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BEGIN:VEVENT
SUMMARY:Joe Harris (Harvard)
DTSTART:20200504T170000Z
DTEND:20200504T183000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/1
DESCRIPTION:Title: Rationality questions in algebraic geometry\nby Joe Harr
is (Harvard) as part of Harvard CMSA Math Science Literature Lecture Serie
s\n\n\nAbstract\nOver the course of the history of algebraic geometry\, ra
tionality questions — motivated by both geometric and arithmetic problem
s — have often driven the subject forward. The rationality or irrational
ity of cubic hypersurfaces in particular have led to the development of ab
elian integrals (dimension one)\, birational geometry (dimension two) and
Hodge theory (dimension 3). But there is still much we don’t understand
about the condition of rationality — we don’t know the answer for cubi
c fourfolds\, for example\; and it’s not known whether rationality 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 current state o
f our knowledge.\n\nPlease register with the livestream link to attend.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Donaldson (Stony Brook)
DTSTART:20200504T190000Z
DTEND:20200504T203000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/2
DESCRIPTION:Title: The ADHM construction of Yang-Mills instantons\nby Simon
Donaldson (Stony Brook) as part of Harvard CMSA Math Science Literature L
ecture Series\n\n\nAbstract\nIn 1978 (Physics Letters 65A) Atiyah\, Hitchi
n\, Drinfeld and Manin (ADHM) described a construction of the general solu
tion of the Yang-Mills instanton equations over the 4-sphere using linear
algebra. This was a major landmark in the modern interaction between geome
try and physics\, and the construction has been the scene for much resea
rch activity up to the present day. In this lecture we will review the bac
kground and the original ADHM proof\, using Penrose’s twistor theory an
d results on algebraic vector bundles over projective 3-space. As time per
mits\, we will also discuss some further developments\, for example the wo
rk of Nahm on monopoles and connections to Mukai duality for bundles over
complex tori.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lydia Bieri (University of Michigan)
DTSTART:20200505T150000Z
DTEND:20200505T163000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/3
DESCRIPTION:Title: Black hole formation\nby Lydia Bieri (University of Mich
igan) as part of Harvard CMSA Math Science Literature Lecture Series\n\n\n
Abstract\nCan black holes form through the focusing of gravitational waves
? \nThis was an outstanding question since the early days of general relat
ivity. In his breakthrough result of 2008\, Demetrios Chrstodoulou answere
d this question with “Yes!” \nIn order to investigate this result\, we
will delve deeper into the dynamical mathematical structures of the Einst
ein equations. Black holes are related to the presence of trapped surfaces
in the spacetime manifold. \nChristodoulou proved that in the regime of p
ure general relativity and for arbitrarily dispersed initial data\, trappe
d surfaces form through the focusing of gravitational waves provided the i
ncoming energy is large enough in a precisely defined way. The proof combi
nes new ideas from geometric analysis and nonlinear partial differential e
quations as well as it introduces new methods to solve large data problems
. These methods have many applications beyond general relativity. D. Chris
todoulou’s result was generalized in various directions by many authors.
It launched mathematical activities going into multiple fields in mathema
tics and physics. In this talk\, we will discuss the mathematical framewor
k of the above question. Then we will outline the main ideas of Christodou
lou’s result and its generalizations\, show relations to other questions
and give an overview of implications in other fields.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20200505T190000Z
DTEND:20200505T203000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/4
DESCRIPTION:Title: Quantum groups\nby Pavel Etingof (MIT) as part of Harvar
d CMSA Math Science Literature Lecture Series\n\n\nAbstract\nThe theory of
quantum groups developed in mid 1980s from attempts to construct and unde
rstand solutions of the quantum Yang-Baxter equation\, an important equati
on 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 program\, l
ow-dimensional topology\, category theory\, enumerative geometry\, quantum
computation\, algebraic combinatorics\, conformal field theory\, integrab
le systems\, integrable probability\, and others. I will review some of th
e main ideas and examples of quantum groups and try to briefly describe so
me of the applications.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Griess (University of Michigan)
DTSTART:20200506T170000Z
DTEND:20200506T183000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/5
DESCRIPTION:Title: My life and times with the sporadic simple groups\nby Ro
bert Griess (University of Michigan) as part of Harvard CMSA Math Science
Literature Lecture Series\n\n\nAbstract\nFive sporadic simple groups were
proposed in 19th century and 21 additional ones arose during the period 19
