## "A world from a sheet of paper". Hirzebruch lecture by Tadashi Tokieda on Wednesday, October 31, University Club Bonn

Starting from just a sheet of paper, by folding, stacking, crumpling, tearing, we will explore a rich variety of phenomena, from magic tricks and geometry to elasticity and the traditional Japanese art of origami. Much of the lecture consists of actual table-top demos, which you can try later with friends and family.

Professor **Tadashi Tokieda** is a professor of mathematics at Stanford University. He grew up as a painter in Japan, became a classical philologist in France, and has been an applied mathematician in the US and Europe. He is active in outreach in the developing world, especially via the African Institute for Mathematical Sciences.

## Symmetric matrices associated with oriented link diagrams.

Motivated by metaplectic invariants of Goldschmidt–Jones,

generalizing the cyclotomic invariants of Kobayashi–Murakami–Murakami,

I will explain a construction which associates to each oriented link

diagram a symmetric matrix with elements being quadratic polynomials

in one indeterminate with integer coefficients. Based on a slightly

modified S-equivalence of Trotter and Murasugi in the space of

symmetric matrices, the construction gives rise to an invariant

of oriented links. In particular, the signature of the matrix is

conjecturally related to the Tristram–Levine signature function.

## Warps and grids for double and triple vector bundles

## What is an Einstein metric?

## What is a Berkovich space?

## What is a Teichmüller polynomial?

## "What is...?" seminar

## Belyi's theorem/dessin d'enfant

## Presentation of number theory aspects of Ihara's paper

## Dinner at Gasthaus "zum Stiefel"

We have arranged a dinner for Thursday evening at 7 pm in the Kaminzimmer at "Im Stiefel".

The price will be 40 EUR per person.

Further information will follow.

## Propagators of the wave equation on low regularity spacetimes

In this talk, I will define the classical and non-classical of the wave equation.

Also, I will give some motivations about why low regularity scenarios are interesting.

Finally, I will focus on the classical ones and its relationship with Quantum Field Theory in spacetimes with limited regularity.

## 10-minute talks

## tba

## tba

## The twisted dynamical zeta functions of Ruelle and Selberg of locally symmetric spaces of rank 1 and applications

The twisted zeta functions of Ruelle and Selberg are dynamical zeta functions, which are represented by Euler-type products over the prime closed geodesics on a compact hyperbolic manifold. For locally symmetric manifolds, harmonic analysis provides a powerful tool, the Selberg trace formula, that one can use to prove the meromorphic continuation of the dynamical zeta functions. These zeta functions have been long studied by Fried, Bunke and Olbrich, Müller, Pfaff, Fedosova and Pohl under certain assumptions for the representation of the fundamental group. In this talk, we will present some results concerning the dynamical zeta functions, which are twisted by arbitrary representations of the fundamental group and their connections to spectral and L

^2-invariants.## The Chevalley-Eilenberg complex of a dgLa

## Deformation functors - a modern approach

We will continue the study of deformation problems by getting to a modern defintion of a deformation functor. These are functors from local differential graded Artinian rings to simplicial sets. The Maurer-Cartan equation provides a such a deformation functor out of a dgLa. The talk includes some discussion on the necessary tools on simplicial sets

## Deformation problems

In this talk we will continue the introduction to deformation problems by taking a different point of view on them:

We will discuss local artinian rings, and how some natural deformation problems can be posed as functors from local artinian rings to sets, or better, to simplicial sets. We will also see what kind of properties such functors satisfy. The talk will include a reminder on the needed definitions and not assume previous knowledge of simplicial sets.

## Guided tour: Castle of Bruehl

Futher information will follow soon.

## Bootstrapping the Kashiwara crystal

tba.

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