Meetings Archive

Heilbronn Colloquium 2024: Simon Foucart

Simon Foucart, Professor of Mathematics, Texas A & M University, USA
Heilbronn Distinguished Visiting Fellow, Isaac Newton Institute for Mathematical Sciences, UK

School of Mathematics, Woodland Road, Bristol BS8 1UG

Tuesday 2nd July 2024

4pm to 5pm

Room 2.04, Fry Building

Colloquium Title: Optimal Recovery as a Worst-Case Learning Theory

This talk showcases the speaker’s recent results in the field of Optimal Recovery, viewed as a trustworthy Learning Theory focusing on the worst case. At the core of several results presented here is a scenario, resolved in the global and the local settings, where the model set is the intersection of two hyperellipsoids. This has implications in optimal recovery from deterministically inaccurate data and in optimal recovery under a multifidelity-inspired model. In both situations, the theory becomes richer when considering the optimal estimation of linear functionals. This particular case also comes with additional results in the presence of randomly inaccurate data.

About the Speaker: Simon Foucart earned a Masters of Engineering from the Ecole Centrale Paris and a Masters of Mathematics from the University of Cambridge in 2001. He received his Ph.D. in Mathematics at the University of Cambridge in 2006, specializing in Approximation Theory. After two postdoctoral positions at Vanderbilt University and University of Paris 6, he joined Drexel University in 2010 before moving to the University of Georgia in 2013. He joined Texas A & M University in 2015 as an associate professor and he is currently a professor of Mathematics. His current work focuses on the modern field of Compressive Sensing, whose theory is exposed in the book ‘A Mathematical Introduction to Compressive Sensing‘ he co-authored with Holger Rauhut.

Simon’s research was recognised by the Journal of Complexity, from which he received the 2010 Best Paper Award. His interests also include the mathematical aspects of metagenomics.

Please  register here attend.

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Heilbronn Annual Conference 2024

The Heilbronn Annual Conference is the Institute’s flagship event. It takes place over two days and it covers a broad range of mathematics, including algebra, combinatorics, data science, geometry, number theory, probability, quantum information. It brings together members of the Institute, distinguished visiting speakers, and other members of the UK mathematical community. This year we welcome eight distinguished speakers, to deliver lectures intended to be accessible to a general audience of mathematicians.

Invited Speakers

Tara Brendle (University of Glasgow, UK)

Chaim Goodman-Strauss (Arkansas, USA)

Barbara M. Terhal (TU Delft, The Netherlands)

Richard Samworth (University of Cambridge, UK)

Josephine Yu (Georgia Institute of Technology, USA)

Christophe Breuil (Université Paris-Saclay, France)

Tim Austin (University of Warwick, UK)

Dipendra Prasad (Indian Institute of Technology Bombay, India)

 

Registration opens Monday 20th May 2024

Click here for more information

Email  heilbronn-coordinator@bristol.ac.uk

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Distinguished Visiting Professor 2024: Romain Tessera

Heilbronn colloquium: Romain Tessera

Romain Tessera, Senior Researcher, Université Paris Cité, France

Wednesday 8 May 2024 4pm to 5pm

Venue Lecture Theatre G.10, Fry Building

Followed by drinks reception 5-6pm in the Staff Common Room, Fry Building

Quantitative Ergodic Theory

Ergodic theory is the study of measure preserving actions of groups on a probability space. These may be studied from two different angles: up to isomorphism, or up to “orbit equivalence”. For the latter we merely require an isomorphism between the probability spaces that preserves the orbits of the group actions, but the groups themselves may no longer be isomorphic.

Orbit equivalence has been intensively studied since the eighties, and one of the most impressive results, due to Ornstein and Weiss, says that any two free ergodic actions of infinite amenable groups (such as Z^d for instance) are orbit equivalent. In other words, all information on the (amenable) groups is lost under orbit equivalence. We shall present a new theory, which emerged from the need to nuance Orstein-Weiss’ theorem. Roughly, one defines a way to measure how “good” an orbit equivalence map is in order to restore some information on the group.

