| October 16, 2019 | Marek Filakovský | Embeddability of simplicial complexes is undecidable |
| October 23, 2019 | Francesca Balestrieri | Uniformity results for Brauer groups of Kummer varieties and applications to rational points |
| October 30, 2019 | Tal Horesh | Equidistribution Properties of Primitive Vectors |
| November 6, 2019 | Alec Shute | Campana points and square-full numbers |
| November 13, 2019 | Florian Wilsch | Integral points of bounded height via universal torsors |
| November 20, 2019 | Dante Bonolis | Pólya-Vinogradov inequality: a modern tragedy |
| November 27, 2019 | Nick Rome | Fibrations with few rational points |
| December 04, 2019 | Tim Browning, Nick Rome | A question of Wooley: progress report and a call for help |
| December 11, 2019 | Tim Browning | The geometric sieve for affine space |
| December 18, 2019 | Maria Anna Sisak | What the Hecke operators |
| January 08, 2020 | Nils Gubela | Wuthering heights: counting rational points on a toric surface |
| January 15, 2020 | Julian Lyczak | On the study of integral points in a family |
| January 22, 2020 | Julian Lyczak | Schmidt 1: interpretation |
| January 29, 2020 | Tal Horesh | Schmidt 2: background |
| February 05, 2020 | Florian Wilsch | Intermezzo: heights and line bundles |
| February 12, 2020 | Tal Horesh & Alec Shute | Schmidt 3: proof of asymptotics |
| February 19, 2020 | Tal Horesh & Alec Shute | Schmidt 4: finishing up (i) |
| February 26, 2020 | Alec Shute | Schmidt 5: finishing up (ii) |
| March 04, 2020 | Damaris Schindler | Manin-Campana for toric varieties |
| March 11, 2020 | Francesca Balestrieri | Poonen-Slavov and random hyperplane sections |
| March 18, 2020 | Dante Bonolis | The power sieve and character sums d’après Munshi |
| March 25, 2020 | Julian Lyczak | Erdös-Strauss cubic surface d’après Bright and Loughran |
| April 01, 2020 | Zhizhong Huang | Arithmetic purity and the geometric sieve |
| April 08, 2020 | Kevin Destagnol | Symmetric products and Manin’s conjecture |
| April 15, 2020 | Adelina Manzateanu | Failures of the Hasse norm theorem in characteristic p |
| April 22, 2020 | Nick Rome | On a paper of Bombieri and Bourgain |
| April 29, 2020 | Alec Shute | Strong approximation and Markoff triples |
| May 06, 2020 | Dante Bonolis | Expanders and sieves |
| May 13, 2020 | Francesca Balestrieri | Generalised obstructions due to Corwin and Schlank |
| May 20, 2020 | Jennifer Park | Average ranks of elliptic curves à la Brumner |
| May 27, 2020 | Carlo Pagano | Random Pell equations |
| June 03, 2020 | Efthymios Sofos | TBA |
| June 10, 2020 | All | Research Snapshots (i) |
| June 17, 2020 | All | Research Snapshots (ii) |
| June 24, 2020 | Vinay Kumaraswamy | A paper of Sarnak and Wong |
| July 08, 2020 | Nick Rome | Stacky failures of the Hasse principle |