65-1975. There were many discussions about the nature of finite simple gro
ups and how sporadic groups are placed in mathematics. While in mathematic
s grad school at University of Chicago\, I became fascinated with the unf
olding story of sporadic simple groups. It involved theory\, detective wor
k and experiments. During this lecture\, I will describe some of the peopl
e\, important ideas and evolution of thinking about sporadic simple groups
. Most should be accessible to a general mathematical audience.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bong Lian (Brandeis/CMSA)
DTSTART:20200522T180000Z
DTEND:20200522T193000Z
DTSTAMP:20260422T212555Z
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 Literature
Lecture Series\n\n\nAbstract\nThis is a brief survey of the early historic
al development of vertex algebras\, beginning in the seventies from Physic
s and Representation Theory. We shall also discuss some of the ideas that
led to various early formulations of the theory’s foundation\, and their
relationships\, as well as some of the subsequent and recent developments
. The lecture is aimed for a general audience.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciprian Manolescu (Stanford)
DTSTART:20200522T163000Z
DTEND:20200522T173000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/7
DESCRIPTION:Title: Four dimensional topology\nby Ciprian Manolescu (Stanfor
d) as part of Harvard CMSA Math Science Literature Lecture Series\n\n\nAbs
tract\nI will outline the history of four-dimensional topology. Some major
events were the work of Donaldson and Freedman from 1982\, and the introd
uction of the Seiberg-Witten equations in 1994. I will discuss these\, 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 homology has
led to numerous applications\, and recently there have also been a few no
vel results (and proofs of old results) using Khovanov homology. The talk
will be accessible to a general mathematical audience.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS)
DTSTART:20200925T173000Z
DTEND:20200925T190000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Jacob Neven Looijenga (Utrecht University)
DTSTART:20201125T140000Z
DTEND:20201125T153000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/9
DESCRIPTION:Title: Theorems of Torelli type\nby Eduard Jacob Neven Looijeng
a (Utrecht University) as part of Harvard CMSA Math Science Literature Lec
ture Series\n\n\nAbstract\nAbstract: Given a closed manifold of even dimen
sion 2n\, then Hodge showed around 1950 that a kählerian complex structu
re on that manifold determines a decomposition of its complex cohomology
. This decomposition\, which can potentially vary continuously with the
complex structure\, extracts from a non-linear given\, linear data. It ca
n contain a lot of information. When there is essentially no loss of data
in this process\, we say that the Torelli theorem holds. We review the
underlying theory and then survey some cases where this is the case. This
will include the classical case n=1\, but the emphasis will be on K3 mani
folds (n=2) and more generally\, on hyperkählerian manifolds. These cases
stand out\, since one can then also tell which decompositions occur.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Jaffe (Harvard University)
DTSTART:20201202T130000Z
DTEND:20201202T143000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/10
DESCRIPTION:Title: Is relativity compatible with quantum theory?\nby Arthu
r Jaffe (Harvard University) as part of Harvard CMSA Math Science Literatu
re Lecture Series\n\n\nAbstract\nAbstract: We review the background\, math
ematical progress\, and open questions in the effort to determine whether
one can combine quantum mechanics\, special relativity\, and interaction t
ogether into one mathematical theory. This field of mathematics is known a
s “constructive quantum field theory.” Physicists believe that such a
theory describes experimental measurements made over a 70 year period and
now refined to 13-decimal-point precision—the most accurate experiments
ever performed.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nigel Hitchin (University of Oxford)
DTSTART:20201204T130000Z
DTEND:20201204T143000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/11
DESCRIPTION:Title: Michael Atiyah: Geometry and Physics\nby Nigel Hitchin
(University of Oxford) as part of Harvard CMSA Math Science Literature Lec
ture Series\n\n\nAbstract\nAbstract: In mid career\, as an internationally
renowned mathematician\, Michael Atiyah discovered that some problems in
physics responded to current work in algebraic geometry and this set him o
n a path to develop an active interface between mathematics and physics wh
ich was formative in the links which are so active today. The talk will fo
cus\, in a fairly basic fashion\, on some examples of this interaction\, w
hich involved both applying physical ideas to solve mathematical problems
and introducing mathematical ideas to physicists.\n
LOCATION:https://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:20260422T212555Z
UID:MathScienceLiterature/13
DESCRIPTION:Title: Quantum topology and new types of modularity\nby Don Za