Short biography

Romain Tessera defended his PhD in 2006 under the co-direction of Thierry Coulhon and Alain Valette. He then spent 2 years as a postdoctoral researcher at Vanderbilt University. Romain has been a researcher in CRNS (France) since 2008, first at École Normale Supérieure de Lyon, then at University of Orsay, and finally as a senior researcher at Université Paris Cité (since 2018). His research focuses on geometric group theory, with incursions in other fields such as ergodic theory, topological rigidity, non-commutative geometry.

 

Please register here to attend

Organised in collaboration with the School of Mathematics, University of Bristol, UK

For more information please email the Heilbronn events team at  heilbronn-coordinator@bristol.ac.uk

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Heilbronn Colloquium 2024: Anna Frishman

Friday 12 April 2024 3pm to 4pm                                                                                                                                 

Anna Frishman, Distinguished Visiting Fellow, Cambridge University, UK and Physics Department, Technion, Israel

Lecture Theatre LG.02, Fry Building,  School of Mathematics, Woodland Road, Bristol BS8 1UG

Followed by a drinks reception 4pm to 5pm in the Staff Common Room, Fry Building.

Title: Universality of Satellite Formation During Breakup of a Fluid Bridge

The breakup of a fluid object is a remarkably singular process. Beautifully, the approach to this singularity can give rise to universal dynamics, occurring around the pinch off points. When breakup is driven by inertia in a symmetric configuration, the pinch off occurs symmetrically at two points, sealing off a satellite fluid drop.

Contrary to the dynamics at pinch off points, not much is known about universal dynamics for satellite formation.

Here we demonstrate the existence of such dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid bridge, which we realize experimentally using a soap-film bubble suspended between two plates. Combining experiments and one-dimensional simulations, we show that a main satellite bubble always forms as the bridge breaks. We discover that the satellite size is a simple function of two non-dimensional control parameters, one dynamical and the other geometrical. These observations can be explained by tracing the bridge evolution over a series of dynamical stages in which the bridge: (i) closely follows a sequence of equilibrium bridge configurations; (ii) stretches as it begins to breakup after reaching an unstable equilibrium; and (iii) follows a universal breakup solution, occurring over a finite spatial region. We explain how stretching in stage (ii) controls the satellite volume, which varies with the control parameters over two orders of magnitude, and the universality of the dynamics makes it highly reproducible.

About the Speaker: Anna Frishman mainly works on turbulence, viewed as an out-of-equilibrium system at the intersection of fluid mechanics and statistical physics. From time to time, she works on problems in fluid mechanics without turbulence, and in statistical mechanics without fluids. Anna did her PhD in physics at the Weizmann Institute of Science under the supervision of Professor Gregory Falkovich, then moved to Princeton University for an independent postdoc at the PCTS. She has been a faculty member in the physics department at the Technion, Israel, since 2019.

Please register here to attend. 

 

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Heilbronn Seminar 2024: Daniel Wise

Daniel Wise, Department of Mathematics & Statistics, McGill University, Montreal, Canada

Friday 15 March 2024 at 13:00

[Lunch will be served at 12:00 in the Fry Building, Staff Common Room]

Venue: Lecture Theatre 2.41, Fry Building, School of Mathematics, University of Bristol, Bristol BS8 1UG

Organised in collaboration with the School of Mathematics, University of Bristol, UK

Registration is free, but required. Please register using this form.

A Small Contribution to the Kervaire Conjecture

I will give a quick survey of the known results and methods towards the Kervaire conjecture in combinatorial group theory. Then I will offer a small but pretty result that offers a new paradigm. This is joint work with Andy Ramirez-Côté.

 

 

Short Biography: Dani Wise grew up in New York and received his BA from Yeshiva University and his PhD from Princeton (1996). After stimulating postdocs and visiting positions at Berkeley, Cornell, and Brandeis, he moved to McGill in 2001, where he is a James McGill Professor. His primary research agenda has been to explore and promulgate the utility and ubiquity of non-positively curved cubical geometry in group theory and topology. He has received an AMS Veblen Prize, the CRM-Fields-PIMS Prize, a Guggenheim Fellowship, a Lobachevsky Medal, and is a Fellow of the Royal Society of London. Dani Wise is currently on Sabbatical at the Weizmann Institute of Science in Israel.

