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BEGIN:VEVENT
SUMMARY:Dalimil Mazac (IAS)
DTSTART:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/1
DESCRIPTION:Title: An introduction to the conformal bootstrap for mathemat
icians\nby Dalimil Mazac (IAS) as part of Sphere packing and the confo
rmal bootstrap\n\n\nAbstract\nConformal field theories are a rich class of
quantum field theories that can be defined and studied fully rigorously i
n a general number of dimensions. In fact\, the definition of a conformal
field theory in n dimensions fits in one line: It is a unitary representat
ion V of the conformal group G=the universal cover of SO(2\,n)\, which is
a direct sum of irreducible lowest-weight modules\, and which admits a cer
tain kind of G-invariant multiplication. In my talk\, I will explain this
definition and some of its consequences. In particular\, I will review tha
t the definition implies stringent bounds on the weights of the irreducibl
e components in V. These bounds are typically obtained using linear and/or
semi-definite programming. The bounds are often sharp -- saturated by phy
sical conformal field theories. In certain special cases\, the sharpness o
f the bounds can be proved using magic functions for sphere packing in 8 a
nd 24 dimensions. The ultimate goal of the conformal bootstrap is to class
ify conformal field theories starting from the above definition. The most
tantalizing finding is that the bounds reveal the existence of many non-tr
ivial solutions of the axioms\, yet no explicit description of any non-tri
vial solution is presently known in n>2.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Tajdini (UCSB)
DTSTART:20201214T180000Z
DTEND:20201214T190000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/2
DESCRIPTION:Title: Fast conformal bootstrap and high-dimensional sphere pa
cking\nby Amir Tajdini (UCSB) as part of Sphere packing and the confor
mal bootstrap\n\n\nAbstract\nThe conformal bootstrap program seeks to map
the space of possible conformal field theories and to identify those on th
e boundary of theory space. In this talk\, I will discuss a numerical meth
od that is applicable to certain bootstrap problems\, such as the spin-les
s modular bootstrap in two dimensions. This method extends the conformal b
ootstrap to the regime of a large number of degrees of freedom which is re
levant to the physics of black holes in three-dimensional gravity. The sam
e method applies to the sphere packing problem and gives new bounds on the
packing density in high dimensions. I will talk about these new bounds an
d give a summary of existing bounds for these problems.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Cohn (Microsoft Research)
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/3
DESCRIPTION:Title: An introduction to sphere packing\nby Henry Cohn (M
icrosoft Research) as part of Sphere packing and the conformal bootstrap\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Simmons-Duffin (Caltech)
DTSTART:20201215T180000Z
DTEND:20201215T190000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/4
DESCRIPTION:Title: Introduction to the crossing equation in higher dimensi
onal CFTs\nby David Simmons-Duffin (Caltech) as part of Sphere packing
and the conformal bootstrap\n\n\nAbstract\nIn a continuation of Dalimil's
talk on Monday\, I will\ndiscuss the crossing equation for higher dimensi
onal CFTs and explain\nsome analytical results that have been derived from
it.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Oliveira (TU Delft)
DTSTART:20201216T150000Z
DTEND:20201216T160000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/5
DESCRIPTION:Title: A quick introduction to conic programming\nby Ferna
ndo Oliveira (TU Delft) as part of Sphere packing and the conformal bootst
rap\n\n\nAbstract\nConic programming is a general optimization framework t
hat encompasses both linear and semidefinite programming. I will give a br
ief overview of the theory of conic programming\, with an eye towards appl
ications to problems like the kissing number problem or the sphere packing
problem.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Maloney (McGill University)
DTSTART:20201216T180000Z
DTEND:20201216T190000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/6
DESCRIPTION:Title: The Siegel-Weil formula and quantum gravity as an avera
ge\nby Alex Maloney (McGill University) as part of Sphere packing and
the conformal bootstrap\n\n\nAbstract\nI will explore the idea that certai
n theories of gravity are not traditional quantum theories\, but are inste
ad averages over ensembles of quantum theories. I will consider the averag
e over free boson conformal field theories in two dimensions\, and compute
the genus g partition function using the Siegel-Weil formula. The result
is a real analytic Eisenstein series which can be interpreted as the sum o
ver geometries in a certain exotic - but in a sense exactly solvable - the
ory of quantum gravity. The techniques used are similar to those used to s
tudy high dimensional sphere packing by averaging over spaces of lattices\
, suggesting an analogy between semi-classical gravity and a theory of ran
dom lattices (or sphere packings) in high dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (NYU)
DTSTART:20201217T150000Z
DTEND:20201217T160000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/7
DESCRIPTION:Title: Microscopic description of Coulomb gases\nby Sylvia
Serfaty (NYU) as part of Sphere packing and the conformal bootstrap\n\n\n
Abstract\nI will review some results on the arrangements of systems of poi
nts with Coulomb\, logarithmic or more generally Riesz interactions (i.e.
inverse powers of the distance)\, possibly with temperature. Motivations c
ome from quantum physics\, statistical mechanics\, random matrix theory\,
approximation theory... We will take a point of view based on the detailed
expansion of the interaction energy to describe the microscopic patterns
formed by the points and local laws on the discrepancies. This allows to o
bserve the effect of the temperature as it gets very large or very small\,
and to connect with crystallization questions.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20201217T180000Z
DTEND:20201217T190000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/8
DESCRIPTION:Title: Colloquium: Sphere packings\, universal optimality\, an
d Fourier interpolation\nby Maryna Viazovska (EPFL) as part of Sphere
packing and the conformal bootstrap\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sridip Pal (IAS)
DTSTART:20201218T150000Z
DTEND:20201218T160000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/9
DESCRIPTION:Title: Modular bootstrap at high energy and Beurling-Selberg e
xtremization\nby Sridip Pal (IAS) as part of Sphere packing and the co
nformal bootstrap\n\n\nAbstract\nWe consider the universality of existence
and saturation of asymptotic bounds in various quantities in 2D conformal
field theory (CFT) . In particular\, we obtain the lower and upper bounds
on the number of operators within a high energy interval [Δ−δ\,Δ+δ]
\, of a modular invariant 2D CFT with a positive spectral density. These
bounds depend on a choice of functions that majorize and minorize the char
acteristic function of the interval [Δ−δ\,Δ+δ] and have Fourier tran
sforms of finite support. The optimization of the bounds over this choice
turns out to be exactly the Beurling-Selberg extremization problem\, widel
y known in analytic number theory. We review solutions of this problem and
present the corresponding bounds on the number of operators. When 2δ ∈
Z≥0 the bounds are saturated by known partition functions with integer-
spaced spectra. Similar results apply to operators of fixed spin and Viras
oro primaries in c > 1 theories. If time permits\, I will briefly sketch o
ver how the analysis can be generalized for asymptotics of OPE coefficient
\, possibly with some additional numerical input and for CFTs with global
symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Gonçalves (University of Bonn)
DTSTART:20201218T180000Z
DTEND:20201218T190000Z
DTSTAMP:20260404T095206Z
UID:SpherePackingAndCFT/10
DESCRIPTION:Title: Sign uncertainty\nby Felipe Gonçalves (University
of Bonn) as part of Sphere packing and the conformal bootstrap\n\n\nAbstr
act\nl will talk about the recent developments of the sign uncertainty pri
nciple and its relation with sphere packing. Time permitting we will explo
re some of the new results in [New Sign Uncertainty Principles\, arxiv.org
/abs/2003.10771].\n
LOCATION:https://stable.researchseminars.org/talk/SpherePackingAndCFT/10/
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