The Erdős Center organised the Automorphic forms conference from 5 - 9 September, 2022. This 5 day conference included 21 invited talks and 15 contributed talks by leading researchers in the theory of automorphic forms from various universities across the world.
The first day of the conference opened with talks by Valentin Blomer, Ian Petrow, Jesse Thorner, Kathrin Bringmann and Nicole Raulf who presented results on the analytic theory of automorphic forms. This included applications of trace formulas, strong subconvexity bounds for L-functions, zero density estimates, modular completions and results towards the quantum unique ergodicity (QUE) conjecture. The first half of the second day boasted leading researchers from the more algebro-geometric theory of the study of automorphic forms, who presented results on p-adic Langlands program. The speakers included Kiran Kedlaya, Pierre Colmez and Benjamin Schraen. The post-lunch talks were given by Min Lee, who spoke about extending Venkatesh’s converse theorem, while Abhishek Saha talked about QUE for Saito–Kurokawa lifts. The next two days had a great mix of speakers who presented many stunning results on the analytic side of the study of automorphic forms, from QUE in level aspect, spectral reciprocity, sup-norm problem, trace formulas and moments of L-functions, to the more representation theoretic side including braiding and moments of L-functions, and Weyl group calculations. The speakers included Jasmin Matz, Raphael Steiner, Peter Humphries, Adrian Diaconu, Vicenţiu Paşol, Alexandru Popa and Djordje Milićević. The last day was opened by Paul Nelson who presented his recent groundbreaking results on subconvexity bounds for GL(n). Matthew Young continued by presenting a sharp large sieve inequality for certain families of automorphic forms. Farrell Brumley presented his work on the mixing conjecture of Michel and Venkatesh. Finally, Jack Buttcane presented his results on GL(n) Bessel functions.
The conference also had 15 contributed talks by various young and upcoming researchers, some of whom are arguably, already the leading researchers in their research areas.
Apart from various mathematical discussions, a wine and cheese party was organised on Monday evening, while some participants organised an informal get-together on the Margit Island after the talks on Friday. A lavish conference dinner was organised at the Trofea Grill on Thursday. It was a great combination of a relaxed environment, good food and great company!
This conference was an amazing opportunity to meet various leading researchers in-person after the pandemic. Personally, this was a very fulfilling experience since I was able to not just socialise, but also discuss mathematics in-person with many colleagues whom I had not met in the last couple of years. Coming from an analytic background, it is rare to interact with people from other areas. This conference exposed me to the leading research from the algebro-geometric perspective and helped me get a more rounded perspective of the state of current research. I am sure everyone had something to take back from this event. Undoubtedly, this conference was a great success, and I hope to be a part of many more such events.