Matthew Krauel

Matthew Krauel
California State University, Sacramento | CSUS · Department of Mathematics and Statistics

PhD

About

12
Publications
346
Reads
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77
Citations
Additional affiliations
August 2016 - present
California State University, Sacramento
Position
  • Professor (Assistant)
August 2014 - July 2016
University of Cologne
Position
  • PostDoc Position
July 2013 - July 2014
University of Tsukuba
Position
  • JSPS Postdoctoral Fellow
Education
September 2006 - June 2012
University of California, Santa Cruz
Field of study
  • Mathematics
September 2002 - June 2006
University of California, Los Angeles
Field of study
  • Mathematics

Publications

Publications (12)
Preprint
The Peer Assisted Learning program at Sacramento State University (PAL) was established in 2012 with one section supporting introductory chemistry. It now serves 17 gatekeeper courses in Biology, Chemistry, Mathematics, Physics, and Statistics, enrolling approximately 1,400 students annually. Adapting the Peer-Led Team Learning model, PAL Facilitat...
Preprint
Full-text available
It is shown that every weak Jacobi form of weight zero and index one on a congruence subgroup of the full Jacobi group can be decomposed into $N=4$ superconformal characters. Additionally, a simple expression for the mock modular form determining the superconformal character coefficients is obtained, as well as a universal completion structure. Alo...
Article
Full-text available
Length spectra for Riemannian metrics have been well studied, while sub-Riemannian length spectra remain largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest loops are the same in both...
Article
Full-text available
We establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply th...
Article
Full-text available
Using the language of vertex operator algebras (VOAs) and vector-valued modular forms we study the modular group representations and spaces of 1-point functions associated to intertwining operators for Virasoro minimal model VOAs. We examine all representations of dimension less than four associated to irreducible modules for minimal models, and de...
Article
One-point theta functions for modules of vertex operator algebras (VOAs) are defined and studied. These functions are a generalization of the character theta functions studied by Miyamoto and are deviations of the classical one-point functions for modules of a VOA. Transformation laws with respect to the group $\operatorname{SL}_2(\mathbb{Z})$ are...
Article
Full-text available
In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of $q$-series related to the $q$-hypergeometric series $\sigma$ from Ramanajun's lost notebook. Our results parallel a theorem of Cohen which says that $\sigma$, along with its partner function $\sigma^*$, interpolate the coefficients of a Maass waveform of eigenvalue $1/4...
Article
We prove an $\text{SL}_2 (\mathbb{Z})$-invariance property of multivariable trace functions on modules for a regular VOA. Applying this result, we provide a proof of the inversion transformation formula for Siegel theta series. As another application, we show that if $V$ is a regular VOA containing a regular subVOA $U$ whose commutant $U^c$ is regu...
Article
Full-text available
We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements in V, the finite-dimensional space spanned by the corresponding 1-point functions for the inequivalent irreduci...
Article
Full-text available
We consider a generalization of Jacobi theta series and show that every such function is a quasi-Jacobi form. Under certain conditions we establish transformation laws for these functions with respect to the Jacobi group and prove such functions are Jacobi forms. In establishing these results we construct other functions which are also Jacobi forms...
Article
Full-text available
Let V be a strongly regular vertex operator algebra. For a state h ∈ V1 satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions TrM qL(0)-c/24ζh(0) (M a V-module) is a vector-valued weak Jacobi form of weight 0 and a certain index 〈h, h〉/2. We discuss refinements and applications of this result when V i...
Article
Full-text available
Let V be a strongly regular vertex operator algebra. For a state h ∈ V 1 satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr M q L(0)−c/24 ζ h(0) (M a V-module) is a vector-valued weak Jacobi form of weight 0 and a certain index h, h/2. We discuss refinements and applications of this result when...

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