Professor Daniel Wise is also giving a Colloquium on Monday 11 March at 16:00 in Lecture Theatre 4, School of Chemistry.

For more information please email the Heilbronn events team at  heilbronn-coordinator@bristol.ac.uk

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Heilbronn Colloquium 2024: Daniel Wise

Daniel Wise, Department of Mathematics & Statistics, McGill University, Montreal, Canada

Monday 11 March 2024 at 16:00

Venue: Lecture Theatre 4, School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS

Organised in collaboration with the School of Mathematics, University of Bristol, UK

Registration is free, but required. Please register using this form

The Cubical Route to Understanding Groups

Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

 

Short Biography: Dani Wise grew up in New York and received his BA from Yeshiva University and his PhD from Princeton (1996). After stimulating postdocs and visiting positions at Berkeley, Cornell, and Brandeis, he moved to McGill in 2001, where he is a James McGill Professor. His primary research agenda has been to explore and promulgate the utility and ubiquity of non-positively curved cubical geometry in group theory and topology. He has received an AMS Veblen Prize, the CRM-Fields-PIMS Prize, a Guggenheim Fellowship, a Lobachevsky Medal, and is a Fellow of the Royal Society of London. Dani Wise is currently on Sabbatical at the Weizmann Institute of Science in Israel.

Professor Daniel Wise is also giving a Seminar on Friday 15 March at 13:00 in Lecture Theatre 2.41, Fry Building.

For more information please email the Heilbronn events team at  heilbronn-coordinator@bristol.ac.uk

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Distinguished Lecture Series 2024: James Maynard (Oxford)

20 – 22 March 2024

Venue: Lecture Theatre G.10, Ground Floor, School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG

Organised in collaboration with the Heilbronn Institute for Mathematical Research.

 

James Maynard, Mathematical Institute, University of Oxford, UK

James Maynard is a professor of Number Theory at the University of Oxford. He works in analytic number theory, particularly the study of prime numbers. He is a fellow of the Royal Society and has been awarded numerous prizes, including the SASTRA Ramanujan Prize, an LMS Whitehead Prize, an EMS Prize, the Compositio Prize, the AMS Cole Prize and a New Horizons Prize.

James was awarded the Fields Medal in 2022 for “contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation”.

 

Wednesday 20 March 2024 (4-5pm followed by drinks reception)

Colloquium: Classical sieve methods

We will give an overview of ‘standard’ sieve methods: what are they? And what are they good for? What can they (and can they not) say about prime numbers? Classical sieve methods are an exceptionally versatile set of techniques that are ubiquitous in analytic number theory, but often fall just short of the task which they were designed for: finding prime numbers. Sometimes these limitations can be side-stepped allowing us to prove results about the existence of primes, such as in work on bounded gaps between primes.

 

Thursday 21 March 2024 (4-5pm)

Primes and sieves II: Prime detecting sieves

We give an overview of how the limitations of ‘standard’ sieves are overcome by introducing extra arithmetic information into the method, which in principle can detect prime numbers and achieve the original goal of sieves. This offers a possible attack to many famous open problems about prime numbers, but unfortunately can currently only be made to work in ‘nice’ situations. Nevertheless, there is a general approach to trying to count primes in sets which are ‘not too sparse’, such as sets with digit restrictions.

 

Friday 22 March 2024 (3-4pm)

Primes and sieves III: Optimality of prime detecting sieves

We will talk about some of the key open questions in sieve theory, and what we would need to have an efficient tool-kit to answer questions about primes. Work-in-progress (with Kevin Ford) allows us demonstrate a provably optimal version of prime-detecting sieves in various settings, as well as demonstrations of the limitations of the current prime-detecting setup.

