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BEGIN:VEVENT
SUMMARY:Joe Harris (Harvard)
DTSTART:20200504T170000Z
DTEND:20200504T183000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/1
DESCRIPTION:Title: Rationality questions in algebraic geometry\nby J
oe Harris (Harvard) as part of Harvard CMSA Math Science Literature Lectur
e Series\n\n\nAbstract\nOver the course of the history of algebraic geomet
ry\, rationality questions — motivated by both geometric and arithmetic
problems — have often driven the subject forward. The rationality or irr
ationality of cubic hypersurfaces in particular have led to the developmen
t of abelian integrals (dimension one)\, birational geometry (dimension tw
o) and Hodge theory (dimension 3). But there is still much we don’t unde
rstand about the condition of rationality — we don’t know the answer f
or cubic fourfolds\, for example\; and it’s not known whether rationalit
y is an open condition or a closed condition in families. In this talk I
’ll try to give an overview of the history of rationality and the curren
t state of our knowledge.\n\nPlease register with the livestream link to a
ttend.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Donaldson (Stony Brook)
DTSTART:20200504T190000Z
DTEND:20200504T203000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/2
DESCRIPTION:Title: The ADHM construction of Yang-Mills instantons\nb
y Simon Donaldson (Stony Brook) as part of Harvard CMSA Math Science Liter
ature Lecture Series\n\n\nAbstract\nIn 1978 (Physics Letters 65A) Atiyah\,
Hitchin\, Drinfeld and Manin (ADHM) described a construction of the gener
al solution of the Yang-Mills instanton equations over the 4-sphere using
linear algebra. This was a major landmark in the modern interaction betwee
n geometry and physics\, and the construction has been the scene for much
research activity up to the present day. In this lecture we will review
the background and the original ADHM proof\, using Penrose’s twistor th
eory and results on algebraic vector bundles over projective 3-space. As t
ime permits\, we will also discuss some further developments\, for example
the work of Nahm on monopoles and connections to Mukai duality for bundle
s over complex tori.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lydia Bieri (University of Michigan)
DTSTART:20200505T150000Z
DTEND:20200505T163000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/3
DESCRIPTION:Title: Black hole formation\nby Lydia Bieri (University
of Michigan) as part of Harvard CMSA Math Science Literature Lecture Serie
s\n\n\nAbstract\nCan black holes form through the focusing of gravitationa
l waves? \nThis was an outstanding question since the early days of genera
l relativity. In his breakthrough result of 2008\, Demetrios Chrstodoulou
answered this question with “Yes!” \nIn order to investigate this resu
lt\, we will delve deeper into the dynamical mathematical structures of th
e Einstein equations. Black holes are related to the presence of trapped s
urfaces in the spacetime manifold. \nChristodoulou proved that in the regi
me of pure general relativity and for arbitrarily dispersed initial data\,
trapped surfaces form through the focusing of gravitational waves provide
d the incoming energy is large enough in a precisely defined way. The proo
f combines new ideas from geometric analysis and nonlinear partial differe
ntial equations as well as it introduces new methods to solve large data p
roblems. These methods have many applications beyond general relativity. D
. Christodoulou’s result was generalized in various directions by many a
uthors. It launched mathematical activities going into multiple fields in
mathematics and physics. In this talk\, we will discuss the mathematical f
ramework of the above question. Then we will outline the main ideas of Chr
istodoulou’s result and its generalizations\, show relations to other qu
estions and give an overview of implications in other fields.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20200505T190000Z
DTEND:20200505T203000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/4
DESCRIPTION:Title: Quantum groups\nby Pavel Etingof (MIT) as part of
Harvard CMSA Math Science Literature Lecture Series\n\n\nAbstract\nThe th
eory of quantum groups developed in mid 1980s from attempts to construct a
nd understand solutions of the quantum Yang-Baxter equation\, an important
equation arising in quantum field theory and statistical mechanics. Since
then\, it has grown into a vast subject with profound connections to many
areas of mathematics\, such as representation theory\, the Langlands prog
