Page 70 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 70
PUBLIC SPEAKERS
Topological explorations in neuroscience
Kathryn Hess, kathryn.hess@epfl.ch
EPFL, Switzerland
The brain of each and every one of us is composed of hundreds of billions of neurons – often
called nerve cells – connected by hundreds of trillions of synapses, which transmit electrical
signals from one neuron to another. In reaction to stimulus, waves of electrical activity traverse
the network of neurons, processing the incoming information. Tools provided by the field of
mathematics called algebraic topology enable us to detect and describe the rich structure hidden
in this dynamic tapestry.
During this talk, I will guide you on a mathematical mystery tour of what topology has
revealed about how the brain processes information.
Crossing Numbers: From Art and Circuit Design to Knots and Number
Theory
Bojan Mohar, mohar@sfu.ca
Simon Fraser University, Canada, and IMFM, Slovenia
In 1864, Sylvester asked what is the probability that four randomly chosen points in the plane
form a convex quadrilateral. During World War II, Paul Turán asked about an optimal design of
railroads connecting n factories with m warehouses. In 1950s, the British painter Anthony Hill
asked how to draw a network of n interconnected nodes with fewest number of crossings. All
these questions are still unresolved. The speaker will overview mathematical foundations of the
common theme — the theory of crossing numbers of graphs — and will show some surprising
relations with other branches of mathematics.
Lie theory without groups
Andrei Okounkov, okounkov@math.columbia.edu
Columbia, United States, and Skoltech, Russian Federation, and HSE, Russian Federation
Group theory and, in particular, Lie group theory is central to many areas of mathematics and
to many applications. Lie theory is a masterpiece of a theory and it may feel nearly complete.
Because of this, and also because of the demand from applications, many Lie theorists have been
exploring new worlds, in which groups yield the center stage to other geometric and algebraic
structures.
68
Topological explorations in neuroscience
Kathryn Hess, kathryn.hess@epfl.ch
EPFL, Switzerland
The brain of each and every one of us is composed of hundreds of billions of neurons – often
called nerve cells – connected by hundreds of trillions of synapses, which transmit electrical
signals from one neuron to another. In reaction to stimulus, waves of electrical activity traverse
the network of neurons, processing the incoming information. Tools provided by the field of
mathematics called algebraic topology enable us to detect and describe the rich structure hidden
in this dynamic tapestry.
During this talk, I will guide you on a mathematical mystery tour of what topology has
revealed about how the brain processes information.
Crossing Numbers: From Art and Circuit Design to Knots and Number
Theory
Bojan Mohar, mohar@sfu.ca
Simon Fraser University, Canada, and IMFM, Slovenia
In 1864, Sylvester asked what is the probability that four randomly chosen points in the plane
form a convex quadrilateral. During World War II, Paul Turán asked about an optimal design of
railroads connecting n factories with m warehouses. In 1950s, the British painter Anthony Hill
asked how to draw a network of n interconnected nodes with fewest number of crossings. All
these questions are still unresolved. The speaker will overview mathematical foundations of the
common theme — the theory of crossing numbers of graphs — and will show some surprising
relations with other branches of mathematics.
Lie theory without groups
Andrei Okounkov, okounkov@math.columbia.edu
Columbia, United States, and Skoltech, Russian Federation, and HSE, Russian Federation
Group theory and, in particular, Lie group theory is central to many areas of mathematics and
to many applications. Lie theory is a masterpiece of a theory and it may feel nearly complete.
Because of this, and also because of the demand from applications, many Lie theorists have been
exploring new worlds, in which groups yield the center stage to other geometric and algebraic
structures.
68