 

For more information please email the Heilbronn events team at  heilbronn-coordinator@bristol.ac.uk

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CMI-HIMR Summer School on Symmetry and Randomness

Hosted by: School of Mathematics, Fry Building, University of Bristol, UK

Jointly funded by the Clay Mathematics Institute and the Heilbronn Institute for Mathematical Research.

This year the summer school will focus on the mathematics of symmetry and randomness, where probability theory comes together with analysis, geometry and group theory to help understand highly symmetric structures. The mini-courses will present aspects of random walks on infinite graphs and groups in connection with geometric group theory; the mathematics of percolation theory especially on large transitive graphs; as well as spectral and mixing time estimates for finite Markov chains with an emphasis on the cut-off phenomenon, and much more. Students will have the opportunity to be introduced to these topics as well as to hear lectures by leading figures in the area.

 

More information is available on the summer school website.

Applications are now open, please apply here. The application deadline is 15th March 2024, 23:45 GMT.

Organisers:

Emmanuel Breuillard (Oxford)
Matthew Tointon (Bristol)

Short Course Lecturers:

Tom Hutchcroft (Caltech)
Justin Salez (Université Paris-Dauphine)
Tianyi Zheng (UC San Diego)

Guest Speakers:

Persi Diaconis (Stanford)
Geoffrey Grimmett (Cambridge)
Tatiana Nagnibeda (Université de Genève)

 

Contact

For queries regarding this event, please contact heilbronn-coordinator@bristol.ac.uk.

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Persi Diaconis (Public Lecture)

Public Lecture 17:00 – 18:00: Lecture Theatre 1, Chemistry Building, Cantock’s Close

Title: THE MATHEMATICS OF SOLITAIRE

Abstract:
One of the embarrassing facts about probability theory: we don’t know the odds of winning at solitaire! I mean ordinary klondike, played on computer screens and cellphones millions of times a day. For example, in Vegas, you can ‘buy a deck for $52 and get $5 for each card turned up on the ace piles. Is this anything like a fair game? I will review what we know (after all, it’s 2023 and the computer is here–surely they know how to play solitaire (nope)). I’ll turn to what we always turn to, Polya’s dictum ‘If there is a hard problem you can’t solve there is an easier problem you can’t solve.” Patience sorting is a simpler form of solitaire and here mathematics can be brought in. The mathematics is hard and interesting (and gives definitive answers involving one main theme of our conference–random matrix theory). Even here, bending the rules back towards Klondike leads to easy to understand and wide open problems.

 

“Persi Diaconis is a world leading statistician working in probability, combinatorics and group theory. He is Professor of Mathematics and Mary Sunseri Professor of Statistics at Stanford University. He is the recipient of many honours and awards, among which are the MacArthur Fellowship, the Rollo Davidson Prize at the University of Cambridge, the Conant Prize and the Euler Prize of the AMS, and the Van Wijngaarden Award, Amsterdam. He gave many prestigious lectures: he was Plenary Speaker at the International Congress of Mathematicians, Berlin, 1984; he was AMS Gibbs Lecturer, 1997; LMS Hardy Lecturer, 2021; Von Neumann Lecturer, SIAM; Inaugural Alexanderson Award Lecturer, AIM, Santa Clara University . Persi Diaconis is an exceptional communicator, and his public lectures are famous. He also had a very unusual career path for a mathematician. He was born in New York in 1945. After graduating from High School at 14, he left home to become a professional magician. When he was 24 years old, he went back to New York to study for a BSc in mathematics at City College, where he graduated in 1971. He then went on to obtain a PhD in Statistics in 1974 at Harvard University.”

 

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Two-Day Logic Meeting

This Two-Day Logic Meeting begins in the afternoon of Friday 30th June and ends in the late afternoon of Saturday 1 July. It will feature talks from renowned researchers in several branches of logic.

The meeting is funded by the School of Mathematics and EPSRC.

 

Confirmed speakers: 

Sam Coskey, University College London

Title: Conjugacy, classification, and complexity

Abstract: We investigate the classification of automorphisms of a countable structure up to conjugacy. We aim to identify the complexity of this classification for a variety of structures. To study the complexity, we use the Borel reducibility hierarchy of equivalence relations.