ram\, low-dimensional topology\, category theory\, enumerative geometry\,
quantum computation\, algebraic combinatorics\, conformal field theory\, i
ntegrable systems\, integrable probability\, and others. I will review som
e of the main ideas and examples of quantum groups and try to briefly desc
ribe some of the applications.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Griess (University of Michigan)
DTSTART:20200506T170000Z
DTEND:20200506T183000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/5
DESCRIPTION:Title: My life and times with the sporadic simple groups
\nby Robert Griess (University of Michigan) as part of Harvard CMSA Math S
cience Literature Lecture Series\n\n\nAbstract\nFive sporadic simple group
s were proposed in 19th century and 21 additional ones arose during the pe
riod 1965-1975. There were many discussions about the nature of finite sim
ple groups and how sporadic groups are placed in mathematics. While in mat
hematics grad school at University of Chicago\, I became fascinated with
the unfolding story of sporadic simple groups. It involved theory\, detect
ive work and experiments. During this lecture\, I will describe some of th
e people\, important ideas and evolution of thinking about sporadic simple
groups. Most should be accessible to a general mathematical audience.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bong Lian (Brandeis/CMSA)
DTSTART:20200522T180000Z
DTEND:20200522T193000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/6
DESCRIPTION:Title: From string theory and Moonshine to vertex algebras\nby Bong Lian (Brandeis/CMSA) as part of Harvard CMSA Math Science Lite
rature Lecture Series\n\n\nAbstract\nThis is a brief survey of the early h
istorical development of vertex algebras\, beginning in the seventies from
Physics and Representation Theory. We shall also discuss some of the idea
s that led to various early formulations of the theory’s foundation\, an
d their relationships\, as well as some of the subsequent and recent devel
opments. The lecture is aimed for a general audience.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciprian Manolescu (Stanford)
DTSTART:20200522T163000Z
DTEND:20200522T173000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/7
DESCRIPTION:Title: Four dimensional topology\nby Ciprian Manolescu (
Stanford) as part of Harvard CMSA Math Science Literature Lecture Series\n
\n\nAbstract\nI will outline the history of four-dimensional topology. Som
e major events were the work of Donaldson and Freedman from 1982\, and the
introduction of the Seiberg-Witten equations in 1994. I will discuss thes
e\, and then move on to what has been done in the last 20 years\, when the
focus shifted to four-manifolds with boundary and cobordisms. Floer homol
ogy has led to numerous applications\, and recently there have also been a
few novel results (and proofs of old results) using Khovanov homology. Th
e talk will be accessible to a general mathematical audience.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS)
DTSTART:20200925T173000Z
DTEND:20200925T190000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/8
DESCRIPTION:by Camillo De Lellis (IAS) as part of Harvard CMSA Math Scienc
e Literature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Jacob Neven Looijenga (Utrecht University)
DTSTART:20201125T140000Z
DTEND:20201125T153000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/9
DESCRIPTION:Title: Theorems of Torelli type\nby Eduard Jacob Neven L
ooijenga (Utrecht University) as part of Harvard CMSA Math Science Literat
ure Lecture Series\n\n\nAbstract\nAbstract: Given a closed manifold of eve
n dimension 2n\, then Hodge showed around 1950 that a kählerian complex
structure on that manifold determines a decomposition of its complex coh
omology. This decomposition\, which can potentially vary continuously wi
th the complex structure\, extracts from a non-linear given\, linear data
. It can contain a lot of information. When there is essentially no loss
of data in this process\, we say that the Torelli theorem holds. We revi
ew the underlying theory and then survey some cases where this is the cas
e. This will include the classical case n=1\, but the emphasis will be on
K3 manifolds (n=2) and more generally\, on hyperkählerian manifolds. Thes
e cases stand out\, since one can then also tell which decompositions occu
r.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Jaffe (Harvard University)
DTSTART:20201202T130000Z
DTEND:20201202T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/10
DESCRIPTION:Title: Is relativity compatible with quantum theory?\nb
y Arthur Jaffe (Harvard University) as part of Harvard CMSA Math Science L
