Meetings Archive

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

Keep up to date with our upcoming events by joining the Heilbronn Event mailing list

 

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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

Keep up to date with our upcoming events by joining the Heilbronn Event mailing list

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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

Keep up to date with our upcoming events by joining the Heilbronn Event mailing list

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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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Professor Nina Snaith – Inaugural Lecture

Title: Random matrix theory: Hollywood’s hippest mathematics

Abstract: With applications to prime numbers and in physics and beyond, random matrices pop up in many unlikely contexts. A random matrix has an associated set of points (eigenvalues) that tend to repel each other, that is, they don’t like to be too close together, and yet don’t leave enormous gaps either. The same phenomenon is found in many naturally occurring systems, such as positions of birds’ nests or origins where replication commences on chromosomes, and in some contexts random matrix theory can model the space between these points. I will tell some stories about the research that has grown out of these connections.


Although this event is free to attend we ask that you please book your place via the Eventbrite page here to allow us to monitor numbers.

Please note, the lecture will begin at 4pm, however we invite attendees to join us in Fry Atrium from 3.15pm for refreshments.

Contact information

For enquiries about this event please contact maths-conference-administrator@bristol.ac.uk.

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One-Day Meeting in Combinatorics

This One-Day Meeting in Combinatorics, taking place in the afternoon of Monday 12th June (1pm-5:30pm) in the University of Bristol’s Fry Building, features talks from four internationally-renowned researchers.

There is no registration fee, and refreshments will be provided during the afternoon coffee break. Please register using the link below if you would like to attend, for catering and room-booking purposes. After the meeting, at around 5:30 pm, some of us will head to a nearby pub; all delegates are invited to join.

Speakers:

Paul Balister (Oxford)
Julia Boettcher (LSE)
Sean Eberhard (QUB)
Alex Scott (Oxford)

Registration

Please register to attend via the following link. There is no fee to attend this event.
Contact information

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

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Professor Tim Burness – Inaugural Lecture

Title: Simple groups, probabilistic methods and applications

Abstract: Group theory is used to study symmetry in a vast range of mathematical and physical systems, from the foundations of quantum physics to the intricacies of the Rubik’s cube. The finite simple groups are the “atoms” in this theory, analogous to the primes in number theory, and they have been a central focus of interest for almost 200 years. An ambitious project to classify these fascinating objects was completed about 20 years ago and this monumental achievement has had a profound influence on group theory and its applications.

In this lecture, I will begin by discussing some of the history around simple groups and their central role in group theory. I will then highlight several more recent developments, where the power of the classification theorem has been combined with probabilistic methods to great effect. For example, I will explain the major impact of these ideas on the study of bases for permutation groups, which is a classical concept introduced in the 19th century, and I will conclude by presenting some recent results on the generation properties of finite groups.


Although this event is free to attend we ask that you please book your place via the Eventbrite page here to allow us to monitor numbers.

Please note, the lecture will begin at 4pm, however we invite attendees to join us in Fry Atrium from 3.15pm for refreshments.

Contact information

For enquiries about this event please contact maths-conference-administrator@bristol.ac.uk.

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Two-Day Geometry Meeting

This Two-Day Geometry Meeting taking place over the afternoon of Monday 22nd May and morning of Tuesday 23rd May will feature six talks from internationally-renowned researchers in a number of fields in geometry. There will also be a lightning talk session for early career researchers.

Partially funded by the Heilbronn Institute for Mathematical Research.

Confirmed speakers:

Ara Basmajian, CUNY Graduate Center

Tara Brendle, University of Glasgow

Cornelia Drutu, University of Oxford

Dawid Kielak, University of Oxford

Christopher Leininger, Rice University

Hugo Parlier, University of Luxembourg

Registration: Please register to attend via the following link. There is no fee to attend this event. Please note, registration closes on Friday 12 May, 11.45pm.

We are able to offer partial funding to early career researchers, so please indicate in the registration form whether or not you would like to request funding. If you would like to apply for funding, please register before midday Friday 28 April. 

Schedule:

Monday 22nd May

13:00 – 13:50 Talk 1: Hugo Parlier, “Universal families of arcs and curves on surfaces”
14:00 – 14:50 Talk 2: Ara Basmajian, “Counting problems on the modular surface”
14:55 – 15:15 Coffee
15:20 – 16:10 Talk 3: Dawid Kielak, “Fibring, one-relator groups, and L2-homology”
16:20 – 17:20 Lightning talks for early career researchers
18:00 – 20:00 Dinner


Tuesday 23rd May

09:30 – 10:20 Talk 4: Tara Brendle, “Semi-direct product structures in mapping class groups of 3-manifolds”
10:25 – 10:45 Coffee
10:50 – 11:40 Talk 5: Christopher Leininger, “Geometry of subgroups of the mapping class group”
11:45 – 12:35 Lunch
12:40 – 13:30 Talk 6: Cornelia Drutu, “Property (T) and a-T-menability revisited”

Abstracts can be found here: Abstracts from Two-day Geometry Meeting (final) (PDF, 74kB).

 

Lightning talks schedule:

Harsh Patil, University of Bristol, “Asymptotic Cones”
Paweł Piwek, University of Oxford, “Group extensions: how to fill in the blank in 1 → N → __ → Q → 1”
David Sheard, King’s College London, “Reflection equivalence in Coxeter groups”
Piotr Mizerka, Polish Academy of Sciences, “Spectral gaps for cohomological Laplacians of SL(n, ℤ)”
Adele Jackson, University of Oxford, “Triangulations of Seifert fibered spaces”
Bin Sun, University of Oxford, “An approach to Simon’s Conjecture via the theory of division rings”
Tudur Lewis, University of Glasgow, “A Dehn surgery approach to the Birman-Craggs and Sato maps”
Riccardo Giannini, University of Glasgow, “Geometric homomorphisms and strata of translation surfaces”
Aaron Calderon, University of Chicago, “What do curves of long (hyperbolic/extremal) length look like?”
Changjie Chen, Brown University, “Morse functions on the moduli space and an investigation of its topology”

Contact information

This event is organised by Viveka Erlandsson (v.erlandsson@bristol.ac.uk) and Luke Jeffreys (luke.jeffreys@bristol.ac.uk).

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

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