The colloquium is organized by Philip Gerlee, Magnus Goffeng and Richard Lärkäng. Feel free to contact any one of us for questions or suggestions for colloquia speakers. Even if the colloquium for the term is fully booked, suggestions for the Mathematical Sciences Seminar are always welcome.

##### Colloquia Autumn 2019

**19-08-28 in Pascal**

Elin Götmark (Chalmers/GU)

Elin Götmark (Chalmers/GU)

*Mathematics for navigation*

What is the shortest travel distance between two cities as the crow flies? How can you determine your position on the Earth by means of the sun or stars? The answer relies on spherical trigonometry. This is old mathematics that first began to develop in Hellenistic times, but most of us do not encounter it in our university courses today. This talk will be accessible to undergraduate students.

**19-09-23 in Euler**

Richard Schoen (University of California, Irvine)

Richard Schoen (University of California, Irvine)

*New perspectives on scalar curvature*

This will be a talk for a general audience explaining the dual role that the scalar curvature plays in differential geometry and in general relativity. Both subjects motivate questions about the geometric structure of spaces with scalar curvature bounded from below. We will describe some of these questions by analogy with similar questions for surfaces where the answers are largely known. In the physical case of dimension three we only have partial knowledge and many questions remain.

**19-10-21 in Euler**

Jeff Steif (Chalmers/GU)

Jeff Steif (Chalmers/GU)

*Noise Sensitivity of Boolean Functions and Critical Percolation*

I will introduce and discuss the notion of noise sensitivity for Boolean functions, which captures the idea that certain events are very sensitive to small perturbations. While a few examples will be given, the main example which we will examine from this perspective is so-called 2-dimensional critical percolation from statistical mechanics. There will also be connections to combinatorics and theoretical computer science. The mathematics behind the story includes, among other things, Fourier analysis on the hypercube, hypercontractivity and a stochastic version of the solution of the Bieberbach conjecture/theorem from geometric function theory (the so-called Schramm-Löwner evolution). Obviously, many of these topics will only be very briefly touched upon.

No background concerning percolation, Fourier analysis, hypercontractivity or geometric function theory will be assumed. [Slides]

**19-11-18 in Pascal**

Pär Kurlberg (KTH)

Pär Kurlberg (KTH)

*Repulsion in number theory and physics*

Zeros of the Riemann zeta function and eigenvalues of quantized chaotic Hamiltonians appears to have something in common. Namely, they both seem to be ruled by random matrix theory and consequently should exhibit "repulsion" in the sense that small gaps between elements are very rare. More mysteriously, while zeros of different L-functions (i.e., generalizations of the Riemann zeta function) are "mostly independent" they also exhibit subtle repulsion effects on zeros of other L-functions.

We will give a survey of the above phenomena. Time permitting we will also discuss repulsion between eigenvalues of "arithmetic Seba billiards", a certain singular perturbation of the Laplacian on the 3D torus ℝ

^{3}/ℤ^{3}. The perturbation is weak enough to allow for arithmetic features from the unperturbed system to be brought into play, yet strong enough to provably induce repulsion.**19-12-16 in Pascal**

Aila Särkkä (Chalmers/GU)

Aila Särkkä (Chalmers/GU)

*Sequential point processes - models for eye movements and sweat gland activation*