Analysseminariet 盲r en seminarieserie vid Matematiska institutionen som v盲nder sig till en bred matematisk publik. Seminariet 盲r 枚ppen f枚r allm盲nheten och alla intresserade 盲r v盲lkomna.
Seminarieserien organiseras av Anders Bj枚rn vid avdelningen Analys och didaktik (ANDI).
Seminariet som oftast h氓lls p氓 engelska 盲r i .
TBA
Sammanfattning: The talk explores the interplay between geometry, topology, and analysis on metric spaces with curvature bounded above, presenting recent results and future directions across three scales. Locally, based on joint work with E. Caputo and T. Ikonen, we discuss the infinity-Poincar茅 inequality on GCBA spaces and p-thick quasigeodesicity, alongside goals to characterize local Poincar茅 inequalities via tangential properties. Globally, in collaboration with D. Marti, A. Mondino, and R. Perales, we introduce a unified notion of orientability for upper-curvature-bound spaces via locally integral currents, and present sharp Lipschitz-volume rigidity results (joint with E. Caputo and D. Marti) relying on target infinity-thick quasiconvexity. Finally, time permitting, we examine the asymptotic geometry of CAT(-1) spaces, outlining a strategy toward rigidity via the analytical properties of their fractal boundaries at infinity.
Sammanfattning: A normed space A is an interpolation space between X and Y if, roughly, it lies between these spaces and linear operators continuous on X and Y are also continuous on A. There is a method to construct such interpolation spaces, the K-method of real interpolation, which allows us to study interpolation spaces without the need to think about operators acting on these spaces. I will apply the K-method to Sobolev spaces on Euclidean domains and show with examples how the geometry of the domain influences the resulting interpolation space. I will present some yet unpublished results on this topic and highlight how certain approaches from analysis on metric spaces can be useful in studying this topic.
This is joint work in progress with Pekka Koskela and Riddhi Mishra (both from University of Jyv盲skyl盲).
Sammanfattning: After a brief introduction to optimal transport theory and its applications to both theoretical and applied mathematical problems, I will focus on the differential structure of the space of probability measures equipped with the Wasserstein distance. In particular, I will discuss the Hilbertian structure of the associated metric Sobolev space and the density of smooth cylinder functions within it. Finally, I will show how these results can be applied to the efficient computation of the Wasserstein distance.
Sammanfattning: In the last three decades there has been increasing interest in extending the Euclidean theory of analysis to less regular settings, such as the setting of metric measure spaces. In this talk, I will discuss two complementary approaches to conducting analysis on non-smooth spaces. The first is to construct analytic tools directly on the given space based on the metric and geometric information it carries. The second is to embed the arbitrary metric space into a familiar ambient space and use the analytic tools available in the latter. I will illustrate through various examples of metric spaces how these approaches lead to metric Sobolev-type classes of mappings and quantitative embedding theorems, as well as to applications to Gehring and V盲is盲l盲 programme of dimension distortion.