iterature Lecture Series\n\n\nAbstract\nAbstract: We review the background
\, mathematical progress\, and open questions in the effort to determine w
hether one can combine quantum mechanics\, special relativity\, and intera
ction together into one mathematical theory. This field of mathematics is
known as “constructive quantum field theory.” Physicists believe that
such a theory describes experimental measurements made over a 70 year per
iod and now refined to 13-decimal-point precision—the most accurate expe
riments ever performed.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/10
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nigel Hitchin (University of Oxford)
DTSTART:20201204T130000Z
DTEND:20201204T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/11
DESCRIPTION:Title: Michael Atiyah: Geometry and Physics\nby Nigel H
itchin (University of Oxford) as part of Harvard CMSA Math Science Literat
ure Lecture Series\n\n\nAbstract\nAbstract: In mid career\, as an internat
ionally renowned mathematician\, Michael Atiyah discovered that some probl
ems in physics responded to current work in algebraic geometry and this se
t him on a path to develop an active interface between mathematics and phy
sics which was formative in the links which are so active today. The talk
will focus\, in a fairly basic fashion\, on some examples of this interact
ion\, which involved both applying physical ideas to solve mathematical pr
oblems and introducing mathematical ideas to physicists.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/11
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Don Zagier (Max Planck Institute for Mathematics and Internationa
l Centre for Theoretical Physics)
DTSTART:20210113T140000Z
DTEND:20210113T153000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/13
DESCRIPTION:Title: Quantum topology and new types of modularity\nby
Don Zagier (Max Planck Institute for Mathematics and International Centr
e for Theoretical Physics) as part of Harvard CMSA Math Science Literature
Lecture Series\n\n\nAbstract\nThe talk concerns two fundamental themes of
modern 3-dimensional topology and their unexpected connection with a them
e coming from number theory. A deep insight of William Thurston in the mid
-1970s is that the vast majority of complements of knots in the 3-sphere\,
or more generally of 3-manifolds\, have a unique metric structure as hype
rbolic manifolds of constant curvature -1\, so that 3-dimensional topology
is in some sense not really a branch of topology at all\, but of differen
tial geometry. In a different direction\, the work of Vaughan Jones and Ed
Witten in the late 1980s gave rise to the field of Quantum Topology\, in
which new types of invariants of knot complements and 3-manifolds are intr
oduced that have their origins in ideas coming from quantum field theory.
These two themes then became linked by Kashaev's famous Volume Conjecture
\, now some 25 years old\, which says that the Kashaev invariant _N of a
hyperbolic knot K (this is a quantum invariant defined for each positive
integer N and whose values are algebraic numbers) grows exponentially as
N tends to infinity with an exponent proportional to the hyperbolic vo
lume of the knot complement. About 10 years ago\, I was led by numerical e
xperiments to the discovery that Kashaev's invariant could be upgraded to
an invariant having rational numbers as its argument (with the original in
variant being the value at 1/N) and that the Volume Conjecture then became
part of a bigger story saying that the new invariant has some sort of str
ange transformation property under the action x -> (ax+b)/(cx+d) of the m
odular group SL(2\,Z) on the argument. This turned out to be only the b
eginning of a fascinating and multi-faceted story relating quantum invaria
nts\, q-series\, modularity\, and many other topics. In the talk\, which i
s intended for a general mathematical audience\, I would like to recount s
ome parts of this story\, which is joint work with Stavros Garoufalidis (a
nd of course involving contributions from many other authors). The "new ty
pes of modularity" in the title refer to a specific byproduct of these inv
estigations\, namely that there is a generalization of the classical notio
n of holomorphic modular form - which plays an absolutely central role in
modern number theory - to a new class of holomorphic functions in the uppe
r half-plane that no longer satisfy a transformation law under the action
of the modular group\, but a weaker extendability property instead. This
new class\, called "holomorphic quantum modular forms"\, turns out to con
