BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200428T160000Z
DTEND:20200428T170000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/1
DESCRIPTION:Title: Geometric stochastic PDEs\nby Martin Hairer (Imperia
l College London) as part of UCLA distinguished lecture series\n\nLecture
held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nWe review Parisi a
nd Wu's stochastic quantisation procedure and apply it to the non-linear s
igma model as well as the Yang-Mills model. We then review a number of rec
ent results on the resulting equations. In particular\, this sheds some ne
w light on an old controversy regarding the interpretation of path integra
ls.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200429T160000Z
DTEND:20200429T170000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/2
DESCRIPTION:Title: Introduction to regularity structures 1\nby Martin H
airer (Imperial College London) as part of UCLA distinguished lecture seri
es\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nI wi
ll give an introduction to the main concepts behind the theory of regulari
ty structures which allows to give meaning to many stochastic PDEs that we
re previously thought to be ill-posed. This combines some of the insights
and tools from (perturbative) QFT with classical PDE theory.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200430T160000Z
DTEND:20200430T170000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/3
DESCRIPTION:Title: Introduction to regularity structures 2\nby Martin H
airer (Imperial College London) as part of UCLA distinguished lecture seri
es\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nI wi
ll give an introduction to the main concepts behind the theory of regulari
ty structures which allows to give meaning to many stochastic PDEs that we
re previously thought to be ill-posed. This combines some of the insights
and tools from (perturbative) QFT with classical PDE theory.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200512T220000Z
DTEND:20200512T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/4
DESCRIPTION:Title: Knot categorification from mirror symmetry\, I\nby M
ina Aganagic (UC Berkeley) as part of UCLA distinguished lecture series\n\
nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nIn the se
ries of lectures\, I will describe two approaches to categorifying quantum
link invariants which work uniformly for all simple Lie algebras\, and or
iginate from geometry and from string theory. Many ingredients that go int
o the story have been found by mathematicians earlier\, but physics spells
out how they should be put together for a uniform framework for the knot
categorification problem. One of the important aspects of both approaches
is that the fact that decategorification gives the quantum link invariants
one set out to categorify\, becomes manifest. \n\nThe first approach is b
ased on derived categories of coherent sheaves on resolutions of slices in
affine Grassmannians. While some elements of it are familiar to mathemati
cians\, others are new. The second approach is perhaps more surprising. It
uses symplectic geometry and is related to the first by two dimensional (
equivariant) mirror symmetry. Unlike previous symplectic geometry based ap
proaches\, it produces a bi-graded homology theory. In both cases\, mirror
symmetry\, and techniques developed by physicists and mathematicians to u
nderstand it play a crucial role. I will also explain the relation to anot
her string theory based approach\, due to Witten.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200513T220000Z
DTEND:20200513T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/5
DESCRIPTION:Title: Knot categorification from mirror symmetry\, II\nby
Mina Aganagic (UC Berkeley) as part of UCLA distinguished lecture series\n
\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nIn the s
eries of lectures\, I will describe two approaches to categorifying quantu
m link invariants which work uniformly for all simple Lie algebras\, and o
riginate from geometry and from string theory. Many ingredients that go in
to the story have been found by mathematicians earlier\, but physics spell
s out how they should be put together for a uniform framework for the knot
categorification problem. One of the important aspects of both approaches
is that the fact that decategorification gives the quantum link invariant
s one set out to categorify\, becomes manifest. \n\nThe first approach is
based on derived categories of coherent sheaves on resolutions of slices i
n affine Grassmannians. While some elements of it are familiar to mathemat
icians\, others are new. The second approach is perhaps more surprising. I
t uses symplectic geometry and is related to the first by two dimensional
(equivariant) mirror symmetry. Unlike previous symplectic geometry based a
pproaches\, it produces a bi-graded homology theory. In both cases\, mirro
r symmetry\, and techniques developed by physicists and mathematicians to
understand it play a crucial role. I will also explain the relation to ano
ther string theory based approach\, due to Witten.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200514T220000Z
DTEND:20200514T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/6
DESCRIPTION:Title: Knot categorification from mirror symmetry\, III\nby
Mina Aganagic (UC Berkeley) as part of UCLA distinguished lecture series\
n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nIn the
series of lectures\, I will describe two approaches to categorifying quant
um link invariants which work uniformly for all simple Lie algebras\, and
originate from geometry and from string theory. Many ingredients that go i
nto the story have been found by mathematicians earlier\, but physics spel
ls out how they should be put together for a uniform framework for the kno
t categorification problem. One of the important aspects of both approache
s is that the fact that decategorification gives the quantum link invarian
ts one set out to categorify\, becomes manifest. \n\nThe first approach is
based on derived categories of coherent sheaves on resolutions of slices
in affine Grassmannians. While some elements of it are familiar to mathema
ticians\, others are new. The second approach is perhaps more surprising.
