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Events
Combinatorics Day

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

23.05.18

Combinatorics Day

This one day event features talks from researchers working in a variety of combinatorial areas, including algebraic combinatorics and geometric combinatorics. Time is also provided for participants to discuss areas of common interest and current problems, with the aim of fostering new research connections.

Program

10:00 - 11:00	Alex Fink (Queen Mary University of London) Universal Tutte characters via combinatorial coalgebras The Tutte polynomial is a favourite invariant of matroids and graphs. So when one is working in a generalisation of these settings, for example arithmetic matroids or ribbon graphs, it is a tempting question to find a counterpart of the Tutte polynomial; answers have been given in many cases. Our work unifies these answers, providing general machinery to turn a combinatorial object with "minor" operations into a coalgebra, and from that coalgebra extract the most general possible Tutte-like invariant. We build on earlier work by Krajewski, Moffatt, and Tanasa, who used Hopf algebras for this purpose. Joint with Clément Dupont and Luca Moci.
11:00 - 11:15	Coffee Break
11:15 - 12:15	Christian Stump (Technische Universität Berlin) Science fiction for Catalan and Shi arrangements Catalan and Shi arrangements for finite Weyl groups and their discrete-geometric structure have been considered in many contexts in Algebraic Combinatorics. Unfortunately, they have resisted from being generalized to more general finite reflection groups so far. I will start this talk with recalling in detail this discrete-geometric structure, and will then discuss surprising numerical observations in the module of derivations of a hyperplane arrangement that indicate that we still miss the "correct" combinatorics to study Catalan and Shi arrangements for general reflection groups. This talk can be seen as a combinatorial guidance of joint work with Torsten Hoge, Toshiyuki Mano and Gerhard Roehrle.
12:20 - 13:10	Lunch
13:10 - 13:40	Günter Ziegler (Freie Universität Berlin) New Proofs from THE BOOK Two new proofs for very old theorems, prepared for the sixth edition of "Proofs from THE BOOK" -- Fermat's Two Squares (after Heath-Brown and Spivak) -- Euler's Series (after Borwein & Borwein) [Joint Work with Martin Aigner]
13:45 - 14:15	Nils Haug (Medizinische Universität Wien) Asymptotics and scaling properties of two-dimensional lattice paths and polygons We consider the generating functions of different models of two-dimensional lattice polygons, weighted with respect to their area and perimeter. Many of them are expected to show similar asymptotic features which do not depend on the exact details of the model, such as the existence of a scaling limit, which is described by the Airy function. For rooted self-avoiding polygons, this scaling behaviour has been conjectured by Guttmann, Richard and Jensen. However, a proof of it seems to be currently out of reach. One can make progress by considering models which are analytically more tractable, such as area-weighted Dyck paths. In this talk I will show how a uniform asymptotic expression for their area-perimeter generating function can be obtained by using the method of steepest descents, generalised to the case of two coalescing saddle points. Afterwards I will explain how a new type of asymptotic behaviour can be observed by adding a perturbation to the area-perimeter generating function of Dyck paths, leading to a model which we call deformed Dyck paths.
14:20 - 15:20	Christian Haase (Freie Universität Berlin) The Kingman Coalescent as a Density on a Space of Trees Randomly pick n individuals from a population and look at their genealogy. The Kingman n-coalescent is a probabilistic model for the tree one obtains this way. It can be described by a probability density function on the space of equidistant trees with its fine fan structure, given by the Bergman fan of the complete graph. I will describe this density and report on work in future with Lena Walter about relations of population genetics and algebraic geometry via the tropical connection.
15:20 - 15:50	Coffee Break
15:50 - 16:50	Quang-Nhat Le (Hebrew University) Couting lattice points in polytopes via Fourier analysis
16:50 - 18:20	Free Discussion
19:00 - 22:00	Conference Dinner at "Brauhaus an der Thomaskirche" (à la carte and on individual payment)

Participants

Marie-Charlotte Brandenburg

FU Berlin

Paul Breiding

MPI MiS

Jan-Marten Brunink

Universität Osnabrück

Amanda Cameron

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Türkü Özlüm Çelik

Max-Planck-Institute

Diego Cifuentes

MPI MiS

Jane Coons

North Carolina State University

Alessio D'Alì

MPI MiS Leipzig

Joscha Diehl

MPI Leipig

Rodica Dinu

University of Bucharest

Eliana Duarte

OVGU

Alex Fink

Queen Mary University of London

Tobias Fritz

MPI MIS

Francesco Galuppi

MPI MiS

Afshin Goodarzi

Free University Berlin

Paul Görlach

Max Planck Institute MIS Leipzig

Christian Haase

Freie Universität Berlin

Corey Harris

MPI MiS

Nils Haug

Medizinische Universität Wien

Nidhi Kaihnsa

Max Planck Institute, Leipzig

Florian Kohl

Freie Universitaet Berlin

Khazhgali Kozhasov

MPI MIS

Benjamin Kutschan

TU Berlin

Quang-Nhat Le

Hebrew University

Xue Liu

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Mateusz Michalek

MPI MiS

Jorge Alberto Olarte

Freie Universität Berlin

Marta Panizzut

TU Berlin

Manuel Radons

TU Berlin

Yue Ren

MPI MIS

Mahsa Sayyary Namin

MPI MIS

Benjamin Schröter

TU Berlin

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences

Johanna Steinmeyer

Freie Universität Berlin

Christian Stump

Technische Universität Berlin

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Lorenzo Venturello

Universität Osnabrück

Tobias Weihrauch

Universität Leipzig

Milena Wrobel

MPI MIS

Oguzhan Yürük

TU Berlin

Günter Ziegler

Freie Universität Berlin

Scientific Organizers

Amanda Cameron

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Xue Liu

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Administrative Contact

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail