Page 56 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 56
INVITED SPEAKERS
mating, and other genetic and evolutionary mechanisms. The effect of these mechanisms, and
the way in which they interact with one another, is also influenced by the spatial structure of
the population. The hunt for adequate mathematical models with which to investigate the in-
teraction between the forces of evolution and spatial structure is still very much in progress.
Capturing stochastic effects in a biologically meangingful way is particularly challenging. In
this talk we shall explore some of the progress that has been made, and some of the remaining
challenges.
Recent Results on Lieb-Thirring Inequalities
Rupert Frank, rlfrank@caltech.edu
Caltech, United States, and LMU Munich, Germany
Lieb-Thirring inequalities are a mathematical expression of the uncertainty and exclusion prin-
ciples in quantum mechanics. Since their discovery in 1975 they have played an important role
in several areas of analysis and mathematical physics. We provide a gentle introduction to clas-
sical aspects of this subject and present some recent progress. Finally, we discuss extensions, in
the spirit of Lieb-Thirring inequalities, of several inequalities in harmonic analysis to the setting
of families of orthonormal functions.
Laplacians on infinite graphs
Aleksey Kostenko, aleksey.kostenko@fmf.uni-lj.si
University of Ljubljana, Slovenia, and University of Vienna, Austria
There are two different notions of a Laplacian operator associated with graphs: discrete graph
Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs).
Both objects have a venerable history as they are related to several diverse branches of mathe-
matics and mathematical physics.
The existing literature usually treats these two Laplacian operators separately. In this talk, I
will focus on the relationship between them (spectral, parabolic and geometric properties). One
of our main conceptual messages is that these two settings should be regarded as complementary
(rather than opposite) and exactly their interplay leads to important further insight on both sides.
Based on joint work with Noema Nicolussi.
Exponential sums over finite fields
Emmanuel Kowalski, kowalski@math.ethz.ch
ETH Zürich, Switzerland
Exponential sums are among the simplest mathematical objects that one can imagine, but also
among the most remarkably useful and versatile in number theory.
This talk will survey the history, the mysteries and the surprises of such sums over finite
fields, with a focus on questions related to the distribution of values of families of exponen-
tial sums. General principles and applications will be illustrated by concrete examples, where
sums of two squares, Sidon sets, Larsen’s Alternative, the variance of arithmetic functions over
54
mating, and other genetic and evolutionary mechanisms. The effect of these mechanisms, and
the way in which they interact with one another, is also influenced by the spatial structure of
the population. The hunt for adequate mathematical models with which to investigate the in-
teraction between the forces of evolution and spatial structure is still very much in progress.
Capturing stochastic effects in a biologically meangingful way is particularly challenging. In
this talk we shall explore some of the progress that has been made, and some of the remaining
challenges.
Recent Results on Lieb-Thirring Inequalities
Rupert Frank, rlfrank@caltech.edu
Caltech, United States, and LMU Munich, Germany
Lieb-Thirring inequalities are a mathematical expression of the uncertainty and exclusion prin-
ciples in quantum mechanics. Since their discovery in 1975 they have played an important role
in several areas of analysis and mathematical physics. We provide a gentle introduction to clas-
sical aspects of this subject and present some recent progress. Finally, we discuss extensions, in
the spirit of Lieb-Thirring inequalities, of several inequalities in harmonic analysis to the setting
of families of orthonormal functions.
Laplacians on infinite graphs
Aleksey Kostenko, aleksey.kostenko@fmf.uni-lj.si
University of Ljubljana, Slovenia, and University of Vienna, Austria
There are two different notions of a Laplacian operator associated with graphs: discrete graph
Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs).
Both objects have a venerable history as they are related to several diverse branches of mathe-
matics and mathematical physics.
The existing literature usually treats these two Laplacian operators separately. In this talk, I
will focus on the relationship between them (spectral, parabolic and geometric properties). One
of our main conceptual messages is that these two settings should be regarded as complementary
(rather than opposite) and exactly their interplay leads to important further insight on both sides.
Based on joint work with Noema Nicolussi.
Exponential sums over finite fields
Emmanuel Kowalski, kowalski@math.ethz.ch
ETH Zürich, Switzerland
Exponential sums are among the simplest mathematical objects that one can imagine, but also
among the most remarkably useful and versatile in number theory.
This talk will survey the history, the mysteries and the surprises of such sums over finite
fields, with a focus on questions related to the distribution of values of families of exponen-
tial sums. General principles and applications will be illustrated by concrete examples, where
sums of two squares, Sidon sets, Larsen’s Alternative, the variance of arithmetic functions over
54
