Persistent homology is a central object of study in applied
topology. It offers a flexible framework for defining invariants,
called barcodes, of point cloud data and of real valued functions.
Many of the key results of the last several years in the...
We will discuss the notion of loops in linguistic structures,
mainly in dictionaries. In a simplified view, a dictionary is a
graph that links every word (vertex) to a set of alternative words
(the definition) which in turn point to further...
I will continue the exposition of different derandmization
techniques for probabilistic logspace algorithms.
The material of this talk will assume only little knowledge from
the first talk.
Since the foundational results of Thomason and
Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there
has been a lot of effort by many researchers to extend the theory
to hypergraphs. I will present some of this history, and
then...
In 1985 Misha Gromov proved his Nonsqueezing Theorem, and hence
constructed the first symplectic 1-capacity. In 1989 Helmut Hofer
asked whether symplectic d-capacities exist if 1 d n. I will
discuss the answer to this question and its relevance in...
The trace formula has been the most powerful and mainstream tool
in automorphic forms for proving instances of Langlands
functoriality, including character relations. Its generalization,
the relative trace formula, has also been used to prove...