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Vorträge 2022

18.01.2023 | 16:30
01.02.2023 | 16:30

Milena Hering (Edingburgh): Embedding of Algebraic Varieties and Toric Vector bundles

Algebraic varieties are geometric objects that can be described as the zero locus of polynomial equations. While the relationship between geometry and algebra is fundamental to algebraic geometry, it still remains quite mysterious. I will explain some aspects that are known about it, as well as some open questions.  And how toric vector bundles enter the equation.

Ort: Seminarraum 019 Arnimallee 3 14195 Berlin

30.11.2022 | 16:30

Arend Bayer (Edingburgh): Derived Categories, Wall-crossing and Birational Geometry

Birational geometry studies maps between algebraic varieties defined by rational functions. Recently, derived categories, stability conditions and wall-crossing have led to an entirely new approach to fundamental open questions in birational geometry. I will survey these developments, with an emphasis on Hyperkaehler varieties and cubic fourfolds.

Ort: Seminarraum 019 Arnimallee 3 14195 Berlin

23.11.2022 | 16:30

Ana Djurdjevac (FU-Berlin Antrittsvorlesung): Randomness and PDEs: Analysis, Numerics and Applications

We will first consider interacting particle systems that provide powerful models that are useful in many application areas such as sociology (agents), molecular dynamics (proteins) etc. The first model that we will define is a non-linear stochastic PDE that provides a faithful representation of the evolution of the empirical density of a given particle system. This model has a direct applications in the opinion dynamics that will be discussed. Furthermore, we will explain difficulties in numerical approximations of these problems. Instead of considering many particles, next we will consider just one Brownian particle, but which is now evolving on a random domain. Using the rough path analysis, we will investigate different scaling regimes of this system. As a natural question in this setting is how to present a Gaussian random fields on a sphere. One way to do this is using the so-called spherical harmonics. We will discuss the advantages of this approach and challenges in its generalizations to an arbitrary manifold.

Ort: Seminarraum 019 Arnimallee 3 14195 Berlin

09.11.2022 | 16:30

Imre Bárány (Rényi Institute, Budapest): Cells in the box and a hyperplane

It is well known that a line can intersect at most 2 n −1 cells of the  n × n chessboard. What happens in higher dimensions: how many cells of the  d -dimensional [0, n ]^ d box can a hyperplane intersect? We answer this question asymptotically. We also prove the integer analogue of the following fact. If  K,L are convex bodies in  R ^d and  K ⊂ L , then the surface area  K is smaller than that of  L . This is joint work with Péter Frankl.

Ort: Chemistry building Arnimallee 22 14195 Berlin Hörsaal A

30.05.2022 | 16:00 s.t.

János Pach (Rényi Institute, Budapest): Facets of Simplicity

We discuss some notoriously hard combinatorial problems for large classes of graphs and hypergraphs arising in geometric, algebraic, and practical applications. These structures are of bounded complexity: they can be embedded in a bounded-dimensional space, or have small VC-dimension, or a short algebraic description. What are the advantages of low complexity? I will suggest a few possible answers to this question, and illustrate them with classical examples.

Ort: Chemistry building Arnimallee 22 14195 Berlin Hörsaal A

30.05.2022 | 14:15