Slides available here.

Rod Downey, University of Wellington

Title: Algorithmically Random Trigonometric Series

Abstract: Recently, we have seen the uses of the theory of algorithmic randomness to solve questions in classical mathematics. Some of these are purely classical and some have a more algorithmic feel. We will discuss some of these initiatives, illustrating the ideas via some longstanding questions in the theory of random trigonometric series. In particular, Rademacher [Rad22], Steinhaus [Ste30] and Paley and Zygmund [PZ30a, PZ30b, PZ32]initiated the extensive study of random series. Using the theory of algorithmic randomness, which is a mix of computability theory and probability theory, we investigate the effective content of some classical theorems.

We discuss how this is related to an old question of Kahane and Bollobas [Bol01], as reported in [DGTta]. We also discuss how considerations of such algorithmic questions about random series seems to lead to new notions of algorithmic randomness.

[Bol01] Bela Bollobas. Random graphs, volume 73 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, second
edition, 2001.
[DGTta] R. Downey, N. Greenberg and A. Tanggarra. Algorithmically random series, and uses of algorithmic randomness in mathematics. Submitted.
[PZ30a] R. E. A. C. Paley and A. Zygmund. On some series of functions (1). Mathematical Proceedings of the Cambridge Philosophical Society, 26(4):337–257, 1930.
[PZ30b] R. E. A. C. Paley and A. Zygmund. On some series of functions (2). Mathematical Proceedings of the Cambridge Philosophical Society,26(4):458–474, 1930.
[PZ32] R. E. A. C. Paley and A. Zygmund. On some series of functions, (3). Mathematical Proceedings of the Cambridge Philosophical Society, 28(2):190–205, 1932.
[Rad22] H. Rademacher. Einige sätze über Reihen von allgemeinen Orthogonal-Funktionen. Mathematische Annalen, 87:112–138, 1922.
[Ste30] Hugo Steinhaus. Uber die wahrscheinlichkeit dafur, das der konvergenzkreis einer Potenzreihe ihre natürliche Grenze ist. Mathematische Zeitschrift, 31(1):408–416, 1930.

Slides available here.

Kentaro Fujimoto & Philipp Schlicht, University of Bristol

Title: Some open problems in second-order set theory

Kentaro Fujimoto’s slides are available here.

Philipp Schlicht’s slides are available here.

Richard Matthews, University of Creteil, Paris

Title: A guide to Krivine Realizability

Abstract: The method of realizability was first developed by Kleene and is seen as a way to extract computational content from mathematical proofs. Traditionally, these models only satisfy intuitionistic logic, however the method was extended by Krivine to produce models which satisfy full classical logic and even Zermelo Fraenkel set theory with choice. In this talk we will discuss how to construct realizability models of ZF and its connections with intuitionistic realizability, double negation translations and the method of forcing. We will then present recent results concerning ordinals and large cardinals in these realizability models. This is joint work with Laura Fontanella and Guillaume Geoffroy.

Slides available here.

Fedor Pakhomov, University of Ghent

Title: On limits of incompleteness theorems

Abstract: In this talk I will give a survey of several recent results
about the limits of incompletess theorems.  Based on the papers:
[1] Pakhomov, F., & Visser, A. (2022). Finitely axiomatized theories
lack self‐comprehension. Bulletin of the London Mathematical Society, 54(6), 2513-2531.
[2] Murwanashyaka, J., Pakhomov, F., & Visser, A. (2023). There are no
minimal essentially undecidable theories. Journal of Logic and Computation.

Slides available here.

Paul Shafer, University of Leeds

Title: The logical and computational strength of inside/outside Ramsey theorems

Abstract: Rival and Sands proved that every infinite graph G contains an infinite subset H such that every vertex of G is adjacent to precisely none, one, or infinitely many vertices of H.  We call this result an inside/outside Ramsey theorem because the conclusion provides information about vertices that are inside of H and about vertices that are outside of H.  Rival and Sands also proved a similar statement for infinite partial orders of finite width.  We analyze the strength of these theorems from the perspective of reverse mathematics and the Weihrauch degrees.  We find that they give the first examples from the modern general mathematics literature of theorems that are equivalent to the double jump of weak König’s lemma in the Weihrauch degrees and of theorems that are equivalent to the ascending/descending sequence principle (plus Sigma_2 induction in some cases) in reverse mathematics.  This work is joint with Marta Fiori Carones, Alberto Marcone, and Giovanni Soldà.

