At the next Colloquium, on October 13 at 4:30 pm, Sergey O. Gorchinsky (Doctor of Physical and Mathematical Sciences; Deputy Director for Research, Head of the Department of Algebra and Leading Researcher of the Mathematical Institute of RAS) will give a talk "On the work of Peter Scholze". The seminar will be held in room 417 of the IM SB RAS.
Since ancient times, people have wanted to understand how the solutions of systems of polynomial equations in integers work. Much later it was discovered that one of the most important clues to this problem is the study of representations of the Galois groups of various fields. The properties of representations of Galois groups are related to a number of fundamental questions of modern
arithmetic geometry: Frobenius weight conjectures, modularity, Sato-Tate type conjectures, Langlands correspondence. Recently, impressive progress has been made in all these directions, thanks to the theory of perfectoids created by Peter Scholze and its further development. This theory allows, in particular, to connect the geometric worlds in zero and positive characteristics.
We will try to tell about it in a popular way, for a wide audience. However, students will be welcome to know what a Galois group is and what p-adic numbers are.
