Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
17:00
Robin Thompson

Further Information: 

Models. They are dominating our Lockdown lives. But what is a mathematical model? We hear a lot about the end result, but how is it put together? What are the assumptions? And how accurate can they be?

In our first online only lecture Robin Thompson, Research Fellow in Mathematical Epidemiology in Oxford, will explain. Robin is working on the ongoing modelling of Covid-19 and has made many and varied media appearances in the past few weeks. We are happy to take questions after the lecture.

Watch live:

https://twitter.com/oxunimaths?lang=en
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Thompson

Oxford Mathematics Public Lectures are generously supported by XTX Markets

  • Oxford Mathematics Public Lectures
14 April 2020
14:00
Ron Peled

Further Information: 

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

Color each vertex of an infinite graph blue with probability $p$ and red with probability $1-p$, independently among vertices. For which values of $p$ is there an infinite connected component of blue vertices? The talk will focus on this classical percolation problem for the class of planar graphs. Recently, Itai Benjamini made several conjectures in this context, relating the percolation problem to the behavior of simple random walk on the graph. We will explain how partial answers to Benjamini's conjectures may be obtained using the theory of circle packings. Among the results is the fact that the critical percolation probability admits a universal lower bound for the class of recurrent plane triangulations. No previous knowledge on percolation or circle packings will be assumed.

  • Combinatorial Theory Seminar
21 April 2020
14:00
Agelos Georgakopoulos

Further Information: 

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

We prove that for Bernoulli bond percolation on $\mathbb{Z}^d$, $d\geq2$, the percolation density $\theta(p)$ (defined as the probability of the origin lying in an infinite cluster) is an analytic function of the parameter in the supercritical interval $(p_c,1]$. This answers a question of Kesten from 1981.

The proof involves a little bit of elementary complex analysis (Weierstrass M-test), a few well-known results from percolation theory (Aizenman-Barsky/Menshikov theorem), but above all combinatorial ideas. We used a new notion of contours, bounds on the number of partitions of an integer, and the inclusion-exclusion principle, to obtain a refinement of a classical argument of Peierls that settled the 2-dimensional case in 2018. More recently, we coupled these techniques with a renormalisation argument to handle all dimensions.

Joint work with Christoforos Panagiotis.

  • Combinatorial Theory Seminar
28 April 2020
12:00
Abstract

We consider random graph models where graphs are generated by connecting not only pairs of nodes by edges but also larger subsets of
nodes by copies of small atomic subgraphs of arbitrary topology. More specifically we consider canonical and microcanonical ensembles
corresponding to constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such
models. We also introduce a procedure that enables the distributions of multiple atomic subgraphs to be combined resulting in more coarse
grained models. As a result we obtain a general class of models that can be parametrized in terms of basic building blocks and their
distributions that includes many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs (Karrer & Newman PRE 2010, Bollobas et al. RSA 2011), random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree corrected and directed versions. We show that the entropy expressions for all these models can be derived from a single expression that is characterized by the symmetry groups of their atomic subgraphs.

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