Page 600 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 600
A JOURNEY FROM PURE TO APPLIED MATHEMATICS (MS-53)
Independent sets in random subgraphs of the hypercube
Gal Kronenberg, kronenberg@maths.ox.ac.uk
University of Oxford, United Kingdom
Independent sets in bipartite regular graphs have been studied extensively in combinatorics,
probability, computer science and more. The problem of counting independent sets is particu-
larly interesting in the d-dimensional hypercube {0, 1}d, motivated by the lattice gas hardcore
model from statistical physics. Independent sets also turn out to be very interesting in the con-
text of random graphs. In this talk we will review some fundamental results, and discuss new
results on random subgraphs of the hypercube. This talk is based on joint work with Yinon
Spinka.
Identifying 3D Genome Organization in Diploid Organisms via Euclidean
Distance Geometry
Kaie Kubjas, kaie.kubjas@aalto.fi
Aalto University, Finland
The 3D organization of the genome plays an important role for gene regulation. Chromosome
conformation capture techniques allow one to measure the number of contacts between genomic
loci that are nearby in the 3D space. In this talk, we study the problem of reconstructing the
3D organization of the genome from whole genome contact frequencies in diploid organisms,
i.e. organisms that contain two indistinguishable copies of each genomic locus. In particular,
we study the identifiability of the 3D organization of the genome and optimization methods for
reconstructing it. This talk is based on joint work with Anastasiya Belyaeva, Lawrence Sun and
Caroline Uhler.
On arithmetic functions orthogonal to deterministic sequences
Joanna Kułaga-Przymus, joanna.kulaga@gmail.com
Nicolaus Copernicus University in Torun´, Poland
The arithmetic Möbius function µ is believed to behave randomly. One way to express such
a behaviour is the content of Sarnak’s conjecture from 2010 on the Möbius disjointness from
all deterministic sequences. In 2015 Veech formulated a (dynamical) property of the Möbius
function itself and he conjectured that this property is equivalent to Sarnak’s conjecture. My
talk will be devoted to the strategy of the proof of Veech’s conjecture and some consequences
of this equivalence.
The talk is based on a joint work with Adam Kanigowski, Mariusz Leman´czyk and Thierry
de la Rue.
598
Independent sets in random subgraphs of the hypercube
Gal Kronenberg, kronenberg@maths.ox.ac.uk
University of Oxford, United Kingdom
Independent sets in bipartite regular graphs have been studied extensively in combinatorics,
probability, computer science and more. The problem of counting independent sets is particu-
larly interesting in the d-dimensional hypercube {0, 1}d, motivated by the lattice gas hardcore
model from statistical physics. Independent sets also turn out to be very interesting in the con-
text of random graphs. In this talk we will review some fundamental results, and discuss new
results on random subgraphs of the hypercube. This talk is based on joint work with Yinon
Spinka.
Identifying 3D Genome Organization in Diploid Organisms via Euclidean
Distance Geometry
Kaie Kubjas, kaie.kubjas@aalto.fi
Aalto University, Finland
The 3D organization of the genome plays an important role for gene regulation. Chromosome
conformation capture techniques allow one to measure the number of contacts between genomic
loci that are nearby in the 3D space. In this talk, we study the problem of reconstructing the
3D organization of the genome from whole genome contact frequencies in diploid organisms,
i.e. organisms that contain two indistinguishable copies of each genomic locus. In particular,
we study the identifiability of the 3D organization of the genome and optimization methods for
reconstructing it. This talk is based on joint work with Anastasiya Belyaeva, Lawrence Sun and
Caroline Uhler.
On arithmetic functions orthogonal to deterministic sequences
Joanna Kułaga-Przymus, joanna.kulaga@gmail.com
Nicolaus Copernicus University in Torun´, Poland
The arithmetic Möbius function µ is believed to behave randomly. One way to express such
a behaviour is the content of Sarnak’s conjecture from 2010 on the Möbius disjointness from
all deterministic sequences. In 2015 Veech formulated a (dynamical) property of the Möbius
function itself and he conjectured that this property is equivalent to Sarnak’s conjecture. My
talk will be devoted to the strategy of the proof of Veech’s conjecture and some consequences
of this equivalence.
The talk is based on a joint work with Adam Kanigowski, Mariusz Leman´czyk and Thierry
de la Rue.
598