It uses symplectic geometry and is related to the first by two dimensional
(equivariant) mirror symmetry. Unlike previous symplectic geometry based
approaches\, it produces a bi-graded homology theory. In both cases\, mirr
or symmetry\, and techniques developed by physicists and mathematicians to
understand it play a crucial role. I will also explain the relation to an
other string theory based approach\, due to Witten.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anima Anandkumar (Caltech)
DTSTART:20220413T220000Z
DTEND:20220413T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/7
DESCRIPTION:Title: Heralding Scientific Breakthroughs through AI at Superco
mputing Scale\nby Anima Anandkumar (Caltech) as part of UCLA distingui
shed lecture series\n\n\nAbstract\nMany scientific applications currently
rely on the use of brute-force numerical methods performed on high-perform
ance computing (HPC) infrastructure. However\, these methods have their li
mits even with the growing hardware capabilities\, e.g. for fine-scale cli
mate prediction and large-molecule quantum chemistry. Can artificial intel
ligence (AI) methods augment or even entirely replace these brute-force ca
lculations to obtain million-x speed-ups? Can we make groundbreaking new d
iscoveries because of such speed-ups? I will present exciting recent advan
ces that build new foundations in AI that are applicable to a wide range o
f problems such as fluid dynamics and quantum chemistry.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anima Anandkumar (Caltech)
DTSTART:20220414T220000Z
DTEND:20220415T001500Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/8
DESCRIPTION:Title: Neural operator: Learning in infinite dimensions with ap
plications to PDEs\nby Anima Anandkumar (Caltech) as part of UCLA dist
inguished lecture series\n\n\nAbstract\nStandard neural networks assume fi
nite-dimensional inputs and outputs\, and hence\, are unsuitable for model
ing phenomena such as those arising from the solutions of Partial Differen
tial Equations (PDE). We introduce neural operators that can learn operato
rs\, which are mappings between infinite dimensional spaces. By framing ne
ural operators as non-linear compositions of kernel integrations\, we esta
blish that they can universally approximate any operator. They are indepen
dent of the resolution or grid of training data and allow for zero-shot ge
neralization to higher resolution evaluations. We find that the Fourier ne
ural operator can solve turbulent fluid flows with a 1000x speedup compare
d to numerical solvers. I will outline several applications where neural o
perator has shown orders of magnitude speedup.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220425T220000Z
DTEND:20220425T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/9
DESCRIPTION:Title: From combinatorics to dynamics and back again\nby Br
yna Kra (Northwestern) as part of UCLA distinguished lecture series\n\n\nA
bstract\nA striking example of the interactions between additive combinato
rics and ergodic theory is Szemeredi’s Theorem that a set of integers wi
th positive upper density contains arbitrarily long arithmetic progression
s. Soon thereafter\, Furstenberg used Ergodic Theory to gave a new proof o
f this result\, leading to the development of combinatorial ergodic theory
. These tools have led to uncovering new patterns that must occur in suffi
ciently large sets of integers and an understanding of what types of struc
tures control these behaviors. We start with an overview of the types of p
atterns that occur in any sufficiently large set\, start with the classica
l setting of the arithmetic progressions in Szemeredi’s seminal result a
nd then turning to the more difficult question of infinite patterns\, incl
uding the recent solution of the Erdos Sumset Conjecture by Moreira\, Rich
ter\, and Robertson\, and its generalizations.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220426T220000Z
DTEND:20220426T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/10
DESCRIPTION:Title: Translating combinatorial questions into dynamical ones
\nby Bryna Kra (Northwestern) as part of UCLA distinguished lecture se
ries\n\n\nAbstract\nFurstenberg’s proof of Szemeredi’s Theorem introdu
ced the Correspondence Principle\, a general technique for translating a c
ombinatorial problem into a dynamical one. While the original formulation
suffices for certain patterns\, including arithmetic progressions and some