tain many other functions of a more number-theoretical nature as well as t
he original examples coming from quantum invariants.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/13
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Spielman (Yale University)
DTSTART:20210128T020000Z
DTEND:20210128T033000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/14
DESCRIPTION:Title: Discrepancy Theory and Randomized Controlled Trials<
/a>\nby Dan Spielman (Yale University) as part of Harvard CMSA Math Scienc
e Literature Lecture Series\n\n\nAbstract\nDiscrepancy theory tells us tha
t it is possible to partition vectors into sets so that each set looks sur
prisingly similar to every other. By “surprisingly similar” we mean m
uch more similar than a random partition. I will begin by surveying fundam
ental results in discrepancy theory\, including Spencer’s famous existen
ce proofs and Bansal’s recent algorithmic realizations of them.\n\nRando
mized Controlled Trials are used to test the effectiveness of intervention
s\, like medical treatments. Randomization is used to ensure that the tes
t and control groups are probably similar. When we know nothing about the
experimental subjects\, uniform random assignment is the best we can do.\
n\nWhen we know information about the experimental subjects\, called covar
iates\, we can combine the strengths of randomization with the promises of
discrepancy theory. This should allow us to obtain more accurate estimat
es of the effectiveness of treatments\, or to conduct trials with fewer ex
perimental subjects.\n\nI will introduce the Gram-Schmidt Walk algorithm o
f Bansal\, Dadush\, Garg\, and Lovett\, which produces random solutions to
discrepancy problems. I will then explain how Chris Harshaw\, Fredrik Sä
vje\, Peng Zhang and I use this algorithm to improve the design of randomi
zed controlled trials. Our Gram-Schmidt Walk Designs have increased accura
cy when the experimental outcomes are correlated with linear functions of
the covariates\, and are comparable to uniform random assignments in the w
orst case.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/14
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya (Simons Center for Geometry and Physics)
DTSTART:20210223T140000Z
DTEND:20210223T153000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/15
DESCRIPTION:Title: Homological (homotopical) algebra and moduli spaces
in Topological Field theories\nby Kenji Fukaya (Simons Center for Geom
etry and Physics) as part of Harvard CMSA Math Science Literature Lecture
Series\n\n\nAbstract\nModuli spaces of various gauge theory equations and
of various versions of (pseudo) holomorphic curve equations have played im
portant role in geometry in these 40 years. Started with Floer's work peop
le start to obtain more sophisticated object such as groups\, rings\, or c
ategories from (system of) moduli spaces. I would like to survey some of t
hose works and the methods to study family of moduli spaces systematically
.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/15
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART:20210330T130000Z
DTEND:20210330T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/16
DESCRIPTION:Title: On the History of quantum cohomology and homological
mirror symmetry\nby Maxim Kontsevich (IHÉS) as part of Harvard CMSA
Math Science Literature Lecture Series\n\n\nAbstract\nAbout 30 years ago\,
string theorists made remarkable discoveries of hidden structures in alge
braic geometry. First\, the usual cup-product on the cohomology of a comp
lex projective variety admits a canonical multi-parameter deformation to s
o-called quantum product\, satisfying a nice system of differential equati
ons (WDVV equations). The second discovery\, even more striking\, is Mir
ror Symmetry\, a duality between families of Calabi-Yau varieties acting a
s a mirror reflection on the Hodge diamond.\n\n Later it was realized that
the quantum product belongs to the realm of symplectic geometry\, and a h
alf of mirror symmetry (called Homological Mirror Symmetry) is a duality b
etween complex algebraic and symplectic varieties. The search of correct d
efinitions and possible generalizations lead to great advances in many dom
ains\, giving mathematicians new glasses\, through which they can see fami
liar objects in a completely new way.\n \nI will review the history of maj
or mathematical advances in the subject of HMS\, and the swirl of ideas ar
ound it.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/16
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (IAS)
DTSTART:20210406T130000Z
DTEND:20210406T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/17
