## Upcoming and past lectures held at the colloquium

**Time:**July 10, 2019 at 12:00PM

**Lecture room:**(A101)

**About the lecturer**: Pavel Exner is the scientific director at
the Doppler Institute, Prague, Czech
Republic.
He graduated from the Charles
University and obtained a DrSc degree
from the JINR Dubna institute in 1990.
He worked at the Charles University,
Joint Institute for Nuclear Research,
Dubna and is currently employed at the
Czech Academy of Sciences.
His research is concerned with spectral
and scattering properties of quantum
waveguides, quantum mechanics on
graphs and manifolds, decay and
resonance effects.
He held the following offices in the
international organizations:
European Math. Society: Vice-president
2005-10, President 2015-18.
International Association of
Mathematical Physics: Secretary 2006-
08, President 2009-11 IUPAP:
Commission Secr. and Chair 2002-08,
Vice-president 2005-08. European
Research Council: Scientic Council
Member since 2005, Vice-president
2011-14 Academia Europaea, Section
Vice chair 2012-18, Chair since 2018.
Selected awards include: JINR First
Prize 1985, elected member of
Academia Europaea 2010, Neuron Prize
2016.

**Lecture abstract**: This talk deals with relations between topology and spectra with
the aim to show that a nontrivial topology of the configuration
space can lead to a variety of spectral types. We focus on second order equations used to describe periodic quantum systems. Such
a PDE in a Euclidean space has typically the spectrum which is
absolutely continuous, consisting of bands and gaps, the number
of the latter being determined by the dimensionality. If analogous
second-order operators on metric graphs are considered, a
number of different situations may arise. Using simple examples,
we show that the spectrum may then have a pure point or a fractal
character, and also that it may have only a finite but nonzero
number of open gaps. Furthermore, motivated by recent attempts
to model the anomalous Hall effect, we investigate a class of vertex
couplings that violate the time reversal invariance. We find
spectra of lattice graphs with the simplest coupling of this type
and demonstrate that it depends substantially on the parity of the
vertices, and discuss some consequences of this property.

**Time:**May 22, 2019 at 12:00PM

**Lecture room:**(A001)

**About the lecturer**: Tomoyuki Arakawa is Professor at Research Institute for Mathematical Sciences (RIMS), Kyoto University, Japan (2010–). He was educated at Kyoto University and at Nagoya University, Japan. His research is concerned with representation theory and vertex algebras. He was awarded MSJ Takebe Katahiro Special Prize (2004), JSPS Young Scientist Prize (2008), MSJ Algebra Prize (2013), MSJ Autumn Prize (2017), and JSPS Prizes for Science and Technology (2019). He was an invited speaker at the International Congress of Mathematics in Rio de Janeiro in 2018.

**Lecture abstract**: Physical theories often predict interesting dualities in mathematics. In this lecture I will talk about a certain remarkable duality arising from 4-dimensional N=4 superconformal field theories in physics, which was recently discovered by Beem and Rastelli, inspired by a work of Anne Moreau and myself.

**Time:**December 19, 2018 at 12:00PM

**Lecture room:**(A001)

**About the lecturer**: Endre Süli is Professor of Numerical
Analysis
in
the
Mathematical
Institute, University of Oxford, Fellow
and Tutor in Mathematics at
Worcester College, Oxford and Chair
of the Faculty of Mathematics at the
University of Oxford (2018--).
He was educated at the University of
Belgrade and at St Catherine's
College, Oxford.
His research is concerned with the
mathematical analysis of numerical
algorithms for nonlinear partial
differential equations.
Endre Süli is a Foreign Member of the
Serbian Academy of Sciences and Arts
(2009), Fellow of the European
Academy of Sciences (2010), Fellow
of the Society for Industrial and
Applied Mathematics (SIAM, 2016)
and Fellow of the Institute of
Mathematics and its Applications
(FIMA, 2007).
Other honours include: Charlemagne
Distinguished Lecture (2011), IMA
Service Award (2011), Professor
Hospitus
Universitatis
Carolinae
Pragensis, (2012–), Distinguished
Visiting Chair Professor Shanghai
Jiao
Tong
University
(2013–),
President, SIAM UK and RI Section
(2013–2015), London Mathematical
Society/New Zealand Mathematical
Society Forder Lecturer (2015), Aziz
Lecture (2015), BIMOS Distinguished
Lecture (2016), John von Neumann
Lecture (2016). He was invited
speaker at the International Congress
of Mathematicians in Madrid in 2006,
and was Chair of the Society for the
Foundations
of
Computational
Mathematics (2002–2005).

**Lecture abstract**: The mathematical analysis of numerical methods for partial differential
equations (PDEs) is a rich and active field of modern applied
mathematics. The steady growth of the subject is stimulated by ever-
increasing demands from the natural sciences, engineering and
economics to provide accurate and reliable approximations to
mathematical models involving PDEs whose exact solutions are either
too complicated to determine in closed form or, in many cases, are not
known to exist. While the history of numerical solution of ordinary
differential equations is firmly rooted in 18th and 19th century
mathematics, the mathematical foundations of the field of numerical
solution of PDEs are much more recent: they were first formulated in a
landmark paper Richard Courant, Karl Friedrichs, and Hans Lewy
published in 1928. The aim of the lecture is to survey recent
developments in the area of numerical analysis of partial differential
equations, focusing in particular on discontinuous Galerkin finite
element methods, whose mathematical analysis has been an area of
active research during the past decade.