## Rational points on quartic del Pezzo surfaces with a conic bundle structure

There are three possibilities for the quotient of the Brauer group of X modulo constants when X is a del Pezzo surface of degree four over the rational numbers . In this talk we will explain how often each of them occurs when X ranges across a family of quartic del Pezzo surfaces equipped with a conic bundle structure. We will also give an explicit description of the generators of this quotient which allows us to calculate the frequency of such surfaces violating the Hasse principle. This talk is based on a joint work in progress with Cecília Salgado.

## An introduction to quantum computing and quantum error correction (with a connection to Howe duality)

Recently, Gurevitch and Howe have associated a notion of "rank" to representations of the symplectic group, and showed that "highest rank" representations satisfy a form of Howe duality over finite fields (c.f. talk on the 20th). Montealegre-Mora and me then realized that the rank-deficient reps occurring in this context can be characterized in terms of certain quantum error correcting codes. The purpose of this talk is to explain the background of this development, i.e. why physicists care about these objects in the first place.

## Homotopy versus Isotopy: Spheres with Duals in 4-Manifolds, II

This will be an experimental “Jazz session” where both of us will be explaining our recent results together. We’ll also be encouraging audience participation and are aiming not only at 4-manifolds experts.

## Homotopy versus Isotopy: Spheres with Duals in 4-Manifolds, I

This will be an experimental “Jazz session” where both of us will be explaining our recent results together. We’ll also be encouraging audience participation and are aiming not only at 4-manifolds experts.

## "Pentagramma Mirificum". Hirzebruch lecture by Sergey Fomin on Friday, November 8, University Club Bonn

**Pentagramma Mirificum** (the miraculous pentagram) is a beautiful geometric construction studied by Napier and Gauss. Its algebraic description yields the simplest instance of cluster transformations, a remarkable family of recurrences which arise in diverse mathematical contexts, from representation theory and enumerative combinatorics to theoretical physics and classical geometry (Euclidean, spherical, or hyperbolic).

## Spaces, Categories, and the Cobar Construction

In topology, there are two ways to think about fiber bundles on connected spaces. Generally speaking, parallel transport along loops starting and ending at a basepoint gives rise to a map of groups from the loop space (i.e., the space of loops) to the group of automorphisms of the fiber. This map determines, and is determined by, the bundle. A bundle also determines, and is determined by, a map of spaces from its base to the classifying space of the automorphisms of its fibre. Thinking of fiber bundles in two ways establishes a duality between connected spaces and groups.

## The Hodge and de Rham Chern characters of holomorphic connections, II

Joint with Cheyne Glass, Micah Miller, and Thomas Tradler.

## The Hodge and de Rham Chern characters of holomorphic connections, I

Joint with Cheyne Glass, Micah Miller, and Thomas Tradler.

## tba

## Persistent homology (from a mathematical point of view)

The goal of the talk is to present the basics of persistent homology which is one of the primary tools in applied algebraic topology and topological data analysis.

We hope to explain the mathematical ideas behind it, some of its current challenges and relations to sheaf theory.

## Fibre surfaces, knots, and elastic strings

## tba

## On a mean value result for a product of L-functions

The asymptotic behaviour of moments of L-functions is of special interest to number theorists and there

are conjectures that predict the shape of the moments for families of L-functions of a given symmetry type.

However, only some results for the first few moments are known. In this talk we will consider the asymptotic

behaviour of the first moment of the product of a Hecke L-function and a symmetric square L-function

in the weight aspect. This is joint work with O. Balkanova, G. Bhowmik, D. Frolenkov.

## Higher structures in rational homotopy theory, II

## Higher structures in rational homotopy theory, I

## From almost purity to functional analysis

Faltings' almost purity theorem asserts that, in p-adic geometry, things become simpler when passing to certain highly ramified, largely non-geometric, coverings. The coverings in question are somewhat akin to covering an interval by a Cantor set. I will show how embracing this idea has led us (with Dustin Clausen) to recast the basic notions of topology, leading to a better setup in which to do algebra with topological groups.

## Perturbing an isoradial triangulation

The theory of random Delaunay triangulations of the plane has been proposed by

David-Eynard and others as a discrete model for 2-dimensional quantum gravity: In this model

the role of a continuous metric is played by a Delaunay triangulation while flat metrics

correspond to isoradial triangulations (on which one can define a theory of discrete analyticity).

Like the continuous case, the partition function for this discrete theory is given by a suitably

normalized determinant of a Beltrami-Laplace operator which varies with the choice of

## "surprise"

## Algebraic geometry of the Lagrangian correspondence of Gaiotto

## A simplicial and categorical background for Hopf algebras in number theory and physics

We will discuss how simplicial and categorical structures lead to Hopf algebras.

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