[Aec-friends] SFB-Meeting, Friday, Oct 25, TU Wien
Christian Krattenthaler
christian.krattenthaler at univie.ac.at
Mon Oct 21 17:04:25 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.
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Schedule:
Location: Seminarraum Freihaus grün 03 B
Freihaus, Wiedner Hauptstr. 8-10, Turm A, 3. Stock
12:30 Lunch at Cafe Restaurant Resselpark at Karlsplatz
https://restaurant-resselpark.at/
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
function
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
Abstract:
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.
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"A q-Aanlogue for Euler's evaluations of the Riemann zeta function"
Ankush Goswami (JKU)
Abstract: [see the attachment]
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"Walks in the three-quarter plane"
Amélie Trotignon (JKU)
Abstract:
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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