Institute of
Discrete Mathematics and Geometry



Arbeitsgemeinschaft Diskrete Mathematik

Info: Das Seminar AGDM wird gemeinsam mit Kollegen der Universität Wien veranstaltet.

Ort: TU-Wien, Freihaus (4., Wiedner Hauptstraße 8-10), Dissertantenraum, grüner Turm (A), 8. Stock.


Aktueller Termin



Wichtig: WIR BEGINNEN SCHON UM 15:00 !!!

Zeit: Dienstags, 15.00 - 17:00h,

Datum: 25.6.2019

Zeit:15.00 - 15.50
Titel 1: "Furstenberg's transversality conjectures in the integers"
Vortragender: Florian Richter

Zeit:16.00 - 16.50
Titel 2: "The boundary monomer-dimer model and the Gaussian free field"
Vortragender: Nathanael Berestycki



Inhalt 1: In the late 1960's, Hillel Furstenberg proposed a series of conjectures in seeking to make precise the heuristic that there is no common structure between digit expansions in distinct prime bases. While his famous x2, x3 conjecture in ergodic theory remains unsolved, recent solutions to the equally momentous transversality conjectures of his, which concern the dimension of sumsets and intersections of p- and q- invariant sets, now shed new light on old problems. In this talk, I will explain how to use tools from fractal geometry and uniform distribution to establish natural analogues of Furstenberg's transversality conjectures in the integers. This talk is based on joint work with Daniel Glasscock and Joel Moreira.

Inhalt 2: We study the dimer model in which particles on the boundary are allowed to form monomers with some fixed weight z>0 called the monomer fugacity. The main question is to show conformal invariance in the scaling limit of the associated height function. We prove that on certain domains in the upper half plane the scaling limit is given by a Gaussian free field with Neumann (or free) boundary conditions on the part of the boundary containing the monomers, for arbitrary fixed fugacity z>0. The starting point of the proof is a bijection due to Giuliani, Jauslin and Lieb to a dimer configuration on a graph which is nonbipartite. Applying classical Kasteleyn theory we are led to the analysis of a random walk on a graph but where some transitions have negative rates. Nevertheless, using fine properties of an auxiliary random walk (which boil down to describing precisely the oscillations of its potential kernel) we are able to give a meaning and analyse the scaling limit of its Green function, eventually leading us to the result. This is joint work (in progress) with Marcin Lis (Vienna) and Wei Qian (Cambridge).


 

Vorträge in früheren Jahren

Übersicht: Vorträge Zeitraum 2005 - 2018


Bereits gehaltene Vorträge

Datum: 4.6.2019
Titel: "The parking function poset"
Vortragende: Jakob Steininger

Datum: 28.5.2019
Titel: "The parking function poset"
Vortragende: Matthieu Josuat-Verges (Universite de Marne-la-Vallee)

Datum: 21.5.2019
Titel: "Real zeros and the alternatingly increasing property"
Vortragende: Liam Solus (KTH Stockholm)

Datum: 14.5.2019
Titel: "Identities and periodic oscillations of divide-and-conquer recurrences splitting at half"
Vortragende: Hsien-Kuei Hwang (Academica Sinica, Taipei, Taiwan)

Datum: 30.4.2019
Titel: "Unique path partitions: motivation, classification and counting"
Vortragende: Nils Gubela

Datum: 9.4.2019
Titel: "A partial theta function Borwein conjecture"
Vortragende: Michael Schlosser (Univ. Wien)

Datum: 2.4.2019
Titel: "An analytic proof of the Borwein Conjecture"
Vortragende: Chen Wang (Univ. Wien)

Datum: 26.3.2019
Titel: "Counting cubic and 4-regular labelled planar graphs"
Vortragende: Marc Noy (Universitat Politècnica de Catalunya)

Datum: 19.3.2019
Titel: "Naruse's hook length formula and its variations (after Igor Pak, Alejandro Morales and Greta Panova)"
Vortragende: Christian Krattenthaler (Univ. Wien)

Datum: 5.3.2019
Titel: "Parabolic Cataland -- A Type-A Story and so on"
Vortragende: Henri Muehle (TU Dresden)

Datum: 22.1.2019
Titel: "Sums of Digits of Primes"
Vortragende: Michael Drmota (TU Wien)

Datum: 15.1.2019
Titel: "The Zeckendorf Sum-of-Digits Function"
Vortragende: Clemens Müllner (TU Wien)

Datum: 8.1.2019
Titel: "Promotion on oscillating and alternating tableaux and rotation of matchings and permutations"
Vortragende: Stephan Pfannerer (TU Wien)

Datum: 18.12.2018
Titel: "A bijection between permutation matrices and descending plane partitions without special parts, which respects the quadruplet of statistics considered by Behrend, Di Francesco and Zinn-Justin"
Vortragende: Markus Fulmek (Univ. Wien)

Datum: 11.12.2018
Titel: "Steep-bounce zeta map in parabolic Cataland"
Vortragende: Wenjie Fang (TU Graz)

Datum: 27.11.2018
Titel: "Mahonian-Stirling pairs of combinatorial statistics for labeled forests"
Vortragende: Svetlana Poznanovikj (Clemson University)

Datum: 20.11.2018
Titel: "Perfect $k$-colored matchings and $k+2$-gonal tilings"
Vortragende: Lukas Andritsch (Univ. Graz)

Datum: 13.11.2018
Titel: "Fishburn family and Euler--Stirling statistics"
Vortragende: Emma Yu Jin (TU Wien)

Datum: 6.11.2018
Titel: "Enumeration problems related to computational models"
Vortragende: Katarzyna Grygiel (TU Wien)

Datum: 23.10.2018
Titel: "On some elementary polynomial identites Involving q-trinomial coefficients"
Vortragende: Alexander Berkovich (University of Florida)

Datum: 16.10.2018
Titel: "Alternating sign matrices and a constant term approach"
Vortragende: Ilse Fischer (Univ. Wien)

Datum: 9.10.2018
Titel: "The Operator Formula for Monotone Triangles: A Combinatorial Approach"
Vortragende: Hans Höngesberg (Univ. Wien)