to stratification hyperplanes. By using Kapranov and Schechtman's recent analysis hyperplane arrangements, find an equivalence categories from finite-dimensional modules over algebra given explicit generators relations. We also define equivariant affine...
In the 1990s, J. H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using visualization he named "topograph," revisited reduction of BQFs and solution Diophantine equations such as Pell's equation. It appears that crux his is coincidence between arithmetic group [Formula: see text] Coxeter type There are many groups, each may have unforeseen applications to arithmetic. We introduce Conway's topograph generalizations other groups....