DESCRIPTION:by Edward Witten (IAS) as part of Harvard CMSA Math Science Li
terature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/17
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Shor (MIT)
DTSTART:20210408T130000Z
DTEND:20210408T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/18
DESCRIPTION:by Peter Shor (MIT) as part of Harvard CMSA Math Science Liter
ature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/18
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Voisin (Collège de France)
DTSTART:20210413T130000Z
DTEND:20210413T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/19
DESCRIPTION:by Claire Voisin (Collège de France) as part of Harvard CMSA
Math Science Literature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/19
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Ma (University of California\, Berkeley)
DTSTART:20210416T170000Z
DTEND:20210416T183000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/20
DESCRIPTION:Title: Deep Networks from First Principles\nby Yi Ma (U
niversity of California\, Berkeley) as part of Harvard CMSA Math Science L
iterature Lecture Series\n\n\nAbstract\nIn this talk\, we offer an entirel
y “white box’’ interpretation of deep (convolution) networks from th
e perspective of data compression (and group invariance). In particular\,
we show how modern deep layered architectures\, linear (convolution) opera
tors and nonlinear activations\, and even all parameters can be derived fr
om the principle of maximizing rate reduction (with group invariance). All
layers\, operators\, and parameters of the network are explicitly constru
cted via forward propagation\, instead of learned via back propagation. Al
l components of so-obtained network\, called ReduNet\, have precise optimi
zation\, geometric\, and statistical interpretation. There are also severa
l nice surprises from this principled approach: it reveals a fundamental t
radeoff between invariance and sparsity for class separability\; it reveal
s a fundamental connection between deep networks and Fourier transform for
group invariance – the computational advantage in the spectral domain (
why spiking neurons?)\; this approach also clarifies the mathematical role
of forward propagation (optimization) and backward propagation (variation
). In particular\, the so-obtained ReduNet is amenable to fine-tuning via
both forward and backward (stochastic) propagation\, both for optimizing t
he same objective. This is joint work with students Yaodong Yu\, Ryan Chan
\, Haozhi Qi of Berkeley\, Dr. Chong You now at Google Research\, and Prof
essor John Wright of Columbia University.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/20
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Freed (University of Texas at Austin)
DTSTART:20210420T130000Z
DTEND:20210420T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/21
DESCRIPTION:by Dan Freed (University of Texas at Austin) as part of Harvar
d CMSA Math Science Literature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/21
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20210427T130000Z
DTEND:20210427T143000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/22
DESCRIPTION:by Frances Kirwan (University of Oxford) as part of Harvard CM
SA Math Science Literature Lecture Series\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/22
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiu Klainerman (Princeton University)
DTSTART:20210615T150000Z
DTEND:20210615T173000Z
DTSTAMP:20260404T095208Z
UID:MathScienceLiterature/23
DESCRIPTION:Title: Nonlinear stability of Kerr black holes for small an
gular momentum\nby Sergiu Klainerman (Princeton University) as part of
Harvard CMSA Math Science Literature Lecture Series\n\n\nAbstract\nAccord
ing to a well-known conjecture\, initial data sets\, for the Einstein va
cuum equations\, sufficiently close to a Kerr solution with parameters $a\
, m$\, $|a|/m <1$\, have maximal developments with complete future null in
finity and with domain of outer communication (i.e complement of a future
event horizon) which approaches (globally) a nearby Kerr solution.\n\n
I will describe the main ideas in my recent joint work with Jeremie Szefte
l concerning the resolution of the conjecture for small angular momentum\,
i.e. $\, $|a|/m $ sufficiently small. The work\, ArXiv:2104.11857v1\, al
so depends on forthcoming work on solutions of nonlinear wave equations in
realistic perturbations of Kerr\, with Szeftel and Elena Giorgi\, which
I will also describe.\n
LOCATION:https://stable.researchseminars.org/talk/MathScienceLiterature/23
/
END:VEVENT
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