# Colloquium

The Colloquium is held on Mondays at 4pm on Zoom with meeting number 938 9042 5892.

### Fall Quarter, 2021

- October 11,
**Daniil Rudenko** (U. Chicago)

Goncharov depth conjecture and volumes of orthoschemes
**Abstract**: Goncharov conjectured that any multiple polylogarithm can be expressed via polylogarithms of depth at most half of the weight. In the first part of the talk I will explain how this conjecture fits into the general scheme of conjectures about polylogarithms. In the second part of the talk I will sketch the proof of the Goncharov conjecture. The proof is based on an explicit formula, involving a summation over trees that correspond to decompositions of a polygon into quadrangles. Surprisingly, almost the same formula gives a volume of a hyperbolic orthoscheme generalising the formula of Lobachevsky in dimension 3 to an arbitrary dimension.

- October 25,
**Laura Rider** (University of Georgia)

Examples of t-structures in Geometric Representation Theory
**Abstract**: In this talk, I’ll discuss the notion of `t-structure’. In the cases I’ll present, a t-structure is a way to relate two (a priori unrelated) abelian categories. When this happens, we hope to utilize better homological properties to gain traction on our problems. As time permits, I’ll spend some extra time on the examples of constructible sheaves, coherent sheaves, and Koszul duality.

- November 15,
**Ian Hambleton** (McMaster University)

Euler Characteristics and 4-manifolds
**Abstract**: The topology and total curvature of a Riemann surface is determined by a single integer, the Euler characteristic (Leonhard Euler, 1707-1783). In dimension four, the Euler characteristic gives an interesting invariant for finitely presented groups. The talk will survey some recent joint work with Alejandro Adem on this theme.

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