Zeit und Ort

Donnerstag, 23.7.26, 15:00–16:30, Hörsaal 2

Zeit und Ort

Dienstag, 21.7.26, 14:15–15:15, Seminarraum 226, HH10

Zeit und Ort

Montag, 20.7.26, 16:15–17:45, Seminarraum 404

Zusammenfassung

Prime geodesic theorems describe the asymptotic behavior of the distribution of prime closed geodesics. In particular, for a hyperbolic surface, the prime geodesic counting function has the same leading asymptotic as the prime number counting function. The optimal bound on the remainder term remains, however, an open conjecture. In this talk, we will discuss the so-called Gallagherian PGT; that means, we allow the asymptotics to fail on a set of finite logarithmic measure. We improve and extend recent results of this type established by Gušić for compact locally symmetric spaces to new settings. This is a joint work with Jørgen Olsen Lye.

Zeit und Ort

Mittwoch, 15.7.26, 15:30–17:00, online, mailen Sie an Frau Mildenberger bei Interesse

Zusammenfassung

The derived functors \(lim^n\) of the inverse limit measure n-dimensional obstructions to the inverse limit functor preserving exact sequences. Whether or not certain derived limits vanish carries surprisingly deep set theoretic content involving higher dimensional infinitary combinatorics. The vanishing of certain derived limits \(lim^nA\) has been the focus of considerable set theoretic focus and has implications in both strong homology and condensed mathematics. This talk will focus on the combinatorial principles behind the vanishing of \(lim^nA\) and recent developments regarding when they do and do not vanish.

Zeit und Ort

Mittwoch, 15.7.26, 14:15–15:45, SR 125/126 (E1)

Zeit und Ort

Dienstag, 14.7.26, 16:15–17:45, Seminarraum 125

Zusammenfassung

A surface of least area that intersects a given support surface at a constant angle is called a minimal capillary surface. Minimal capillary surfaces arise naturally in the context of fluid dynamics as the idealized interface between two fluids in a container bounded by the support surface. In recent years, minimal capillary surfaces have been shown to capture aspects of the geometry of the support surface that appear to be beyond the reach of established tools in geometric analysis. In this talk, I will describe some of these developments, including my contributions in joint work with M. Eichmair such as the resolution of the Penrose inequality in extrinsic geometry conjectured by G. Huisken and the characterization of stable minimal capillary surfaces in the so-called tangential limit.

Zeit und Ort

Dienstag, 14.7.26, 14:30–16:00, online, mailen Sie an Frau Mildenberger bei Interesse

Zusammenfassung

Forcing axioms are principles occurring naturally in set theory, which can be seen as generalizations of the Baire Category Theorem. Classical strong forcing axioms, such as PFA or MM, offer a uniformly "saturated" picture of a very low initial segment of the universe. Namely the sets that are hereditarily of cardinality less than the second uncountable cardinal. Forcing axioms have proven to be extremely successful in obtaining consistency results, not only in set theory, but also in other areas of mathematics such as measure theory, topology, group theory, Boolean algebras, and Banach space theory. Most notable is Shelah's proof of the independence of the Whitehead problem in group theory. These two reasons have motivated the search for consistent high analogs of the known classical forcing axioms and the developement of new forcing iteration techniques.

In this talk, I will give an overview of the technique of forcing with side conditions and present some consistency results that contribute towards the search of consistent high forcing axioms.

Zeit und Ort

Montag, 13.7.26, 16:15–17:45, Seminarraum 404

Zusammenfassung

Given a Morse function on a closed smooth manifold and a Morse-Smale pseudo-gradient vector field adapted to it, one can construct a topological category called the flow category associated with this data. Its objects are the critical points of the function and its morphism spaces are the spaces of possibly broken gradient trajectories connecting critical points. This topological category models an infinity category, which can be thought of as providing a homotopy coherent notion of composition of unbroken trajectories connecting critical points. On the other hand, such trajectories determine paths on the manifold, that have the property to be exit paths with respect to the stratification by the stable manifolds of the gradient. A construction of Lurie associates an infinity category to this stratification, which can be thought of as providing a notion of homotopy coherent composition of exit paths. I will define these objects more precisely and then present a result I obtained asserting that these two infinity categories are equivalent.