gier (Max Planck Institute for Mathematics and International Centre for T
heoretical Physics) as part of Harvard CMSA Math Science Literature Lectur
e Series\n\n\nAbstract\nThe talk concerns two fundamental themes of modern
3-dimensional topology and their unexpected connection with a theme comin
g 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 mor
e generally of 3-manifolds\, have a unique metric structure as hyperbolic
manifolds of constant curvature -1\, so that 3-dimensional topology is in
some sense not really a branch of topology at all\, but of differential ge
ometry. 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 n
ew types of invariants of knot complements and 3-manifolds are introduced
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 hyperb
olic knot K (this is a quantum invariant defined for each positive integer
N and whose values are algebraic numbers) grows exponentially as N te
nds to infinity with an exponent proportional to the hyperbolic volume of
the knot complement. About 10 years ago\, I was led by numerical experime
nts to the discovery that Kashaev's invariant could be upgraded to an inva
riant having rational numbers as its argument (with the original invariant
being the value at 1/N) and that the Volume Conjecture then became part o
f a bigger story saying that the new invariant has some sort of strange tr
ansformation property under the action x -> (ax+b)/(cx+d) of the modular
group SL(2\,Z) on the argument. This turned out to be only the beginnin
g of a fascinating and multi-faceted story relating quantum invariants\, q
-series\, modularity\, and many other topics. In the talk\, which is inten
ded for a general mathematical audience\, I would like to recount some par
ts of this story\, which is joint work with Stavros Garoufalidis (and of c
ourse involving contributions from many other authors). The "new types of
modularity" in the title refer to a specific byproduct of these investigat
ions\, namely that there is a generalization of the classical notion of ho
lomorphic modular form - which plays an absolutely central role in modern
number theory - to a new class of holomorphic functions in the upper half-
plane that no longer satisfy a transformation law under the action of the
modular group\, but a weaker extendability property instead. This new cl
ass\, called "holomorphic quantum modular forms"\, turns out to contain ma
ny other functions of a more number-theoretical nature as well as the orig
inal examples coming from quantum invariants.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Spielman (Yale University)
DTSTART:20210128T020000Z
DTEND:20210128T033000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/14
DESCRIPTION:Title: Discrepancy Theory and Randomized Controlled Trials\nby
Dan Spielman (Yale University) as part of Harvard CMSA Math Science Liter
ature Lecture Series\n\n\nAbstract\nDiscrepancy theory tells us that it is
possible to partition vectors into sets so that each set looks surprising
ly similar to every other. By “surprisingly similar” we mean much mor
e similar than a random partition. I will begin by surveying fundamental r
esults in discrepancy theory\, including Spencer’s famous existence proo
fs and Bansal’s recent algorithmic realizations of them.\n\nRandomized C
ontrolled Trials are used to test the effectiveness of interventions\, lik
e medical treatments. Randomization is used to ensure that the test and c
ontrol groups are probably similar. When we know nothing about the experi
mental subjects\, uniform random assignment is the best we can do.\n\nWhen
we know information about the experimental subjects\, called covariates\,
we can combine the strengths of randomization with the promises of discre
pancy theory. This should allow us to obtain more accurate estimates of t
he effectiveness of treatments\, or to conduct trials with fewer experimen
tal subjects.\n\nI will introduce the Gram-Schmidt Walk algorithm of Bansa
l\, Dadush\, Garg\, and Lovett\, which produces random solutions to discre
pancy problems. I will then explain how Chris Harshaw\, Fredrik Sävje\, P
eng Zhang and I use this algorithm to improve the design of randomized con
trolled trials. Our Gram-Schmidt Walk Designs have increased accuracy when
the experimental outcomes are correlated with linear functions of the cov
ariates\, and are comparable to uniform random assignments in the worst ca
se.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Fukaya (Simons Center for Geometry and Physics)
DTSTART:20210223T140000Z
DTEND:20210223T153000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/15
DESCRIPTION:Title: Homological (homotopical) algebra and moduli spaces in Topo
logical Field theories\nby Kenji Fukaya (Simons Center for Geometry an
d Physics) as part of Harvard CMSA Math Science Literature Lecture Series\
n\n\nAbstract\nModuli spaces of various gauge theory equations and of vari
ous versions of (pseudo) holomorphic curve equations have played important
role in geometry in these 40 years. Started with Floer's work people star
t to obtain more sophisticated object such as groups\, rings\, or categori
es from (system of) moduli spaces. I would like to survey some of those wo
