Workshop

Diophantine equations, combinatorics, analysis in number theory: emerging researchers

19 Jun 2025 - 20 Jun 2025

ICMS, Bayes Centre, Edinburgh

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Scientific Organisers

Kirsti Biggs, Uppsala University

Akshat Mudgal, University of Warwick

Javier Pliego, University of Genova

About Workshop

This two-day workshop for Early Career Researchers was an opportunity for young researchers at PhD and postdoctoral level working in the areas of number theory, additive combinatorics and harmonic analysis to present their work and to meet other early career researchers in these fields. The participants were able to network with each other, build new collaborations and share experiences, while also being in a relatively informal setting. The event consisted of various research/survey talks along with some problem sessions.

This workshop was a satellite conference to the Diophantine equations, combinatorics, analysis in number theory (DECANT) workshop held at ICMS, 23-27 June 2025.

Programme

THURSDAY 19 JUNE

09.00-09.20

Registration and refreshments

09.20-09.30

Welcome and housekeeping

09.30-10.20

Lasse Grimmelt, University of Oxford

Averages of $\mathrm{SL}_2(\mathbb{R})$ Automorphic Kernel and arithmetic applications

Abstract

10.25-11.15

Jonathan Chapman, University of Warwick

Counting commuting integer matrices

Abstract

11.15-11.40

Refreshments

11.40-12.30

Rajula Srivastava, University of Edinburgh

Counting, Curvature and Convex Duality

Abstract

12.30-14.00

Lunch

14.00-14.50

Nick Rome, TU Graz

Towards a conjecture of Wooley

Abstract

14.55-15.45

Mengdi Wang, École Polytechnique Fédérale de Lausanne

On Szemerédi 's theorem in sparse sets of primes

Abstract

15.45-16.15

Refreshments

16.15-16.40

Hrit Roy, University of Edinburgh

An extension of the Bourgain--Demeter--Guth decoupling theorem

Abstract

16.45-17.10

Philip Holdridge, University of Warwick

Random Diophantine Equations with Prime Variables

Abstract

17.10-18.00

Welcome reception hosted at ICMS

FRIDAY 20 JUNE

10.00-10.25

Firdavs Rakhmonov, University of St Andrews

Lp averages of the Fourier transform in finite fields: orthogonal projections, incidence geometry, and the restriction problem

Abstract

10.30-10.55

Kate Thomas, University of Oxford

Sums of Niven numbers via the circle method

Abstract

11.00-11.30

Refreshments

11.30-11.55

Fred Tyrell, University of Bristol

Bounded Exponential Sums with Multiplicative Coefficients

Abstract

12.00-12.25

Sophie Maclean, King's College London

Energy increment methods in Szemerédi-type theorems

Abstract

12.30-14.00

Lunch

14.00-14.25

James Cumberbatch, Purdue University

Smooth Integers with Restricted Digits

Abstract

14.30-14.55

Daniel Flores, Purdue University

$K$-multimagic squares and magic squares of $k$th powers via the circle method

Abstract

15.00-15.25

Rena Chu, Duke University

Short character sums evaluated at homogeneous polynomials

Abstract

15.30-16.00

Refreshments

16.00-16.25

Edna Jones, Tulane University

On the local-global conjecture for 3-dimensional Kleinian sphere packings

Abstract

16.30-16.55

Kiseok Yeon, University of California, Davis

The global solubility for homogeneous polynomials with random coefficients over thin sets

Abstract

Resources

Programme

DECANT webpage

Sponsors and Funders