Events
Department of Mathematics and Statistics
Texas Tech University
A circle domain $\Omega$ in the Riemann sphere is a domain each of whose boundary components is either a circle or a point. A circle domain $\Omega$ is called conformally rigid if every conformal map from $\Omega$ onto another circle domain is the restriction of a Möbius transformation. In this talk I will present some new rigidity theorems for circle domains satisfying a certain quasihyperbolic condition. As a corollary, John and Hölder circle domains are rigid. This provides new evidence for a conjecture of He and Schramm, relating rigidity and conformal removability. This talk is based on joint work with Malik Younsi.Watch online Tuesday the 1st at 4 PM via this Zoom link -- meeting ID 5370 7942, passcode 311075
In this talk, we provide a Zagier-type formula for the multiple t-values (special Hurwitz zeta values),
\begin{align*}
\displaystyle t(k_{1}, k_{2}, \ldots, k_{r})
&=2^{-(k_{1}+k_{2}+\ldots +k_{r})}\zeta(k_{1}, k_{2}, \ldots, k_{r}; -\tfrac{1}{2}, -\tfrac{1}{2}, \ldots, -\tfrac{1}{2})\\
&=\sum_{1\leq n_{1}< n_{2}< \ldots < n_{r}}
\frac{1}{(2n_{1}-1)^{k_{1}} (2n_{2}-1)^{k_{2}} \ldots (2n_{r}-1)^{k_{r}}}.
\end{align*}
Our formula is similar to Zagier’s formulas for multiple zeta values $\zeta(2, \ldots, 2, 3)$ and will involve $\mathbb{Q}$-linear combinations of powers of $\pi$ and odd zeta values. The derivation of the formula for $t(2, \ldots, 2, 3)$ relies on a rational zeta series approach via a Gauss hypergeometric function argument.
Join Zoom Meeting
https://zoom.us/j/92803844645?pwd=S2M4dGMwK1RyclMza3dabjl6dk5BQT09
Meeting ID: 928 0384 4645
Passcode: 419696
This is a joint zoom presentation with the Biomath seminar group
Watch online Wednesday the 2nd at 4 PM via this Zoom link