Forder Lecture Tour 2020


Forder Tour 2020

The Forder Lectureship is one of a pair of reciprocal exchanges between the New Zealand and London Mathematical Societies. The lectureship was established in 1986 and is normally awarded every two years to "to a research mathematician from the United Kingdom who has made an eminent contribution to the field of mathematics and who can also speak effectively at a more popular level".
 


Henry Forder | Itinerary | Titles and Abstracts | Short Bio


Henry Forder

The Forder lectureship was established by the London Mathematical Society and the New Zealand Mathematical Society in 1986 in honour of Henry Forder, who was born in Norfolk, England in 1889 but spent most of his mathematical career in Auckland, New Zealand. A mathematical biography of Henry Forder can be found here.

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Itinerary

9th March University of Auckland, Auckland
    14:00-15:00, 303-101
   Additive number theory through the model-theoretic lens

10th March University of Auckland, Auckland
    15:00-16:00, 303-G14
   Ramsey multiplicity of patterns in finite abelian groups

11th March Auckland University of Technology, Auckland
    11:00-12:00
   What Fourier analysis can and cannot tell us about the integers

11th March Auckland University of Technology, Auckland
    18:00-19:00, Room 126, Sir Paul Reeves Building
   The power of randomness

12th March Waikato University, Hamilton
    16:10-17:00, S. 1.01
   What Fourier analysis can and cannot tell us about the integers

12th March Waikato University, Hamilton
    18:10-19:10, S. 1.02
   The power of randomness

16th March Massey University Palmerston North, Palmerston North
    12:00-13:00, SSLB3
   The usefulness of useless (mathematical) knowledge

16th March Massey University Palmerston North, Palmerston North
    15:00-16:00, ScB3.31
   What Fourier analysis can and cannot tell us about the integers

18th March Victoria University Wellington, Wellington
    11:00-12:00, Cotton Building, Room 350
   What Fourier analysis can and cannot tell us about the integers

18th March Victoria University Wellington, Wellington
    18:00-19:00, RHLT1, Rutherford House, Pipitea Campus
   The usefulness of useless (mathematical) knowledge

19th March University of Canterbury, Christchurch
    14:00-14:50, Jack Erskine 315
   What Fourier analysis can and cannot tell us about the integers

19th March University of Canterbury, Christchurch
    18:00-19:00, E8 (Engineering Core Lecture Theatre)
   The power of randomness

Unfortunately I have had to return to the UK earlier than planned as a result of the COVID-19 outbreak in Europe and associated travel restrictions. The last three talks of this tour have therefore been CANCELLED. My sincere apologies for any inconvenience this may cause to those who were planning to attend, and many thanks to my hosts for their understanding.

Cancelled: 23rd March University of Otago, Dunedin
    17:30-18:30 venue tbc
   The usefulness of useless (mathematical) knowledge

Cancelled: 24th March University of Otago, Dunedin
   11:00-12:00, venue tbc
   What Fourier analysis can and cannot tell us about the integers

Cancelled: 26th March Massey University Albany, Auckland
    12:00-13:00, venue tbc
   Additive number theory through the model-theoretic lens

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Titles and Abstracts

Specialist seminars

Title: Efficient regularity lemmas
Abstract: Since Szemerédi's seminal work in the 70s, regularity lemmas have proven
to be of fundamental importance in many areas of discrete mathematics. This talk will survey some of the classical results in both the graph and the arithmetic context, examine the connections between the two settings, and describe a flurry of recent work on regularity decompositions under additional assumptions such as stability and bounded VC-dimension. This is joint work with Caroline Terry (University of Chicago).
Title: Ramsey multiplicity of patterns in finite abelian groups
Abstract: It is well known (and a result of Goodman) that a random 2-colouring of the
edges of the complete graph K_n contains asymptotically the minimum number of monochromatic triangles (K_3s). Erdos conjectured that this was also true of monochromatic copies of K_4, but his conjecture was disproved by Thomason in 1989. The question of determining for which small graphs Goodman’s result holds true remains wide open. In this talk we explore an arithmetic analogue of this question: what can be said about the number of monochromatic additive configurations in 2-colourings of finite abelian groups? The techniques used to address this question, which include additive combinatorics and quadratic Fourier analysis, originate in quantitative approaches to Szemeredi’s theorem. This is joint work with Alex Saad (University of Oxford).
Title: Szemerédi's theorem in the primes
Abstract: Green and Tao famously proved in 2005 that any subset of the primes of
fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to zero sufficiently slowly contains a 3-term term progression. This was followed by work of Helfgott and de Roton, and Naslund, who improved the bounds on the relative density in the case of 3-term progressions. We present an analogous result for longer progressions by combining a quantified version of the relative Szemeredi theorem given by Conlon, Fox and Zhao with Henriot's estimates of the enveloping sieve weights. This is joint work with Luka Rimanic (ETH Zurich).

