# Special Year Seminar

## Special Year Seminar

I will briefly review the concept of completely monotone functions, and then describe recent observations of how they appear in Feynman integrals and scattering amplitudes.

This talk is based on reference https://arxiv.org/pdf/2407.05755.

## Special Year Seminar I

Lecture Series Framework: * A unifying framework for
F1-geometry, tropical schemes and matroid theory. In this series of
3 lectures, I will present a recent approach towards F1-geometry
and its links to tropical geometry, matroid theory,
Lorentzian*...

## Special Year Seminar II

The second lecture features the nuts and bolts of the invariants from first lecture, which we call foundations. We explain the structure theorem for foundations of ternary matroids, which is rooted in Tutte's homotopy theorem. We show how this...

## Special Year Seminar II

The theme of the third lecture is the notion of points over F1, the field with one element. Several heuristic computations led to certain expectations on the set of F1-points: for example the Euler characteristic of a smooth projective complex...

## Special Year Seminar

Chapter 14 of the classic text "Computational Complexity" by Arora and Barak is titled "Circuit lower bounds: complexity theory's Waterloo". I will discuss the lower bound problem in the context of algebraic complexity where there are barriers...

## Special Year Seminar

A class of tensors, called "concise (m,m,m)-tensors of minimal border rank", play an important role in proving upper bounds for the complexity of matrix multiplication. For that reason Problem 15.2 of "Algebraic Complexity Theory" by Bürgisser...

## Special Year Seminar II

A valuation is a finitely additive measure on the class of all convex compact subsets of $R^n$. Over the past two decades, a number of structures has been discovered on the space of translation invariant smooth valuations. Recently, these findings...