Slides available here.

Johannes Stern, University of Bristol

Title: From Intuitionistic Kripke Frames to Strong Kleene Supervaluation and Theories of Naive Truth.

Abstract: I show how starting from intuionistic Kripke frames one can develop a supervaluational framework that lends itself to inductively defining a truth predicate in the presence of an intutionistic conditional.

Slides available here.

Xinhe Wu, University of Bristol

Title: Full and Mixed Models

Abstract: In this talk, I discuss two special kinds of Boolean-valued models: full models and mixed models. I show that these models are more “classical” than the others, as some classical model-theoretic results can only be generalized to these them. In particular, the Łoś ultraproduct theorem and (a strong version of) downward Lowenheim-Skolem theorem can only be generalized to full models, and the theorem that every countably incomplete ultraproduct is ω1-saturated and the theorem that Σ^1_1 formulas are preserved under ultraproducts can only be generalized to mixed models.

Slides available here.

Bokai Yao, University of Notre Dame

Title: Reflection with Absolute Generality

Abstract: Traditionally, reflection principles in set theory claim that the set-theoretic universe is indescribable. It is natural to consider reflection principles with absolute generality, which asserts that the universe containing everything, including sets and urelements, is indescribable. In the first part of this talk, I will consider the first-order reflection principle in urelement set theory. With the Axiom of Choice, first-order reflection holds just in case urelements are arranged in a certain way, and this equivalence falls apart without AC.  In the second part of this talk, I will present my joint work with Joel Hamkins on second-order reflection principles with urelements. A standard version of second-order reflection, due to Paul Bernays, is often considered as a weak large cardinal axiom in set theory. With abundant urelements, however, Bernays’ second-order reflection principle interprets a supercompact cardinal.

Slides available here.

 

Schedule:

Friday 30th June

14:00-15:00 – Richard Matthews

15:00-15:30 – Break

15:30-16:30 – Rod Downey

16:30-16:45 – Break

16:45-17:15 – Xinhe Wu

17:15-17:45 – Kentaro Fujimoto & Philipp Schlicht

 

Saturday 1st July

09:00-10:00 – Fedor Pakhomov

10:00-10:30 – Break

10:30-11:30 – Paul Shafer

11:30-12:00 – Sam Coskey

12:00-14:00 – Lunch

14:00-14:30 – Bokai Yao

14:30-15:30 – Johannes Stern

All talks will take place in G.13, Fry Building.

 

List of participants:

Sam Coskey – University College London
Joseph Deakin – University of Cambridge
Rod Downey – University of Wellington
Ugur Efem – Dyson Institute of Engineering and Technology
Kentaro Fujimoto – University of Bristol
Colin Harling – NSSL
Charles Harris – University of Bristol
Alex Kavvos – University of Bristol
Clara List – Universität Hamburg
Xianrui Liu – University of Bristol
Richard Matthews – University of Creteil, Paris
Michael Mooney – University of Bristol
Fedor Pakhomov – University of Ghent
Sherwin Pereira – University of Bristol
Simone Picenni – University of Bristol
Cécilia Pradic – Swansea University
Paul Shafer – University of Leeds
Philipp Schlicht – University of Bristol
Johannes Stern – University of Bristol
Esme Weil – University of Bristol
Xinhe Wu – University of Bristol
Bokai Yao – University of Notre Dame

 

Registration

This event has now passed and registration is closed.

 

This event is organised by Kentaro Fujimoto (kentaro.fujimoto@bristol.ac.uk) and Philipp Schlicht (philipp.schlicht@bristol.ac.uk).

For practical information please contact maths-conference-administrator@bristol.ac.uk.

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