Events
Department of Mathematics and Statistics
Texas Tech University
A theorem of Lehto (1955) states that for every measurable function $\psi$ on the unit circle $\mathbb T,$ there is a
function $f$ holomorphic in the unit disc $\mathbb{D}$, having $\psi$ as radial limit a.e. on $\mathbb{T}.$ In this talk,
an analogous boundary value problem for holomorphic functions in the polydisc in $\mathbb{C}^n,$ will be presented.
Lehto's proof was based on an approximation theorem of Bagemihl and Seidel (1954). They showed that for a continuous
function $\psi$ on $\mathbb{D},$ and an $F_\sigma$ set $E\subset \mathbb{T}$ of the first category, there exists a
holomorphic function $h$ in $\mathbb{D}$ such that $\psi-h$ has vanishing radial limits as we move to the boundary
via radii ending in $E$. We generalized similar approximating theorems for harmonic functions on Riemannian manifolds
(with completely different proofs); that is, for Riemannian manifolds $M$ and $N,$ and a (harmonic) line bundle
$(M, N, \pi, \mathbb{R}),$ continuous functions on $M$ can be approximated by harmonic ones such that the limit on some
special subset of $M$ (roughly fibres of an $F_\sigma$ polar set in $N$) tends to zero as we move to the ideal
boundary of $M.$
Joint work with Paul. M. Gauthier, Université de Montréal, Montréal, Québec, Canada.
To join the talk on Zoom please click
here.
 | Wednesday
Jan. 26
|
| Algebra and Number Theory
No Seminar
|
Abstract: We argue that media slant constitutes a source of ambiguity and show
that the uncertainty stemming from slanted news is priced in the cross section of US stocks.
Our identification of slanted news stocks is based on a combination of a news proxy using
Wikipedia page view data and mutual fund managers' aggregated portfolio positions.
We find that slanted news stocks earn a premium of roughly 1% in announcement months
over their unslanted peers, which peaks on the announcement day itself.
Our results further show that the premium is compensating for the exposure to a slanted
news mimicking factor.
This is joint work with Prof. Marliese Uhrig-Homburg
 | Wednesday
26
3:30 PM
MA 115
|
| Topology and Geometry
Severin Bunk
Mathematical Institute, University of Oxford
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