## Upcoming conferences & activities

## Workshop on 4-manifolds, September 16 - 20, 2019

**Workshop on 4-manifolds, September 16 - 20, 2019**

#### Organizers

Jeffrey Meier (University of Georgia)

Arunima Ray (MPIM Bonn)

#### Confirmed Speakers:

Robert Gompf (UT Austin)

Sergei Gukov (Caltech)

András Juhász (Oxford)

Du Pei (Caltech)

Lisa Piccirillo (UT Austin)

Juanita Pinzón-Caicedo (North Carolina State University/MPIM Bonn)

Mark Powell (Durham)

Rob Schneiderman (CUNY)

Hannah Schwartz (Bryn Mawr/MPIM Bonn)

Laura Starkston (UC Davis)

András Stipsicz (Alfred Renyi)

Alex Zupan (University of Nebraska Lincoln)

## Upcoming Talks

Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## Recent developments in Quantum Topology -- Cancelled --

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

## "What is...?" seminar

## Homotopy versus Isotopy: Spheres in 5-manifolds, I

## Homotopy versus Isotopy: Spheres in 5-manifolds, II

## Rationality of Fano 3-folds over nonclosed fields

The rationality problem for smooth Fano threefolds over algebraically closed fields is basically solved.

In this talk I will discuss rationality of forms of these Fanos over nonclosed fields of characteristic 0.

I will concentrate on the case where the Picard number equals 1.

The talk is based on joint work with Alexander Kuznetsov (in progress).

## 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.

## Chebyshev’s bias for products of k primes and Greg Martin’s conjecture

For any $k\geq 1$, we study the distribution of the difference between the number of integers $n\leq x$ with $\omega(n)=k$ or $\Omega(n)=k$ in two different arithmetic progressions, where $\omega(n)$ is the number of distinct prime factors of $n$ and $\Omega(n)$ is the number of prime factors of $n$ counted with multiplicity . Under some reasonable assumptions, we show that, if $k$ is odd, the integers with $\Omega(n)=k$ have preference for quadratic non-residue classes; and if $k$ is even, such integers have preference for quadratic residue classes.

## Puzzles about trisections of 4-manifolds

A trisection of a smooth 4-manifold is a very natural kind of decomposition into three elementary pieces which I will describe. Trisections are a natural 4-dimensional analogue of Heegaard splittings of 3-manifolds, a class of decompositions into two pieces that have yielded tremendous insight into 3-dimensional topology, so the philosophy is that trisections should give a way to port 3-dimensional techniques, questions and results to dimension four.

## 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.

## tba

## Mathematical events in Bonn

##### Bonn Mathematics Calendar

All mathematical events in Bonn are listed in the Bonn Mathematics Calendar. For directions see the map.

##### University Calendar

All lectures and courses at Bonn University can be found in the university calendar.

## Recurring seminars, series and courses

Detailed list of recurring seminars, series of talks, and courses or lectures comprising multiple talks. For an overview see also the calendar.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## IMPRS Minicourse

## Representation theory learning seminar

## Extra talk

## Seminar on Algebra, Geometry and Physics

## Seminar Algebraic Geometry (SAG)

## Higher Differential Geometry Seminar

## Archived Events

To narrow the list of events displayed please select year and event type or fill the search fields, then press *Apply*.

## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## "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).

## 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

## Workshop on 4-manifolds, September 16 - 20, 2019

**Workshop on 4-manifolds, September 16 - 20, 2019**

#### Organizers

Jeffrey Meier (University of Georgia)

Arunima Ray (MPIM Bonn)

#### Confirmed Speakers:

Robert Gompf (UT Austin)

Sergei Gukov (Caltech)

András Juhász (Oxford)

Du Pei (Caltech)

Lisa Piccirillo (UT Austin)

Juanita Pinzón-Caicedo (North Carolina State University/MPIM Bonn)

Mark Powell (Durham)

Rob Schneiderman (CUNY)

Hannah Schwartz (Bryn Mawr/MPIM Bonn)

Laura Starkston (UC Davis)

András Stipsicz (Alfred Renyi)

Alex Zupan (University of Nebraska Lincoln)

## tba

## 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.

## Puzzles about trisections of 4-manifolds

A trisection of a smooth 4-manifold is a very natural kind of decomposition into three elementary pieces which I will describe. Trisections are a natural 4-dimensional analogue of Heegaard splittings of 3-manifolds, a class of decompositions into two pieces that have yielded tremendous insight into 3-dimensional topology, so the philosophy is that trisections should give a way to port 3-dimensional techniques, questions and results to dimension four.

## Chebyshev’s bias for products of k primes and Greg Martin’s conjecture

For any $k\geq 1$, we study the distribution of the difference between the number of integers $n\leq x$ with $\omega(n)=k$ or $\Omega(n)=k$ in two different arithmetic progressions, where $\omega(n)$ is the number of distinct prime factors of $n$ and $\Omega(n)$ is the number of prime factors of $n$ counted with multiplicity . Under some reasonable assumptions, we show that, if $k$ is odd, the integers with $\Omega(n)=k$ have preference for quadratic non-residue classes; and if $k$ is even, such integers have preference for quadratic residue classes.

## 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.

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