Analysis Seminars
This seminar series is aimed at staff, postgraduates, and final year undergraduates at the University of St Andrews; anybody else who is interested in attending is welcome to join. The intention is to provide a background in analysis, with an emphasis on the research interests of the group.
The seminar takes place on Tuesday afternoons at 15:00 in Tutorial Room 1A of the Mathematics Institute. A list of past seminars can be found here.
Spring 2026
September 22, 2026
Steve Cantrell:We introduce and discuss a moduli space of functions (quasi-morphisms) on subshifts of finite type which we equip with a metric that measures the 'distortion' required to move from one function to another. We’ll discuss the fundamental properties of this space and explain how pressure curves form geodesics (locally length minimising paths) connecting quasi-morphisms.
September 29, 2026
Antti Käenmäki:Exponential separation rules out a dimension drop for planar self-conformal sets and measures, by a recent theorem of Feng and Rapaport, but it is hard to verify for a concrete non-linear system. Bárány, Kolossváry, and Troscheit made it checkable on the real line through a dual iterated function system; the quantity their condition separates is the pre-Schwarzian derivative. I will explain how this carries the construction to the plane and one level higher, to the Schwarzian, and how the resulting conditions are C^2-open and dense, making the absence of a dimension drop C^2-generic in the plane.
October 6, 2026
Jonathan Fraser:If a measure in Euclidean space has ‘flat parts’, for example, anisotropic cuboids which contain a lot of mass, then this is an ‘enemy’ of Fourier decay. I will explore this idea by trying to derive explicit upper bounds for the Fourier dimension of a measure in terms of quantitative notions of flatness. I will also discuss several applications of these ideas.
October 13, 2026
Markus Myllyoja:In this talk I will discuss the visible parts and orthogonal projections of the affine fractal percolation. For all directions apart from the y-axis, typical visible parts and orthogonal projections behave in a manner one might expect, and their dimension equals the minimum of one and dimension of the affine percolation. For the non-expectional case of the y-axis, the visible part exhibits more complicated behaviour and I will discuss its Hausdorff and box dimensions. During the talk, I may also mention that the projection contains an interval to all directions except the y-axis provided that the dimension of the percolation is larger than one. Based on joint work with Eeva Kuure and Aleksi Pyörälä.
October 20, 2026
Firdavs Rahkmonov:TBC
October 27, 2026
Saeed Shabaanian:TBC
November 3, 2026
Alex Iosevich:TBC
November 10, 2026
Riku Anttila:TBC
November 17, 2026
Mike Todd:TBC
November 24, 2026
Ryan Bushling:TBC
December 1, 2026
Lars Olsen:TBC