Speaker: Chris Marks (Cal State Chico)
Title: Vector-valued modular forms and the bounded denominator conjecture
Abstract: This talk will primarily serve as an introduction to modular
forms, both scalar and vector-valued. After working through definitions
and the group theoretic background, I’ll discuss the so-called Bounded
Denominator Conjecture concerning Fourier coefficients of modular forms.
Speaker: Andreas Weinmann (Hochschule Darmstadt and Helmholtz Center Munich)
Title: Variational methods for the restauration of manifold-valued images and data
Abstract: Nonlinear manifolds appear as data spaces in various applications. One example in image processing is diffusion tensor imaging, where the data sitting in every voxel is a positive matrix representing the diffusibility of water molecules measured at the corresponding spatial location. Another example is color image processing, where instead of the RGB representation often other formats such as HSI or HSV are used which employ a circle to represent the hue of a color. A third example are registration problems (e.g., between a camera and an ultrasound devise) where time series of euclidean motions appear. Since the measured data is often noisy, regularization of these nonlinear data is necessary. In this talk, we propose algorithms for the variational regularization of manifold-valued data using non-smooth functionals. In particular, we deal with algorithms for TV regularization and with higher order methods including the TGV denoising of manifold-valued data. We present concrete applications in medical imaging tasks.
David Webb will continue to discuss results from Adam Day’s paper on amenability and symbolic dynamics.
Speaker: Christopher Marks (Cal. State Chico)
Title: Vector-valued modular forms and CM Jacobians
Abstract: In this talk, I will explain how vector-valued modular forms
may be used to compute explicitly periods of modular curves, and how the
application of this technique to noncongruence subgroups of the modular
group should soon yield new examples of Jacobians of modular curves with
complex multiplication (i.e., CM Jacobians).
This week in the Logic Seminar in Keller 314, David Ross will give an easy proof of a slight extension of a result of Lagarias on the Diophantine equation
$$ c(1/x_1+cdots+1/x_s)+b/(x_1 x_2cdots x_s)=a$$
The proof will be nonstandard, but really only require a sufficiently-saturated ordered field extension of $mathbb R$.