Colloquia

Title: What Fourier analysis can and cannot tell us about the integers
Abstract: It is surprisingly straightforward to count the number of solutions to simple
equations such as x+y=2z or x-y=z^2, where x, y and z in a "random-looking" subset of the integers. The discrete Fourier transform provides a natural way of quantifying what we mean by random-looking, but fails us once we start to consider arithmetic progressions of length greater than three and other more sophisticated structures. This failure opens the door to a rich and still evolving theory of higher-degree Fourier analysis, which we shall try and catch a glimpse of in this talk.
This talk aims to be accessible to postgraduate students across all areas of mathematics.
Title: Additive number theory through the model-theoretic lens
Abstract: A long-standing open problem in additive number theory is the following:
how large does a set of integers have to be before it is guaranteed to contain a non-trivial arithmetic progression of length 3? In the first half of this talk we shall survey recent progress on this problem, and the techniques used to solve it and related questions about additive structures in finite abelian groups. In particular, we shall explain the idea behind the so-called "arithmetic regularity lemma" pioneered by Green, which is a group-theoretic analogue of Szemerédi's celebrated regularity lemma for graphs. In the second half of the talk we shall describe a host of recent results showing that under natural model-theoretic assumptions the conclusions of such regularity lemmas can be significantly strengthened. Most of the relevant model-theoretic notions were conceived several decades ago and have been studied extensively in an abstract context since, but it is only now that their significance in the finitary setting is becoming apparent.
This talk aims to be accessible to postgraduate students across all areas of mathematics.

Public lectures

Title: The power of randomness
Abstract: Far from taking us down the road of unpredictability and chaos, randomness
has the power to help us solve a fascinating range of problems. This talk will lead the audience on a thought-provoking mathematical journey from penalty shoot-outs to internet security and patterns in the primes.
Title: The usefulness of useless (mathematical) knowledge
Abstract: The talk's title is a play on the title of a famous essay by Abraham Flexner,
the founding director of the Institute for Advanced Study in Princeton. Written in 1939--and recently supplemented by a companion piece written by the Institute's current director Robbert Dijkgraaf--its central thesis is that 'the search for answers to deep questions, motivated solely by curiosity and without concern for applications, often leads not only to the greatest scientific discoveries but also to the most revolutionary technological breakthroughs'. In a world dominated by the desire for immediate impact and quick returns, this premise has (again) become acutely relevant as funding for the basic sciences is being called into question. This talk elaborates on this theme in the context of mathematical research in number theory, combinatorics and harmonic analysis, drawing on striking examples from across the centuries.

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Short Bio

Julia Wolf is a University Lecturer in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, and a Fellow of her alma mater, Clare College. After obtaining a PhD in pure mathematics under the supervision of Fields medalist Timothy Gowers, she held a sequence of postdoctoral appointments in the United States between 2007 and 2010. From 2010 to 2013, she was a Hadamard Associate Professor at Ecole Polytechnique in Paris, and from 2013 until her return to Cambridge in 2018 a Heilbronn Reader at the University of Bristol, where she also served as the Associate Chair of the Heilbronn Institute for Mathematical Research for three years. In 2016 Julia received the Anne Bennett Prize of the London Mathematical Society in recognition of her "contributions to additive number theory, combinatorics and harmonic analysis, and to the mathematical community".

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This page was last updated 19th March 2020.