rks and the methods to study family of moduli spaces systematically.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART:20210330T130000Z
DTEND:20210330T143000Z
DTSTAMP:20260422T212555Z
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 Sc
ience Literature Lecture Series\n\n\nAbstract\nAbout 30 years ago\, string
theorists made remarkable discoveries of hidden structures in algebraic g
eometry. First\, the usual cup-product on the cohomology of a complex pro
jective variety admits a canonical multi-parameter deformation to so-calle
d quantum product\, satisfying a nice system of differential equations (WD
VV equations). The second discovery\, even more striking\, is Mirror Sym
metry\, a duality between families of Calabi-Yau varieties acting as a mir
ror reflection on the Hodge diamond.\n\n Later it was realized that the qu
antum product belongs to the realm of symplectic geometry\, and a half of
mirror symmetry (called Homological Mirror Symmetry) is a duality between
complex algebraic and symplectic varieties. The search of correct definiti
ons and possible generalizations lead to great advances in many domains\,
giving mathematicians new glasses\, through which they can see familiar ob
jects in a completely new way.\n \nI will review the history of major math
ematical advances in the subject of HMS\, and the swirl of ideas around it
.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (IAS)
DTSTART:20210406T130000Z
DTEND:20210406T143000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Shor (MIT)
DTSTART:20210408T130000Z
DTEND:20210408T143000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Voisin (Collège de France)
DTSTART:20210413T130000Z
DTEND:20210413T143000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Ma (University of California\, Berkeley)
DTSTART:20210416T170000Z
DTEND:20210416T183000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/20
DESCRIPTION:Title: Deep Networks from First Principles\nby Yi Ma (Universi
ty of California\, Berkeley) as part of Harvard CMSA Math Science Literatu
re Lecture Series\n\n\nAbstract\nIn this talk\, we offer an entirely “wh
ite box’’ interpretation of deep (convolution) networks from the persp
ective of data compression (and group invariance). In particular\, we show
how modern deep layered architectures\, linear (convolution) operators an
d nonlinear activations\, and even all parameters can be derived from the
principle of maximizing rate reduction (with group invariance). All layers
\, operators\, and parameters of the network are explicitly constructed vi
a forward propagation\, instead of learned via back propagation. All compo
nents of so-obtained network\, called ReduNet\, have precise optimization\
, geometric\, and statistical interpretation. There are also several nice
surprises from this principled approach: it reveals a fundamental tradeoff
between invariance and sparsity for class separability\; it reveals a fun
damental connection between deep networks and Fourier transform for group
invariance – the computational advantage in the spectral domain (why spi
king neurons?)\; this approach also clarifies the mathematical role of for
ward propagation (optimization) and backward propagation (variation). In p
articular\, the so-obtained ReduNet is amenable to fine-tuning via both fo
rward and backward (stochastic) propagation\, both for optimizing the same
objective. This is joint work with students Yaodong Yu\, Ryan Chan\, Haoz
hi Qi of Berkeley\, Dr. Chong You now at Google Research\, and Professor J
ohn Wright of Columbia University.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Freed (University of Texas at Austin)
DTSTART:20210420T130000Z
DTEND:20210420T143000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20210427T130000Z
DTEND:20210427T143000Z
DTSTAMP:20260422T212555Z
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://researchseminars.org/talk/MathScienceLiterature/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiu Klainerman (Princeton University)
DTSTART:20210615T150000Z
DTEND:20210615T173000Z
DTSTAMP:20260422T212555Z
UID:MathScienceLiterature/23
DESCRIPTION:Title: Nonlinear stability of Kerr black holes for small angular m
omentum\nby Sergiu Klainerman (Princeton University) as part of Harvar
d CMSA Math Science Literature Lecture Series\n\n\nAbstract\nAccording to
a well-known conjecture\, initial data sets\, for the Einstein vacuum eq
uations\, sufficiently close to a Kerr solution with parameters $a\, m$\,
$|a|/m <1$\, have maximal developments with complete future null infinity
and with domain of outer communication (i.e complement of a future event h
orizon) which approaches (globally) a nearby Kerr solution.\n\nI will
describe the main ideas in my recent joint work with Jeremie Szeftel conce
rning the resolution of the conjecture for small angular momentum\, i.e. $
\, $|a|/m $ sufficiently small. The work\, ArXiv:2104.11857v1\, also depe
nds on forthcoming work on solutions of nonlinear wave equations in realis
tic perturbations of Kerr\, with Szeftel and Elena Giorgi\, which I will
also describe.\n
LOCATION:https://researchseminars.org/talk/MathScienceLiterature/23/
END:VEVENT
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