Zurückliegende Veranstaltungen

Twinned conference on "Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras", June 30 - July 11, 2025

Quantum Field Theory and Quantum Statistical Mechanics are central to high energy physics and condensed matter physics and they also raise deep questions in mathematics.  The application of operator algebras to these areas of physics is well known. Recent developments indicate that to understand QFT properly a further ingredient is needed: homotopy theory and infinity-categories.

Conference on "Asymptotic Counting and L-Functions", May 5 - 9, 2025

Many interesting arithmetic functions such as class numbers, Fourier coefficients of modular forms, have a rather varying behavior that is only partially understood. However, often it is possible to determine some (possibly weighted) average for them. The approach is often to associate an L-series to the arithmetic quantity of interest and study whether this has an analytic continuation, study the location of its zeros and poles.

Classical Kloosterman sums defined by $S(m,n;c):=\sum_{x\in (\mathbb{Z}/c\mathbb{Z})^*}e\Big(\frac{mx+n\overline{x}}{c}\Big)$ for $m,n\in\mathbb{Z}$ and $c\in\mathbb{Z}^+$ have become ubiquitous in Number Theory appearing for example in Fourier coefficients of classical Poincaré series and therefore in the geometric side of relative trace formulae of Petersson-Kuznetsov type.
Working with relative trace formulae over $\mathrm{GL}_n$ requires understanding of more general Kloosterman sums.