infinite configurations\, higher order generalizations have required refi
nements of these tools.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220427T220000Z
DTEND:20220427T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/11
DESCRIPTION:Title: Dynamical structure theorems and infinitary combinatori
cs\nby Bryna Kra (Northwestern) as part of UCLA distinguished lecture
series\n\n\nAbstract\nIn joint work with Joel Moreira\, Florian Richter\,
and Donald Robertson\, we use ergodic methods to prove a k-fold generaliza
tion of the Erdos Sumset Conjecture. We give an overview of the dynamical
structures that are used to prove this result.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220517T220000Z
DTEND:20220517T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/12
DESCRIPTION:Title: Contractibility as uniqueness\nby Emily Riehl (John
s Hopkins) as part of UCLA distinguished lecture series\n\n\nAbstract\nWha
t does it mean for something to exist uniquely? Classically\, to say that
a set A has a unique element means that there is an element x of A and any
other element y of A equals x. When this assertion is applied to a space
A\, instead of a mere set\, and interpreted in a continuous fashion\, it e
ncodes the statement that the space is contractible\, i.e.\, that A is con
tinuously deformable to a point. This talk will explore this notion of con
tractibility as uniqueness and its role in generalizing from ordinary cate
gories to infinite-dimensional categories.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220518T220000Z
DTEND:20220518T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/13
DESCRIPTION:Title: Path induction and the indiscernibility of identicals\nby Emily Riehl (Johns Hopkins) as part of UCLA distinguished lecture s
eries\n\n\nAbstract\nMathematics students learn a powerful technique for p
roving theorems about an arbitrary natural number: the principle of mathem
atical induction. This talk introduces a closely related proof technique c
alled “path induction\,” which can be thought of as an expression of L
eibniz’s “indiscernibility of identicals”: if x and y are identified
\, then they must have the same properties\, and conversely. What makes th
is interesting is that the notion of identification referenced here is giv
en by Per Martin-Löf’s intensional identity types\, which encode a more
flexible notion of sameness than the traditional equality predicate in th
at an identification can carry data\, for instance of an explicit isomorph
ism or equivalence. The nickname “path induction” for the elimination
rule for identity types derives from a new homotopical interpretation of t
ype theory\, in which the terms of a type define the points of a space and
identifications correspond to paths. In this homotopical context\, indisc
ernibility of identicals is a consequence of the path lifting property of
fibrations. Path induction is then justified by the fact that based path s
paces are contractible.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220519T220000Z
DTEND:20220519T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/14
DESCRIPTION:Title: Arrow induction and the dependent Yoneda lemma\nby
Emily Riehl (Johns Hopkins) as part of UCLA distinguished lecture series\n
\n\nAbstract\nArguably the least straightforward theorem of 1-category the
ory to extend to ∞-categories is the Yoneda lemma. The aim of this talk
will be to present a few new perspectives on this result that can be used
both to generalize its statement and provide a model-independent proof. Be
cause we work at a level of abstraction in which an ∞-category is simply
an object in a suitable “∞-cosmos\,” no prior acquaintance with ∞
-categories will be required. We show that Ross Street’s “Chevalley cr
iterion” gives rise to two model-independent characterizations of “car
tesian fibrations” of ∞-categories in terms of the presence of certain
right adjoints. In fact\, cartesian arrows can be characterized similarly
in terms of the presence of certain “relative” right adjoints\, from
which the characterization of cartesian fibrations follows by considering
the generic cartesian lift of the universal arrow. These notions can then
be used to state and prove a fibrational form of the Yoneda lemma. By an a
nalogy in which arrows in an ∞-category are thought of as directed paths
\, there is a principle of “arrow induction” that categorifies the pri
