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:Majorization provides a way to compare how “spread out” the entries of two vectors are. It has important applications in additive combinatorics, with classical results by Hardy, Littlewood and Pólya for the integers and by Lev for cyclic groups of prime order. In this talk, I will establish a powerful majorization theorem for the hypercube Z_2^n and explain the compression method behind its proof. As an application, we determine the maximum number of solutions to a_1+...+a_k=0, where a_i are in A_i and A_1,...,A_k are subsets of the hypercube with prescribed sizes. We also establish the corresponding minimum and characterize all extremal sets when these sets are identical and k is odd. For k=3, this counts Schur triples, and we recover a theorem of Samotij and Sudakov. Finally, I will discuss a related convexity inequality and an analogue of Pollard’s theorem for the hypercube that strengthens and extends a result of Bollobás and Leader. Based on joint work with Sophie Huczynska and Chi Hoi Yip.
October 27, 2026 (3pm)
Saeed Shabaanian:Suppose you toss a fair coin n times. How long is the longest run of heads? Erdős and Rényi studied its asymptotic growth in 1970. A natural extension in symbolic dynamics concerns the asymptotic behaviour of the longest common substring between and within sequences. In this talk, we take this question a step further. Given a sequence of thresholds (k_n), we ask whether the length of the longest common substring exceeds (k_n) for all sufficiently large n, or for infinitely many n, almost surely. More precisely, given a countable Markov shift and a positive integer-valued map κ(n). For each n, we consider the set of all pairs of distinct points whose longest common substring within the first n symbols in the first point and the first κ(n) symbols in the second point has length greater than k_n. We give conditions on the thresholds under which the liminf and limsup of these sets have measure zero or one.
October 27, 2026 (3:30pm)
Corey de Wit:The dynamical, ergodic and geometric properties of Iterated Function Systems (IFSs) depend particularly on how the images of its attractor under IFS maps overlap. When these overlaps are minimal, they behave in predictable ways and allow for fruitful analysis. When the overlaps are substantial however, they can proliferate under the self-referential process and lead to chaos!, and calculating fractal dimensions and analysing the underlying measures can become difficult. Two extensively studied conditions which call for ‘nice’ overlaps are weak separation and finite type. It is conjectured these two conditions are equivalent, however it has only been proven for certain classes of IFS’s, mainly on the line. We will briefly discuss these notions, and introduce a symbolic subshift addressing the ‘top’ of the attractor, which when sofic, sheds a different light on this problem.
November 3, 2026
Alex Iosevich:Back in the 1970s, Agmon and Hormader observed that if one considers the partial differential equation P(D)u=0, then the support of û is contained in the zero variety of the symbol P. They asked for L^p integrability of u that guarantees that u is identically 0, which can be viewed as a version of the Fourier Uncertainty Principle. We are going to discuss some recent results on this problem in the Euclidean (joint work with Shantanu Deodhar), Riemannian (joint work with Azita Mayeli and Emmett Wyman), and arithmetic (joint work with Zhihe Li and Ella Yu) setting. The interplay of ideas between the various settings will be emphasized throughout.
November 10, 2026
Riku Anttila:TBC
November 17, 2026
Mike Todd:TBC
November 24, 2026
Ryan Bushling:TBC
December 1, 2026
Lars Olsen:TBC