Location: 4421 (CS Thesis Room)
Time: Tuesdays 4pm  5pm (unless otherwise noted)
Organizer: Delaram Kahrobaei (faculty adviser )
Student organizers: Jonathan Gryak
Date 
Topic 
06/16

Kelsey Horan (CS, GC)
Title: Applications of Group Theory to Data Science 
07/07
3:30PM

Bianca Sosnovski (Math and CS, QCC)
Title: A new platform semigroup for the TillichZemor hash function scheme
Abstract:
In this talk, I will present a new candidate as platform for the
TillichZemor general scheme of hash functions (1994) with the goal of
improving the security of the scheme. The underlying platform is the
noncommutative (semi)group of linear functions under composition. This a
joint work with V. Shpilrain. 
07/07
4:00PM

Jordi Delgado (Math, UPC Barcelona)
Title: On Algorithmic Recognition of Certain Classes of Groups
Abstract:
I will introduce the standard framework for recognition problems in group theory, then move to a more specific setting: namely group extensions by infinite cyclic groups.
For this family, I will review some folklore facts and previous partial results which we use to provide an argument that implies the undecidability of the BNS invariant (a nice geometrical invariant on which I would also like to say a few words).
This is joint work with B. Cavallo, D. Kahrobaei, and E. Ventura.

07/21 
Armin Weiß (Universität Stuttgart, Germany)
Title: Amenability of Schreier Graphs and Strongly Generic Algorithms
for the Conjugacy Problem, Part 1  Amenability of Schreier graphs of
HNN extensions and Amalgamated Products
Abstract:
In various occasions the conjugacy problem in finitely
generated amalgamated products and HNN extensions can be decided
efficiently for elements which cannot be conjugated into the base
groups. This observation asks for a bound on how many such elements
there are. Such bounds can be derived using the theory of amenable
graphs:
We examine Schreier graphs of amalgamated products and HNN extensions. For an amalgamated product $G =H\star_AK $ with $[H:A]\geq [K:A]\geq 2$, the Schreier graph with respect to $H$ or $K$ turns out to be nonamenable if and only if $[H:A]\geq 3$. Moreover, for an HNN extension of the form $G = \left< \, H,b \;\middle \; bab^{1}=\phi(a), a \in A \, \right>$, we show that the Schreier graph of $G$ with respect to the subgroup $H$ is nonamenable if and only if $A\neq H \neq \phi(A)$.
As application of these
characterizations we show that under certain conditions the conjugacy
problem in fundamental groups of finite graphs of groups with free
abelian vertex groups can be solved in polynomial time on a strongly
generic set. Furthermore, the conjugacy problem in groups with more than
one end can be solved with a strongly generic algorithm which has
essentially the same time complexity as the word
problem. These are
rather striking results as the word problem might be easy, but the
conjugacy problem might be even undecidable. Finally, our results yield
another proof that the set where the conjugacy problem of the Baumslag
group $\mathrm{\bf{G}}_{1,2}$ is decidable in polynomial time is also
strongly generic.
The first talk will cover the characterization theorem of nonamenable Schreier graphs. 
07/28 
Armin Weiß (Universität Stuttgart, Germany) Title: Amenability of Schreier Graphs and Strongly Generic Algorithms
for the Conjugacy Problem, Part 2  Strongly Generic Algorithms for the Conjugacy Problem
Abstract: See abstract for 07/21
In the second talk we will focus on its applications to the conjugacy problem.

08/04

Serena Yuan (Math, NYU)
Title: A New Cryptographic Hash Function Involving Modified Cayley Graphs

08/11

Alexander Wood (CS, GC)
Title: Generic Case Complexity in Group Theory


 
