Archive | Meetings

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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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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Heilbronn Colloquium 2023: Iosif Polterovich

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

Venue: Lecture Theatre 2.41, School of Mathematics, Fry Building, Woodland Road, University of Bristol

Title: Nodal count via topological data analysis

Abstract:   A nodal domain of a function is a connected component of the complement to its zero set. The celebrated Courant nodal domain theorem implies that the number of nodal domains of a Laplace eigenfunction is controlled by the corresponding eigenvalue. There have been many attempts to find an appropriate generalization of this statement in various directions: to linear combinations of eigenfunctions, to their products, to other operators. It turns out that these and other extensions of Courant’s theorem can be obtained if one counts the nodal domains in a coarse way, i.e. ignoring small oscillations. The proof uses multiscale polynomial approximation in Sobolev spaces and the theory of persistence barcodes originating in topological data analysis. The talk is based on a joint work with L. Buhovsky, J. Payette, L. Polterovich, E. Shelukhin and V. Stojisavljević. No prior knowledge of spectral geometry and topological persistence will be assumed.

Register here

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Heilbronn Colloquium 2023: Jinho Baik

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

Venue: Lecture Theatre 2.41, School of Mathematics, Fry Building, Woodland Road, University of Bristol

KPZ Limit Theorems

Jinho Baik, University of Michigan, USA  

One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers define two-dimensional random fields. The KPZ universality conjectures that an appropriately scaled height function converges to a model-independent universal random field for a large class of models. We survey some of the limit theorems and discuss changes that arise when we consider different domains. In particular, we present recent results on periodic domains. We also comment on integrable probability models, integrable differential equations, and universality

  Register here

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Heilbronn Colloquium 2023: Nalini Anantharaman

Monday 13 February 2023 at 15:00 Organised in collaboration with the School of Mathematics, University of Bristol, UK   Venue: Lecture Theatre 2.41, School of Mathematics, Fry Building, Woodland Road, University of Bristol  

Uncertainty Principle and Uncertainty Inequalities

Nalini Anantharaman, Institute for Advanced Mathematical Research (IRMA), University of Strasbourg, France We shall discuss mathematical forms of the uncertainty principle and its relationship with quantum unique ergodicity. Register here Join the Heilbronn Event mailing list to keep up to date with our upcoming events.
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Heilbronn Colloquium 2023: Nalini Anantharaman

Monday 13 February 2023 at 15:00 Organised in collaboration with the School of Mathematics, University of Bristol, UK   Venue: Lecture Theatre 2.41, School of Mathematics, Fry Building, Woodland Road, University of Bristol   Uncertainty Principle and Uncertainty Inequalities Nalini Anantharaman, Institute for Advanced Mathematical Research (IRMA), University of Strasbourg, France   We shall discuss […]

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CMI-HIMR Summer School on Probabilistic Group Theory

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.

In recent years, probabilistic methods have been at the heart of many spectacular advances in group theory and related areas, finding a diverse range of applications. This summer school will introduce a wide audience of graduate students and early career researchers to some of the most exciting recent developments. The programme will feature four short courses from world-leading experts in the area, together with tutored problem sessions for participants.

 

More information on the summer school website

Applications are now open, please apply here. The application deadline is 24th February 2023, 23:59 GMT.

Confirmed lecturers:

Martin Liebeck (Imperial College London)

Cheryl Praeger (University of Western Australia)

Aner Shalev (Hebrew University of Jerusalem)

Pham Huu Tiep (Rutgers University)

Guest lecturers:

Emmanuel Breuillard (Oxford)

Ben Green (Oxford)

Colva Roney-Dougal (St Andrews)

 


Applications are now open, please apply here. The application deadline is 24th February 2023, 23:59 GMT.

If you have any questions, please contact heilbronn-coordinator@bristol.ac.uk. Visit the summer school’s event website for further information.

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Fry Conference Series: New Perspectives in Pure Mathematics

This is the last in a series of conferences being held to celebrate the move of the School of Mathematics at the University of Bristol to the recently refurbished Grade II listed Fry Building at the heart of the university campus.

Taking place over three days (in the Fry Building), this international conference features a distinguished line-up of speakers, covering a range of recent advances in number theory, combinatorics, algebra, geometry and logic.

Visit the event website to view the programme and to register.

