[Aec-friends] SFB-Meeting, Friday, Oct 25, TU Wien

Christian Krattenthaler christian.krattenthaler at univie.ac.at
Tue Oct 22 14:12:11 CEST 2019

Dear Colleagues,

we invite you to the next SFB-meeting on Friday, Oct 25 at the TU Wien.
We are looking forward to your participation.

With best regards,
Michael (for the TU Wien team)

P.S. Please let me know whether you will join for lunch.
We will first make a reservation for 20 people and will adapt accordingly.



Location: Seminarraum Freihaus grün 03 B
                    Freihaus, Wiedner Hauptstr. 8-10, Turm A, 3. Stock

12:30            Lunch at Cafe Restaurant Resselpark at Karlsplatz

14:00-14:45  Marc Noy (UPC Barcelona)
                       Limiting probabilities of first order properties of 
sparse random graphs

14:45-15:15 Break

15:15-15:45 Ankush Goswami (JKU)
                      A q-Aanlogue for Euler's evaluations of the Riemann zeta 

15:45-16:15 Amélie Trotignon (JKU)
                         Walks in the three-quarter plane

16:15-          Discussions


"Limiting probabilities of first order properties of sparse random graphs"
Marc Noy (UPC Barcelona

Given a property A of graphs expressible in the language of first order (FO) 
logic, we are interested in the limiting probability that a random graph 
satisfies A. We consider this question in the G(n,p) model when p=c/n and c > 0 
is a constant. It is well-known that there is a phase transition in the 
structure of G(n,c/n) at c = 1. Lynch showed that FO logic cannot capture this 
transition. Instead of individual properties we study the closure L(c) of the 
set of all limiting probabilities of FO properties and find the following 
dichotomy. There is a critical value c0 ~ 0.93 such that: if c > c0 then L(c) 
is the whole interval [0,1], while if c < c0 there is at least one gap, that 
is, one subinterval not covered by L(c).
This is is joint work with Alberto Larrauri and Tobias Müller.

"A q-Aanlogue for Euler's evaluations of the Riemann zeta function"
Ankush Goswami (JKU)

Abstract: [see the attachment]


"Walks in the three-quarter plane"
Amélie Trotignon (JKU)

Enumeration of lattice walks in cones has many applications in combinatorics 
and probability theory. These objects are amenable to treatment by many 
techniques: combinatorics, complex analysis, probability theory, computer 
algebra and Galois theory of difference equations. While walks restricted to 
the first quadrant have been well studied, the case of non-convex cones has 
been approached recently. In this talk, we extend the analytic method of the 
study of walks in the quarter plane to the three-quarter plane applying the 
strategy of splitting the domain into two symmetric convex cones. This method 
is composed of three main steps: write a system of functional equations, which 
may be simplified into one simple equation under symmetry conditions; transform 
the functional equation into a boundary value problem; and solve this problem 
using conformal mapping. The result is a contour integral expression for the 
generating function. The advantage of this method is the uniform treatment of 
models corresponding to different step sets.

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