Weekly Bulletin

Large language models like ChatGPT can do all sorts of things – including writing correct computer code. But how good are they at mathematics? Do mathematicians need to start worrying that they will be soon out of a job? More realistically, will we get to the stage where modern computer tools such as large language models and interactive theorem provers will be able to help working mathematicians to do their research? I'll give an overview of where we are and speculate about where we're going.

More information: https://math.ethz.ch/news-and-events/events/lecture-series/paul-bernays-lectures/bernays-2023.htmlcall_made

I will give a live demo of how to use the Lean interactive theorem prover, and discuss uses, and potential future uses, of such tools in teaching, research, and communication of mathematics.

More information: https://math.ethz.ch/news-and-events/events/lecture-series/paul-bernays-lectures/bernays-2023.htmlcall_made

Over last decade, various variant of stable maps modular space has been studied in connection to gauged linear sigma model. In this talk, we first propose the notion R-map to conceptualize these new modular space. The bulk of talk is to compactify these (open) moduli space by logarithmic R-map which carry two virtual fundamental cycles. Applications will be discussed. This is joint work with Qile Chen and Felix Janda.

In December 2020 Peter Scholze raised the question of whether a certain technical result in the Clausen-​Scholze theory of condensed mathematics could be formally verified in an interactive theorem prover. Nineteen months later a team led by Johan Commelin and Adam Topaz showed that the answer was "yes". I'll give a background to the theory of condensed mathematics and will then explain what the question was, what it reduced to, and how it was solved by a diverse team of people collaborating effectively online in what is essentially a new way. I will also explain the doors which have been opened because of this work.

More information: https://math.ethz.ch/news-and-events/events/lecture-series/paul-bernays-lectures/bernays-2023.htmlcall_made