Organisers:

David Ellis (Bristol)
Céline Maistret (Bristol)

Scientific committee:

David Ellis (Bristol) – Combinatorics section
Kentaro Fujimoto (Bristol) – Logic section
John Mackay (Bristol) – Geometry section
Céline Maistret (Bristol) – Number Theory section
Jeremy Rickard (Bristol) – Algebra section

Confirmed Speakers:

Jonathan Chapman (Bristol)
Ben Green (Oxford)
Scott Harper (St Andrews)
Alessandra Iozzi (ETH Zurich)
Franziska Jahnke (Muenster)
Autumn Kent (Wisconsin)
Jungwon Lee (Warwick)
Shoham Letzter (UCL)
Menachem Magidor (Jerusalem)
Irene Pasquinelli (Bristol)
Ross Paterson (Bristol)
Michael Rathjen (Leeds)
Aner Shalev (Jerusalem)
Donna Testerman (EPFL)
Jack Thorne (Cambridge)

Visit the event website to view the programme and to register.

 

We are very grateful indeed for financial support from the Heilbronn Institute for Mathematical Sciences, the London Mathematical Society and the Clay Mathematics Institute.

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Random matrices from quantum chaos to the Riemann zeta function. A celebration in honour of Jon Keating’s 60th birthday.

School of Mathematics, Fry Building, University of Bristol, UK

Random Matrix Theory (RMT) is ubiquitous in the mathematical and physical sciences because of its broad range of applications and its predictive power, which allow accurate calculations and asymptotic analysis that are not accessible through traditional techniques. The interdisciplinary nature of RMT is epitomized by Prof. Jon Keating’s career, which has been characterized by the rare ability of initiating new areas of research by bringing together areas of mathematics that on the surface have little in common. This conference will feature leading mathematicians working at the interface of quantum chaos, analytic number theory, probability and random matrix theory.

Visit the event website to view the programme and to register.

Organisers:
Emma Bailey (CUNY)
Tamara Grava (Bristol)
Francesco Mezzadri (Bristol)
Nina Snaith (Bristol)
Brian Winn (Loughborough)

Speakers:
Louis-Pierre Arguin (CUNY)
Emma Bailey (CUNY)
Michael Berry (Bristol)
Brian Conrey (AIM)
Neil O’Connell (UCD)
Persi Diaconis (Stanford)
Alexandra Florea (UC Irvine)
Yan Fyodorov (KCL)
Alice Guionnet (Lyon)
Alexander Its, (IUPUI)
Jens Marklof (Bristol)
Zeev Rudnick (Tel Aviv)
Peter Sarnak (Princeton)
Nick Simm (Sussex)
Kannan Soundararajan (Stanford)

 

Visit the event website to view the programme and to register.

 


We are very grateful indeed for financial support from the Heilbronn Institute for Mathematical Sciences, the American Institute of Mathematics, and the London Mathematical Society.

If you have any questions, please contact heilbronn-coordinator@bristol.ac.uk.

Join the Heilbronn Event mailing list to keep up to date with our upcoming events.

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Heilbronn Colloquium 2022: Pierre Del Moral

14 September 2022 at 16:00 – 17:00 We are delighted to welcome Professor Pierre Del Moral, INRIA at the University of Bordeaux, to the University of Bristol to deliver a Heilbronn Colloquium.

The colloquium with take place in Lecture theatre 2.41, Fry Building at 16:00 – 17:00 followed by a wine reception in the Fry Common Room.

Title: Stability of positive semigroups and their mean field interpretations

Abstract: This talk is concerned with the stability of positive semigroups and their mean field particle interpretations.

We present a stochastic interpolation methodology based on backward semigroup techniques to obtain sharp quantitative estimates uniformly with respect to the time parameter. The stability analysis discussed in this talk is based on the extension of V-norm contraction methods for Markov operators, to nonlinear normalized semigroups. In the context of unnormalized models, we also present extensions of Perron-Frobenius and Krein-Rutman theorems for positive operators to time-varying positive semigroups.

We illustrate the impact of these stochastic perturbation techniques in the context of diffusion Monte Carlo ground state calculation, Feynman-Kac branching particle interpretations as well as McKean-Vlasov interacting diffusions.

The talks will be held in-person only. Spaces are limited in the room, so we ask that you please register via this form if you are intending to come in person. Once capacity is reached, we will close registration and any current remaining spaces will be allocated on a first come basis.


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