Tue, 26 May 2026
14:00
L5

A proof of the Kim-Vu sandwich conjecture

Richard Montgomery
(University of Warwick)
Abstract
The random regular graph G_d(n) is selected uniformly at random from all d-regular graphs on a fixed set of n vertices. Compared to the binomial random graph G(n,p), the lack of independence between the appearance of the edges has made the random regular graph in practice usually much harder to study. In 2004, Kim and Vu conjectured that when d is much larger than log n it is possible to 'sandwich' the random regular graph G_d(n) between two binomial random graphs with a similar edge density, allowing properties of the random regular graph to be inferred from those of the binomial random graph. I will discuss a recent proof of this conjecture, building on work of Gao, Isaev and McKay who proved the conjecture for d at least (log n)^4.
 
This is joint work with Natalie Behague and Daniel Il'kovic.
Mon, 08 Jun 2026 09:00 -
Thu, 31 Dec 2026 17:00
Mathematical Institute

Paul Ouwerkerk - The Oxford Variations

Further Information

We are delighted to introduce our latest exhibition in the Andrew Wiles Building. Visual artist Paul Ouwerkerk has created 30 new paintings where he plays with the perspective plane in paintings that are generated from self-composed number sequences. The handcrafted canvases are the result of a process in which the artist, after defining a rigid grid as starting point, leaves space for intuition and industrious manual application to elaborate towards the final result.

Visually these paintings can often be interpreted as unfolded polyhedra, dissolving into mathematical landscape perspectives. The rule-based compositions are sometimes derailed purposefully during the painting process, as if to ‘break-the-code’. Painting techniques and materials play a pivotal role in the creation of these works and the materialisation of these abstract illusions.

Paul Ouwerkerk lives and works in Amsterdam. He has a background in art, photography and design. His previous work experience is intermingled with the world of architecture, urbanism and landscape design. Since 2017 he has been painting his abstract ‘Dynamic Geometry’ series.

9 a.m. - 5 p.m. Monday to Friday.

Image of one of the works
 

Photo of Ellie Guha

Short stories - summer special

Okay, it isn't technically summer here in the UK, but the asphalt is baking hot and the cows are panting under the trees in the meadow. So what better way to celebrate than staying cool by watching a few maths films.
Temperature of an active nematic
 Armas, J Jain, A Lier, R Physical Review Research volume 8 issue 2 (13 Apr 2026)
Mon, 25 May 2026
16:00
C3

Lindelöf hypothesis and zero density estimates

Vishal Gupta
(University of Oxford)
Abstract

The Lindelöf hypothesis is known to be weaker than the Riemann hypothesis and one way to assess the difference in their strength is to consider what can be said about the zeroes of the zeta function under the assumption of the Lindelöf hypothesis. Viewing this question in the context of zero density estimates, we prove that $N(\sigma,T) \leq T^{\frac{4(5-6\sigma)}{3(3-2\sigma)} + o(1)}$. This improves the currently known estimate conditional on the Lindelöf hypothesis, $N(\sigma,T) \leq T^{2(1-\sigma)+o(1)}$ based on the mean value theorem, for $\sigma$ near $3/4$.

Sun, 24 May 2026
17:00
L3

TBA

Henry Towsner
(University of Pennsylvania)
Thu, 04 Jun 2026
11:00
C3

Avoiding logical strength in analysis

Anton Freund
(Universität Würzburg)
Abstract
In reverse mathematics, one classically represents real numbers by Cauchy sequences (q_n) with a known rate of convergence, where typically |q_m-q_n|<2^{-m} for m<n. While this has good reasons, it turns out that "slow" Cauchy sequences (without prescribed rate of convergence) have great advantages as well: In joint work with Nicholas Pischke and Patrick Uftring (arXiv:2605.15151), we have shown that almost all one-dimensional real analysis from the textbook by Simpson can be developed in theories that are Pi^1_1-conservative over RCA_0 (including results that require ACA_0 with the classical representation). This yields a very different picture of the foundations of analysis, which also blurs the boundary between analytical principles and combinatorial principles from the so-called reverse mathematics zoo.
Exploring the relationship between vascular remodelling and tumour growth using agent-based modelling.
 Fan, N Bull, J Byrne, H PLoS computational biology volume 22 issue 5 e1012967 (15 May 2026)
Tensorial permanence of K‐stability for diagonal AH‐algebras
 Seth, A Bulletin of the London Mathematical Society volume 58 issue 5 (22 May 2026)
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