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.

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

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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.

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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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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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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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.