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SUMMARY:Sachi Hashimoto (Boston University)
DTSTART;VALUE=DATE-TIME:20200527T190000Z
DTEND;VALUE=DATE-TIME:20200527T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/1
DESCRIPTION:Title: An obstruction to weak approximation on a Calabi-Yau threefold\nby Sa
chi Hashimoto (Boston University) as part of Experimental Talks in Algebra
ic Geometry\n\n\nAbstract\nIn this talk\, we investigate the arithmetic st
ructure of a class of Calabi-Yau threefolds. These threefolds were constru
cted over the complex numbers by Hosono and Takagi as a linear section of
a double quintic symmetroid\, and have a beautiful and simple story in the
geometry of quadrics over the rational numbers. In forthcoming work with
Honigs\, Lamarche\, and Vogt\, we exhibit an obstruction to weak approxima
tion on these threefolds. For the "experimental" nature of this seminar\,
we will conclude by working through a demonstration in cocalc. Attendees a
re asked to make cocalc accounts to participate fully\; no prior coding ex
perience necessary!\n
LOCATION:https://researchseminars.org/talk/etag2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (University of Wisconsin\, Madison)
DTSTART;VALUE=DATE-TIME:20200603T190000Z
DTEND;VALUE=DATE-TIME:20200603T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/2
DESCRIPTION:Title: Counting elliptic curves with a rational N-isogeny\nby Soumya Sankar
(University of Wisconsin\, Madison) as part of Experimental Talks in Algeb
raic Geometry\n\n\nAbstract\nThe problem of counting elliptic curves over
Q with a rational N isogeny can be rephrased as a question of counting rat
ional points on the moduli stacks X_0(N). In this talk\, I will discuss he
ights on projective varieties and a generalization to stacks of certain ki
nds\, based on upcoming work of Ellenberg\, Satriano and Zureick-Brown. We
will then use this to count points on X_0(N) for low N. This is joint wo
rk with Brandon Boggess.\n
LOCATION:https://researchseminars.org/talk/etag2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin DeVleming (University of California\, San Diego)
DTSTART;VALUE=DATE-TIME:20200617T190000Z
DTEND;VALUE=DATE-TIME:20200617T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/4
DESCRIPTION:Title: Moduli spaces of plane curves\nby Kristin DeVleming (University of Ca
lifornia\, San Diego) as part of Experimental Talks in Algebraic Geometry\
n\n\nAbstract\nCompactifying moduli spaces has been a fundamental problem
in algebraic geometry that has been richly developed in the past 50 years.
In that time\, many different perspectives have been studied and these ha
ve resulted in many different compactifications. Starting from an audience
discussion\, we will consider the moduli space of plane curves of fixed d
egree\, some potential compactifications\, and how they fit together. Base
d on that discussion\, I will mention a few of my favorite proper moduli s
paces of plane curves\, discuss their relationships\, and pose some open q
uestions.\n
LOCATION:https://researchseminars.org/talk/etag2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Kobin (University of California\, Santa Cruz)
DTSTART;VALUE=DATE-TIME:20200701T190000Z
DTEND;VALUE=DATE-TIME:20200701T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/5
DESCRIPTION:Title: Zeta functions in number theory\, algebraic geometry and beyond\nby A
ndrew Kobin (University of California\, Santa Cruz) as part of Experimenta
l Talks in Algebraic Geometry\n\n\nAbstract\nParticipants will have a chan
ce to fondly recall their favourite zeta functions. Together\, we will dis
cuss how different examples relate to/generalize each other. Then I will d
escribe a general framework for studying zeta functions using decompositio
n spaces from homotopy theory.\n
LOCATION:https://researchseminars.org/talk/etag2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takumi Murayama (Princeton University)
DTSTART;VALUE=DATE-TIME:20200624T190000Z
DTEND;VALUE=DATE-TIME:20200624T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/6
DESCRIPTION:Title: Every variety is birational to a weakly normal hypersurface\nby Takum
i Murayama (Princeton University) as part of Experimental Talks in Algebra
ic Geometry\n\n\nAbstract\nClassically\, it is known that every variety is
birational to a projective hypersurface. For curves and surfaces\, this h
ypersurface can be taken to have at worst nodal and at worst ordinary sing
ularities\, respectively. We will prove that in arbitrary dimension\, this
hypersurface can be taken to be weakly normal\, and for smooth projective
varieties of dimension at most five\, this hypersurface can be taken to h
ave semi-log canonical singularities. These results are due to Roberts and
Zaare-Nahandi and to Doherty in characteristic zero\, respectively\, and
to Rankeya Datta and myself in positive characteristic. Attendees will be
asked to do some concrete computations with polynomials.\n
LOCATION:https://researchseminars.org/talk/etag2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Brandt (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20200708T190000Z
DTEND;VALUE=DATE-TIME:20200708T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T073225Z
UID:etag2020/8
DESCRIPTION:Title: Limits of Voronoi and Delaunay Cells\nby Madeline Brandt (University
of California\, Berkeley) as part of Experimental Talks in Algebraic Geome
try\n\n\nAbstract\nVoronoi diagrams of finite point sets partition space i
nto regions. Each region contains all points which are\nnearest to one poi
nt in the finite point set. Voronoi diagrams (and their generalizations an
d variations)\nhave been an object of interest for hundreds of years by ma
thematicians spanning many fields\, and they\nhave numerous applications a
cross the sciences. Recently\, Cifuentes\, Ranestad\, Sturmfels\, and Wein
stein\ndefined Voronoi cells of varieties\, in which the finite point set
is replaced by a real algebraic variety. Each\npoint y on the variety has
a cell of points in the ambient space corresponding to those points which
are\ncloser to y than any other point on the variety. In this talk\, we pr
esent the limiting behavior of Voronoi\ndiagrams of finite sets\, where th
e finite sets are sampled from the variety and the sample size increases.
In\nthis setting\, we observe that many interesting features of the variet
y can be seen in a Voronoi Diagram\,\nincluding its medial axis\, curvatur
es\, normals\, reach\, and singularities.\n
LOCATION:https://researchseminars.org/talk/etag2020/8/
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