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SUMMARY:Özlem Imamoglu (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20200910T120000Z
DTEND;VALUE=DATE-TIME:20200910T125500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/1
DESCRIPTION:Title: On a class number formula of Hurwitz\nby Özlem Imamogl
u (ETH Zürich) as part of Heilbronn Annual Conference 2020\n\nInteractive
livestream: https://zoom.us/j/91698418687\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
URL:https://zoom.us/j/91698418687
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronald de Wolf (CWI and Universiteit van Amsterdam)
DTSTART;VALUE=DATE-TIME:20200910T130000Z
DTEND;VALUE=DATE-TIME:20200910T135500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/2
DESCRIPTION:Title: Efficient algorithms for graph sparsification\nby Ronal
d de Wolf (CWI and Universiteit van Amsterdam) as part of Heilbronn Annual
Conference 2020\n\nInteractive livestream: https://zoom.us/j/99701127745\
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
URL:https://zoom.us/j/99701127745
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Chudnovsky (Princeton University)
DTSTART;VALUE=DATE-TIME:20200910T143000Z
DTEND;VALUE=DATE-TIME:20200910T152500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/3
DESCRIPTION:Title: Induced subgraphs and tree decompositions\nby Maria Chu
dnovsky (Princeton University) as part of Heilbronn Annual Conference 2020
\n\nInteractive livestream: https://zoom.us/j/92928990440\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
URL:https://zoom.us/j/92928990440
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurt Johansson (KTH Royal Institute of Technology)
DTSTART;VALUE=DATE-TIME:20200910T153000Z
DTEND;VALUE=DATE-TIME:20200910T162500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/4
DESCRIPTION:Title: Scaling limits in random tiling models\nby Kurt Johanss
on (KTH Royal Institute of Technology) as part of Heilbronn Annual Confere
nce 2020\n\nInteractive livestream: https://zoom.us/j/96784930584\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
URL:https://zoom.us/j/96784930584
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200911T120000Z
DTEND;VALUE=DATE-TIME:20200911T125500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/5
DESCRIPTION:Title: Random multiplicative functions: progress and problems\
nby Adam Harper (University of Warwick) as part of Heilbronn Annual Confer
ence 2020\n\nInteractive livestream: https://zoom.us/j/92697367076\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
URL:https://zoom.us/j/92697367076
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailsa Keating (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200911T130000Z
DTEND;VALUE=DATE-TIME:20200911T135500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/6
DESCRIPTION:Title: Two-variable singularities and symplectic topology\nby
Ailsa Keating (University of Cambridge) as part of Heilbronn Annual Confer
ence 2020\n\nInteractive livestream: https://zoom.us/j/93514297302\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
URL:https://zoom.us/j/93514297302
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrike Tillmann (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200911T143000Z
DTEND;VALUE=DATE-TIME:20200911T152500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/7
DESCRIPTION:Title: Configurations of monopoles and branch points\nby Ulrik
e Tillmann (University of Oxford) as part of Heilbronn Annual Conference 2
020\n\nInteractive livestream: https://zoom.us/j/92974670553\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
URL:https://zoom.us/j/92974670553
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Lenstra (Universiteit Leiden)
DTSTART;VALUE=DATE-TIME:20200911T153000Z
DTEND;VALUE=DATE-TIME:20200911T162500Z
DTSTAMP;VALUE=DATE-TIME:20200812T063537Z
UID:HAC/8
DESCRIPTION:Title: Indecomposable algebraic integers\nby Hendrik Lenstra (
Universiteit Leiden) as part of Heilbronn Annual Conference 2020\n\nIntera
ctive livestream: https://zoom.us/j/93983719152\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
URL:https://zoom.us/j/93983719152
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