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BEGIN:VEVENT
SUMMARY:Özlem Imamoglu (ETH Zürich)
DTSTART:20200910T120000Z
DTEND:20200910T125500Z
DTSTAMP:20260422T212730Z
UID:HAC/1
DESCRIPTION:Title: On a
class number formula of Hurwitz\nby Özlem Imamoglu (ETH Zürich) as
part of Heilbronn Annual Conference 2020\n\n\nAbstract\nClass number formu
las have long and rich history. In a mostly forgotten paper\, Hurwitz gave
an infinite series representation for the class number of positive defini
te quadratic forms. In this talk I will give an overview of Hurwitz’s fo
rmula and show how similar ideas can be used to give a formula in the inde
finite case as well as a class number formula for binary cubic forms.\n
LOCATION:https://researchseminars.org/talk/HAC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronald de Wolf (CWI and Universiteit van Amsterdam)
DTSTART:20200910T130000Z
DTEND:20200910T135500Z
DTSTAMP:20260422T212730Z
UID:HAC/2
DESCRIPTION:Title: Effi
cient algorithms for graph sparsification\nby Ronald de Wolf (CWI 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. S
parse 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 compute on.
A long line of work by Karger\, Spielman\, Teng\, and others resulted 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)\, while pr
eserving many important properties of G. This then gives nearly-linear-tim
e algorithms for solving various cut problems in graphs\, for graph partit
ioning\, and for solving Laplacian linear systems. We will describe these
developments\, and end with our recent work with Simon Apers showing that
*quantum* algorithms can even compute such a good graph sparsification in
sublinear time.\n
LOCATION:https://researchseminars.org/talk/HAC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Chudnovsky (Princeton University)
DTSTART:20200910T143000Z
DTEND:20200910T152500Z
DTSTAMP:20260422T212730Z
UID:HAC/3
DESCRIPTION:Title: Indu
ced subgraphs and tree decompositions\nby Maria Chudnovsky (Princeton
University) as part of Heilbronn Annual Conference 2020\n\n\nAbstract\nTre
e decompositions are a powerful tool in structural graph theory\, that is
traditionally used in the context of forbidden graph minors.\nConnecting t
ree decompositions and forbidden induced subgraphs has so far remained out
of reach. Recently we obtained several results in this direction\; the ta
lk will be a survey of these results.\n
LOCATION:https://researchseminars.org/talk/HAC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurt Johansson (KTH Royal Institute of Technology)
DTSTART:20200910T153000Z
DTEND:20200910T162500Z
DTSTAMP:20260422T212730Z
UID:HAC/4
DESCRIPTION:Title: Scal
ing limits in random tiling models\nby Kurt Johansson (KTH Royal Insti
tute of Technology) as part of Heilbronn Annual Conference 2020\n\n\nAbstr
act\nLarge random tiling in various regions\, or dimer models on bipartite
graphs\, often show fascinating geometrical patterns. Different parts of
the random tiling can have different types of patterns and you can see cle
ar interfaces between them. Scaling limits close to these interfaces give
rise to point processes that are related to random matrix theory.\n\nI wil
l give an overview of some aspects of this research area and discuss some
of the scaling limits.\n
LOCATION:https://researchseminars.org/talk/HAC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper (University of Warwick)
DTSTART:20200911T120000Z
DTEND:20200911T125500Z
DTSTAMP:20260422T212730Z
UID:HAC/5
DESCRIPTION:Title: Rand
om multiplicative functions: progress and problems\nby Adam Harper (Un
iversity of Warwick) as part of Heilbronn Annual Conference 2020\n\n\nAbst
ract\nA random multiplicative function is a random function on the natural
numbers\, that is constructed from a sequence of independent random varia
bles in a way that respects the multiplicative structure. These objects ar
ise naturally in analytic number theory as models for things like Dirichle
t characters\, but can also be thought of simply as probabilistic objects
with an interesting dependence structure. In this talk I will try to surve
y what we know about random multiplicative functions\, and some open probl
ems\, in a way that is (hopefully) accessible and interesting to number th
eorists\, probabilists\, and others.\n
LOCATION:https://researchseminars.org/talk/HAC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating (University of Cambridge)
DTSTART:20200911T130000Z
DTEND:20200911T135500Z
DTSTAMP:20260422T212730Z
UID:HAC/6
DESCRIPTION:Title: Two-
variable singularities and symplectic topology\nby Ailsa Keating (Univ
ersity of Cambridge) as part of Heilbronn Annual Conference 2020\n\n\nAbst
ract\nStart with a two-variable complex polynomial f with an isolated crit
ical point at the origin. We will survey a range of classical structures a
ssociated to f\, and explain how these can be revisited and enhanced using
insights from symplectic topology. No prior knowledge of singularity theo
ry or symplectic topology will be assumed.\n
LOCATION:https://researchseminars.org/talk/HAC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Tillmann (University of Oxford)
DTSTART:20200911T143000Z
DTEND:20200911T152500Z
DTSTAMP:20260422T212730Z
UID:HAC/7
DESCRIPTION:Title: Conf
igurations of monopoles and branch points\nby Ulrike Tillmann (Univers
ity of Oxford) as part of Heilbronn Annual Conference 2020\n\n\nAbstract\n
Point-particles moving in a background space are mathematically modelled b
y configurations spaces. Data associated to the particles are incorporate
d by giving the configurations labels in a suitable state space. These spa
ces have seen much attention in topology starting with work of McDuff and
Segal in the 1970s. In classical field theory\, however\, point-particles
interact with fields\, and mathematically these give rise to functions on
the complement of a configuration\, and thus to what we call 'configurati
on mapping spaces'. The moduli space of magnetic monopoles provides one su
ch example. Another family of examples is given by branched covering spac
es of the complex plane with prescribed holonomy \, also known as Hurwitz
spaces and were the object of study in Ellenberg\, Venkatesh and Westerla
nd 's celebrated work on the Cohen-Lenstra heuristics. \n\nIn joint work w
ith Martin Palmer we extend their results to configuration mapping spaces
of higher dimensional manifolds and most general 'fields'.\n
LOCATION:https://researchseminars.org/talk/HAC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Lenstra (Universiteit Leiden)
DTSTART:20200911T153000Z
DTEND:20200911T162500Z
DTSTAMP:20260422T212730Z
UID:HAC/8
DESCRIPTION:Title: Inde
composable algebraic integers\nby Hendrik Lenstra (Universiteit Leiden
) as part of Heilbronn Annual Conference 2020\n\n\nAbstract\nThe ring of a
ll algebraic integers carries the structure of a "Hilbert lattice"\, which
means that its additive group may be viewed as a discrete subgroup of a H
ilbert space. As a consequence\, that group is generated by the set of "in
decomposable algebraic integers". There are not too many of those\; in fac
t\, only finitely many for each degree. The lecture surveys what we know a
nd what we would like to know about these indecomposable algebraic integer
s. It represents joint work with Ted Chinburg and Daan van Gent.\n
LOCATION:https://researchseminars.org/talk/HAC/8/
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