20.11.2019 um 17:15 Uhr in 69/125
Dr. Liam Solus (KTH Royal Institute of Technology, Sweden, & MPI Leipzig)
Probability, Combinatorics, and Causality
Causality, the field of mathematical statistics aimed at quantifying causal relationships based on data, is rapidly growing due to its connections and applications to the modern fields of artificial intelligence and machine learning. Causal models are intuitively represented using graphs with directed edges, and consequently the modern theory of causality finds its roots in a marriage between probability and combinatorics: namely, the study of probabilistic graphical models. As a result, many of the data-driven approaches to learning a causal model rely fundamentally on the combinatorics of directed graphs. Recently, modern combinatorics, and its relationship with graph theory, has opened doors that allow for ideas from discrete geometry and algebra to come to bear on this problem of "causal model discovery". In this talk, we will take a tour through these new developments beginning at their roots: we will start with a discussion of probabilistic graphical models and their refinement to causal models, we will see some connections to discrete geometry, and then we will analyze the resulting data-driven learning algorithms for addressing the problem of causal model discovery. Along the way, we will stop and see some resulting combinatorial problems and avenues for future work.
27.11.2019 um 17:15 Uhr in 69/125
Prof. Dr. Max Horn (Universität Siegen)
On the Construction and Classification of ‘Small’ Groups
In this talk, we will review how each finite group can be disassembled into a unique set of "simple" groups, similar to the unique prime factorization of natural numbers. This raises various questions; for example: which simple pieces are there? And: in which ways can one glue these pieces together to form new finite groups? The main focus of this talk will be on this last question, and we will discuss it in the context of classifying (almost) all groups of order at most 20,000.
25.11.2019 um 13:30 Uhr in Raum 69/E23
Hendrik Pasing (Hochschule Ruhr West)
19.11.2019 um 16:15 Uhr in 69/125:
Andrew Newman (TU Berlin)
Enumerating simplicial complexes up to homotopy equivalence
The Dedekind numbers enumerate labeled simplicial complexes on n vertices and grow at a rate which is doubly exponential in n. Here we show that such a rate of growth also holds for simplicial complexes on n vertices even enumerating only up to homotopy equivalence. This is accomplished by exhibiting many possible homology groups which are realizable by simplicial complexes on n vertices. This is direction of research is motivated by surprising properties observed in homology of random complexes and the proof relies on the probabilistic method.
19.11.2019 um 17:15 Uhr in 69/125:
Mitra Koley (Chennai Mathematical Institute, India)
Hilbert-Kunz functions and Hilbert-Kunz multiplicities of Rees algebras
First we define Hilbert-Kunz functions and Hilbert-Kunz multiplicity of a local/graded ring. Then we discuss Hilbert-Kunz functions and Hilbert-Kunz multiplicities of Rees algebras. This is joint work with J.K. Verma and K. Goel.
26.11.2019 um 16:15 Uhr in 69/125:
Joseph Samuel Doolittle (FU Berlin)
26.11.2019 um 17:15 Uhr in 69/125:
Ulrich von der Ohe (Università degli Studi di Genova, Italy)
Algebraic decomposition of functions from evaluations
The task of decomposing certain functions in terms of given vector space bases is historically motivated by physics and recently finds applications in signal and image processing. Prony's work from 1795 remains central to this subject. In this talk, we discuss instances and variations of this problem, their Prony structures and relations. The talk is based on recent joint work with Stefan Kunis and Tim Römer.
28.11.2019 um 16:15 Uhr in 69/125:
Bogdan Ichim (University of Bucharest, Romania)
On a class of Gorenstein polytopes
We present a new class of Gorenstein polytopes, which was found by experimental computations with Normaliz.