## Heilbronn Colloquium 2024: Lillian Pierce

18 Mar 2024, by Events in**Tuesday 11 June 2024** – 16:00

Department of Mathematics, Imperial College London, UK

**Venue**: Room 144, Huxley Building, 180 Queen’s Gate, South Kensington, London SW7 2AZ

The London Heilbronn Colloquia are a series of triannunal lectures by distinguished mathematicians and theoretical physicists at the forefront of current research. They are aimed at a general mathematical audience and informal interaction with the speaker.

**Organisers: **Kevin Smith (Imperial College), Samuel Johnston (Imperial College)

**A Polynomial Sieve: Beyond Separation of Variables**

### Lillian Pierce, Department of Mathematics, Duke University, USA

Many problems in number theory can be framed as questions about counting integral solutions to a Diophantine equation (say, within a certain “box”). If there are very few, or very many variables, certain well-established methods gain an advantage. But sometimes there is extra structure that can be exploited as well. For example: let f be a given polynomial with integer coefficients in n variables. How many values of f are a perfect square? A perfect cube? Or, more generally, a value of a different polynomial of interest, say g? These questions arise in a variety of specific applications, and also in the context of a general conjecture of Serre on counting points in thin sets. We will describe how sieve methods can exploit this type of structure, and explain how a new polynomial sieve method allows greater flexibility, so that the variables in the polynomials f and g can “mix.”

Joint work with Dante Bonolis.

**About the Speaker**: Lillian Pierce received a BA in Mathematics and graduated as valedictorian of Princeton University in 2002. She earned an MSc by Research at the University of Oxford as a Rhodes Scholar in 2004, and a PhD from Princeton in 2009. After postdoctoral positions at the Institute for Advanced Study and University of Oxford and a year as a Bonn Junior Fellow, Pierce took a faculty position at Duke University, where she is presently a Professor of Mathematics. Pierce’s research combines techniques of analytic number theory and harmonic analysis, with particular interests in Diophantine equations, exponential and character sums, class groups, oscillatory integrals, and singular integrals. Pierce has recently founded the journal Essential Number Theory, which aims to deepen the impact of important ideas by encouraging authors to write clear, useful expositions. Pierce’s work has been recognized by a Presidential Early Career Award for Scientists and Engineers, a Simons Fellowship, a Joan and Joseph Birman Fellowship, a Sloan Research Fellowship, a von Neumann Fellowship, and a Marie Curie Fellowship. She was an invited speaker, representing number theory and analysis, at the International Congress of Mathematicians in 2022. Her work in 2024 will be supported by a Simons Research Fellowship and Guggenheim Fellowship.

Information on past and future colloquia is available here.

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