Fri, 06 Nov 2026
13:00
13:00
L4
The Chordal Distance Transform of Geometric Loops and its Persistent Homology
James Binnie
(Cardiff University)
Abstract
From contours of 2D shapes to knotted proteins, many areas of statistics and physical sciences are concerned with data in the form of geometric loops - embeddings of the circle into a Euclidean space. It is desirable to find a representation of the geometry of these loops that is invariant under Euclidean symmetries, and indifferent to how the loops are parametrised. In this joint work with Ka Man Yim (Oxford) and Otto Sumray (MPI Dresden), we propose a novel representation of a loop’s geometry by rep resenting the distance matrix of the loop as a Morse function on a Möbius band - the second finite subset space of the circle. By considering the persistent homology of this function, we obtain a representation of the loop’s geometry that has the desired symmetry invariance. We show that this feature map is stable with respect to perturbations, give a geometric interpretation of the features obtained and explore analogues involving higher order finite subset spaces.
Wed, 02 Dec 2026
11:00 -
13:00
L4
Wed, 18 Nov 2026
11:00 -
13:00
L4
Wed, 04 Nov 2026
11:00 -
13:00
L4
Bridging rough semimartingales and rough stochastic differential equations
Jannis Dause
(TU Berlin)
Abstract
The theory of rough stochastic differential equations (RSDEs) initiated by Friz, Hoquet and Lê in 2021 provides an intrinsic solution theory for stochastic dynamics simultaneously driven by a martingale noise N and a rough path X. Their approach crucially relies on a suitable modification of Lê’s stochastic sewing lemma, which comes with certain moment assumptions on the noise N. While this is usually fine in a continuous setting, the high moment assumptions cause considerable problems for establishing a useful rough stochastic calculus when considering e.g. N to be a general Lévy-type martingale with jumps. For example, an Itô formula for RSDEs driven by such noise is not available in the FHL framework.
In parallel, Friz and Zorin-Kranich in 2023 introduced the notion of rough semimartingales (RSMs), sums of martingales and controlled rough paths, which can be shown to be isomorphic to suitable spaces of Gubinelli’s controlled rough paths. Using this connection one can then build a rough stochastic calculus based on RSMs, which is (almost) moment-free and thus does not face the above issue.
In this talk I will show how we construct the RSM-based rough stochastic calculus and how this can be applied to solutions of càdlàg RSDEs. We show that under suitable coefficient assumptions standard for RSDE well-posedness — and with no moment condition on N beyond those that well-posedness already requires — every RSDE solution is also an RSM. The calculus therefore applies to such solutions, and in particular yields the Itô formula that is unavailable in the FHL framework.
Based on joint works with Peter K. Friz, Arnulf Jentzen, Jost Pieper and Jian Song.
Wed, 25 Nov 2026
11:00 -
13:00
L4
Renormalised models for the fractional Phi4 equation
Salvador Esquivel
((Mathematical Institute University of Oxford))
Abstract
We extend the construction of BPHZ renormalised models in regularity structures via the spectral gap inequality to the fractional heat operator. Its Green’s function fails to be smooth across the entire time-zero hyperplane, violating the classical assumption that kernels are smooth away from the origin. The proof requires a delicate balance between the gain in regularity provided by the spectral gap approach and the limited spatial decay of the kernel.
Joint work with L. Broux and R. Steele.
Tue, 17 Nov 2026
14:00
14:00
L4
Tue, 03 Nov 2026
14:00
14:00
L4
Small maximal independent sets in regular graphs
Adva Mond
((Mathematical Institute University of Oxford))
Abstract
We study the minimum size of a maximal independent set in a regular graph, that is, the smallest sets which are both independent and dominating. In a balanced complete bipartite graph, every maximal independent set contains exactly half of the vertices, so large degree alone does not guarantee a small maximal independent set.
In this talk I will show that regular graphs with bounded codegrees admit much smaller maximal independent sets. Specifically, we show that every $d$-regular graph on $n$ vertices with a moderate codegree bound contains a maximal independent set of size at most $(1+o(1))n (\log d)/d$, as $d$ goes to infinity, and this bound is sharp. The proof is based on a nibble method where, in each step, we sample from the hard-core model. I will also discuss applications.
This is joint work with Matthew Jenssen and Andrey Shapiro.