Category: Math


Schulvortrag @ BRG Viktring

By behackl,

Es war mir eine besondere Freude, heute in meiner ehemaligen Schule, dem BRG Viktring, einen Vortrag aus Mathematik vor den 7. Klassen halten zu dürfen.

Die Vortragsfolien sind hier zu finden.

Summer school: Techniques in Random Discrete Structures

By behackl,

I’m currently in Athens at the summer school “Techniques in Random Discrete Structures”, where I am responsible for the exercise sessions.

An overview over which exercises have already been dealt with, can be found here.

The current versions of the three exercise sheets are available here:

  • Exercises to Phase transitions in random structures (Amin Coja-Oghlan, Frankfurt)
  • Exercises to Gibbs measures in statistical physics and combinatorics (Will Perkins, Birmingham)
  • Exercises to Analytic Combinatorics (Stephan Wagner, Stellenbosch)

Mathematik-Seminar der Hans-Riegel-Stiftung

By behackl,

Today I held an invited workshop on combinatorics and the symbolic method at the Mathematical Institute of Bonn University (Bonn, Germany) for alumni who received a “Hans-Riegel-Fachpreis“, a flyer for this event can be found here.  The (german) slides and corresponding exercises can be found here (lecture slides) and here (exercises).

This was a great opportunity, and I enjoyed holding the workshop a lot. 🙂

 

uni_bonn

The Register Function and Reductions of Binary Trees and Lattice Paths — AofA’16

By behackl,

On July 8 I gave a contributed talk on “The Register Function and Reductions of Binary Trees and Lattice Paths” at this years 27th edition of the International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA’16), which took place in Kraków, Poland.

My Slides can be found here.

IMG_20160708_122453

Submission to Insight2016

By behackl,

I made a submission to Insight2016, which is an exhibition dedicated to the visualization of (scientific) data, taking place in Lakeside Science & Technology Park, Lakeside B11, 9020 Klagenfurt am Wörthersee, Austria, in April and May, 2016.

The picture I submitted is called Climbing Densities, and looks like this:

climbing_densities

Essentially, these are probability densities of a sequence of random variables I’m currently researching. These random variables model some parameter of a combinatorial object for fixed size. The more intensely colored densities represent larger object, so what can be observed is some sort of periodic process, which is also visualized in this gif (1 density per frame):

climbing-densities

More information on these combinatorial object will appear in an upcoming paper (joint work with Helmut Prodinger).

  Category: Math
  Tags:
  Comments: None

Master thesis submitted

By behackl,

Approximately a year after starting this project, I have finally finished and submitted my master thesis titled “Asymptotic Analysis of Lattice Paths and Related Structures” yesterday! Update: the thesis can be found here. 🙂

The thesis was supervised by Clemens Heuberger, and here are the English and the German version of the abstract:

Abstract

While classical combinatorics is mostly “just” about enumerating discrete objects, the field of Analytic Combinatorics is about the precise analysis of the corresponding asymptotic behavior. A broad spectrum of mathematical disciplines is involved in such an “asymptotic analysis”—most prominently, results from classical combinatorics, complex analysis, and probability theory are used.

The central (discrete) objects of study within this thesis are lattice paths and trees. After giving an introduction to some central ideas and methods from Analytic Combinatorics, we discuss various special classes of lattice paths and trees. The analyses of these objects are powered by several different ideas ranging from simple consequences of the fundamental analytic framework up to (new) approaches that are specifically tailored for the given problem structure. The results of these novel approaches have also been submitted for publication in an international journal.

Zusammenfassung

Während sich die klassische Kombinatorik normalerweise “nur” mit dem Abzählen diskreter Objekte beschäftigt, interessieren wir uns im Rahmen der analytischen Kombinatorik für präzise Analysen des entsprechenden asymptotischen Verhaltens. Für eine solche asymptotische Analyse werden Resultate aus einem breiten Spektrum von mathematischen Disziplinen, wie beispielsweise der klassischen Kombinatorik, der Funktionentheorie, und auch der Wahrscheinlichkeitstheorie verwendet.

Innerhalb dieser Masterarbeit spielen Gitterpunktpfade sowie Bäume eine zentrale Rolle. Nachdem wir zunächst einige fundamentale Ideen und Methoden aus der analytischen Kombinatorik vorstellen, widmen wir uns danach der asymptotischen Analyse von diversen speziellen Klassen von Gitterpunktpfaden und Bäumen. Die für diese Analysen verwendeten Ansätze reichen hierbei von einfachen Konsequenzen des zugrundeliegenden analytischen Grundgerüsts bis hin zu (neuen) Ansätzen, die speziell auf den jeweiligen Problemtyp zugeschnitten sind. Die daraus entstandenen neuen Ergebnisse wurden auch bei einem internationalen Journal zur Publikation eingereicht.


As soon as my thesis is graded, I will put a direct link to it from the list of my publications.

  Category: Math
  Tags:
  Comments: 2