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SUMMARY:Özlem Imamoglu (ETH Zürich)
DTSTART:20200910T120000Z
DTEND:20200910T125500Z
DTSTAMP:20260404T095424Z
UID:HAC/1
DESCRIPTION:Title: On a class number formula of Hurwitz\nby Özlem Imamoglu (ETH Züri
ch) as part of Heilbronn Annual Conference 2020\n\n\nAbstract\nClass numbe
r formulas have long and rich history. In a mostly forgotten paper\, Hurwi
tz gave an infinite series representation for the class number of positive
definite quadratic forms. In this talk I will give an overview of Hurwitz
’s formula and show how similar ideas can be used to give a formula in t
he indefinite case as well as a class number formula for binary cubic form
s.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/1/
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SUMMARY:Ronald de Wolf (CWI and Universiteit van Amsterdam)
DTSTART:20200910T130000Z
DTEND:20200910T135500Z
DTSTAMP:20260404T095424Z
UID:HAC/2
DESCRIPTION:Title: Efficient algorithms for graph sparsification\nby Ronald de Wolf (C
WI and Universiteit van Amsterdam) as part of Heilbronn Annual Conference
2020\n\n\nAbstract\nGraphs occur everywhere in discrete mathematics\, but
also in practical problems in logistics\, the internet\, social networks\,
etc. Sparse graphs (i.e.\, ones with few edges) are easier to handle than
dense graphs: they take less space to store and are often cheaper to comp
ute on. A long line of work by Karger\, Spielman\, Teng\, and others resul
ted in nearly-linear-time algorithms that can sparsify any given n-vertex
graph G to another n-vertex graph H whose number of edges is only O(n)\, w
hile preserving many important properties of G. This then gives nearly-lin
ear-time algorithms for solving various cut problems in graphs\, for graph
partitioning\, and for solving Laplacian linear systems. We will describe
these developments\, and end with our recent work with Simon Apers showin
g that *quantum* algorithms can even compute such a good graph sparsificat
ion in sublinear time.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Chudnovsky (Princeton University)
DTSTART:20200910T143000Z
DTEND:20200910T152500Z
DTSTAMP:20260404T095424Z
UID:HAC/3
DESCRIPTION:Title: Induced subgraphs and tree decompositions\nby Maria Chudnovsky (Pri
nceton University) as part of Heilbronn Annual Conference 2020\n\n\nAbstra
ct\nTree decompositions are a powerful tool in structural graph theory\, t
hat is traditionally used in the context of forbidden graph minors.\nConne
cting tree decompositions and forbidden induced subgraphs has so far remai
ned out of reach. Recently we obtained several results in this direction\;
the talk will be a survey of these results.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/3/
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BEGIN:VEVENT
SUMMARY:Kurt Johansson (KTH Royal Institute of Technology)
DTSTART:20200910T153000Z
DTEND:20200910T162500Z
DTSTAMP:20260404T095424Z
UID:HAC/4
DESCRIPTION:Title: Scaling limits in random tiling models\nby Kurt Johansson (KTH Roya
l Institute of Technology) as part of Heilbronn Annual Conference 2020\n\n
\nAbstract\nLarge random tiling in various regions\, or dimer models on bi
partite graphs\, often show fascinating geometrical patterns. Different pa
rts of the random tiling can have different types of patterns and you can
see clear interfaces between them. Scaling limits close to these interface
s give rise to point processes that are related to random matrix theory.\n
\nI will give an overview of some aspects of this research area and discus
s some of the scaling limits.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper (University of Warwick)
DTSTART:20200911T120000Z
DTEND:20200911T125500Z
DTSTAMP:20260404T095424Z
UID:HAC/5
DESCRIPTION:Title: Random multiplicative functions: progress and problems\nby Adam Har
per (University of Warwick) as part of Heilbronn Annual Conference 2020\n\
n\nAbstract\nA random multiplicative function is a random function on the
natural numbers\, that is constructed from a sequence of independent rando
m variables in a way that respects the multiplicative structure. These obj
ects arise naturally in analytic number theory as models for things like D
irichlet characters\, but can also be thought of simply as probabilistic o
bjects with an interesting dependence structure. In this talk I will try t
o survey what we know about random multiplicative functions\, and some ope
n problems\, in a way that is (hopefully) accessible and interesting to nu
mber theorists\, probabilists\, and others.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating (University of Cambridge)
DTSTART:20200911T130000Z
DTEND:20200911T135500Z
DTSTAMP:20260404T095424Z
UID:HAC/6
DESCRIPTION:Title: Two-variable singularities and symplectic topology\nby Ailsa Keatin
g (University of Cambridge) as part of Heilbronn Annual Conference 2020\n\
n\nAbstract\nStart with a two-variable complex polynomial f with an isolat
ed critical point at the origin. We will survey a range of classical struc
tures associated to f\, and explain how these can be revisited and enhance
d using insights from symplectic topology. No prior knowledge of singulari
ty theory or symplectic topology will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Tillmann (University of Oxford)
DTSTART:20200911T143000Z
DTEND:20200911T152500Z
DTSTAMP:20260404T095424Z
UID:HAC/7
DESCRIPTION:Title: Configurations of monopoles and branch points\nby Ulrike Tillmann (
University of Oxford) as part of Heilbronn Annual Conference 2020\n\n\nAbs
tract\nPoint-particles moving in a background space are mathematically mod
elled by configurations spaces. Data associated to the particles are inco
rporated by giving the configurations labels in a suitable state space. Th
ese spaces have seen much attention in topology starting with work of McDu
ff and Segal in the 1970s. In classical field theory\, however\, point-par
ticles interact with fields\, and mathematically these give rise to functi
ons on the complement of a configuration\, and thus to what we call 'conf
iguration mapping spaces'. The moduli space of magnetic monopoles provides
one such example. Another family of examples is given by branched coveri
ng spaces of the complex plane with prescribed holonomy \, also known as
Hurwitz spaces and were the object of study in Ellenberg\, Venkatesh and W
esterland 's celebrated work on the Cohen-Lenstra heuristics. \n\nIn joint
work with Martin Palmer we extend their results to configuration mapping
spaces of higher dimensional manifolds and most general 'fields'.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Lenstra (Universiteit Leiden)
DTSTART:20200911T153000Z
DTEND:20200911T162500Z
DTSTAMP:20260404T095424Z
UID:HAC/8
DESCRIPTION:Title: Indecomposable algebraic integers\nby Hendrik Lenstra (Universiteit
Leiden) as part of Heilbronn Annual Conference 2020\n\n\nAbstract\nThe ri
ng of all algebraic integers carries the structure of a "Hilbert lattice"\
, which means that its additive group may be viewed as a discrete subgroup
of a Hilbert space. As a consequence\, that group is generated by the set
of "indecomposable algebraic integers". There are not too many of those\;
in fact\, only finitely many for each degree. The lecture surveys what we
know and what we would like to know about these indecomposable algebraic
integers. It represents joint work with Ted Chinburg and Daan van Gent.\n
LOCATION:https://stable.researchseminars.org/talk/HAC/8/
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