Upcoming Talks

The seminar will meet at 4:30 on Monday in 2-131 unless otherwise noted.

Click here to add this seminar to your google calendar. If you use a different calendar program, the ics file for this seminar is here:
http://math.mit.edu/topology/topology_seminar.ics

• • Mar 022026

  Daniil Rudenko (University of Chicago)

  $\begingroup $

  Multiple polylogarithms and algebraic K-theory of fields

  I will explain a connection between multiple polylogarithms and the $\mathbb{E}_{\infty}$-algebra $\mathrm{BGL}$. This connection leads to new results in Goncharov's program, including the Universality Conjecture for number fields, and to new computations of K-groups of fields. My main goal is to explain how polylogarithms arise naturally in purely topological questions.

  $\endgroup$
• • Mar 162026

  Sonja Farr (University of Nevada, Reno)

• • Mar 302026

  Adela Zhang (University of Copenhagen)

• • Apr 062026

  Florian Riedel (University of Copenhagen)

• • Apr 132026

  Alexander Petrov (MIT)

  $\begingroup $

  Galois action on higher etale homotopy groups

  Given a complex algebraic variety, the profinite completion of its homotopy type can be recovered in purely algebraic terms as its etale homotopy type. In particular, if the variety was defined over a subfield F of complex numbers, the absolute Galois group of F naturally acts on this profinite completion. The Galois action on the fundamental group has many shared properties with the action on cohomology, in particular one expects (and in some case can) to associate a motive to the appropriately defined pro-algebraic completion of the fundamental group. On the other hand, the Galois action on higher etale homotopy groups turns out to be inconsistent with them arising from a motive: we will see that for some varieties over $\mathbb{Q}$ the (dual of) second etale homotopy group contains a finite-dimensional subrepresentaiton of the Galois group that cannot come from cohomology of an algebraic variety. This phenomenon arises from the difference between the cohomology of a discrete group and that of its pro-finite completion.

  $\endgroup$
• • Apr 272026

  Natalia Pacheco-Tallaj (MIT)

• • May 042026

  Christian Kremer (MPIM)

Email Jeremy Hahn for inquiries about the seminar.

The mailing list for this seminar is the MIT topology google group.
Email Mike Hopkins if you want to join the list.