nciple of “path induction.” We explain how this unravels to a “depen
dent” generalization of the Yoneda lemma. This involves joint work with
Dominic Verity and Mike Shulman.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230509T220000Z
DTEND:20230509T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/15
DESCRIPTION:Title: The UCLA origins of viscosity solutions\nby Craig E
vans (UC Berkeley) as part of UCLA distinguished lecture series\n\n\nAbstr
act\nI will present a motivated introduction to the notion of viscosity so
lutions\, a huge breakthrough in nonlinear PDE\ntheory. The history and pr
ehistory here is strongly tied to the UCLA Mathematics Department.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230510T220000Z
DTEND:20230510T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/16
DESCRIPTION:Title: Passing to limits\, lots of examples\nby Craig Evan
s (UC Berkeley) as part of UCLA distinguished lecture series\n\n\nAbstract
\nThis talk will be an overview of the many applications of viscosity solu
tions\, focussing upon some highlights\, both past and recent.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230511T220000Z
DTEND:20230511T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/17
DESCRIPTION:Title: Recent developments: successes and failures\nby Cra
ig Evans (UC Berkeley) as part of UCLA distinguished lecture series\n\n\nA
bstract\nI will conclude my overview by explaining new perspectives\, new
research opportunities and some really important (but really\nintractable)
open questions.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231128T230000Z
DTEND:20231129T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/18
DESCRIPTION:Title: Unique continuation for discrete harmonic functions
\nby Eugenia Malinnikova (Stanford) as part of UCLA distinguished lecture
series\n\n\nAbstract\nWe discuss a surprising version of the classical Lio
uville theorem. It says that a harmonic function bounded on a large portio
n of the standard square lattice is bounded. The corresponding statement
fails on higher dimensional lattices. The main result was obtained in a jo
int work with Lev Buhovsky\, Alexander Logunov\, and Mikhail Sodin. We wi
ll survey some applications\, describe a recent interesting generalization
by Bon-Rabee\, Cooperman\, and Ganguly\, and list some open problems.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231129T230000Z
DTEND:20231130T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/19
DESCRIPTION:Title: Remez-type inequality for solutions of elliptic equatio
ns\nby Eugenia Malinnikova (Stanford) as part of UCLA distinguished le
cture series\n\n\nAbstract\nThe classical Remez inequality for polynomials
gives a precise bound on the supremum of a polynomial over an interval in
terms of its supremum over a subset of the interval of fixed measure and
the degree of the polynomial. We show that a similar result holds for solu
tions of elliptic PDEs\, where the role of the degree is played by Almgren
’s frequency function. The inequality has applications to nodal geomet
ry of Laplace eigenfunctions. The talk is based on a joint work with Alexa
nder Logunov.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231130T230000Z
DTEND:20231201T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/20
DESCRIPTION:Title: Decay of solutions to real Schrodinger equations on the
plane\nby Eugenia Malinnikova (Stanford) as part of UCLA distinguishe
d lecture series\n\n\nAbstract\nWe consider solutions of Schrödinger equa
tions with bounded real-valued potentials. In the 1960s Landis asked if su
ch solutions decay at most exponentially. We answer the question in dimens
ion two\, where one of the tools is a quasi-conformal change of variables
. The talk is based on a joint work with Alexander Logunov\, Nikolai Nadir
ashvili\, and Fedya Nazarov.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240116T230000Z
DTEND:20240117T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/21
DESCRIPTION:Title: Algebra and representation theory without vector spaces
\nby Pavel Etingof (MIT) as part of UCLA distinguished lecture series\
n\n\nAbstract\nA modern view of representation theory is that it is a stud
y not just of individual representations (say\, finite dimensional represe
ntations of an affine group or\, more generally\, supergroup scheme G over
an algebraically closed field k) but also of the category Rep(G) formed b
y them. The properties of Rep(G) can be summarized by saying that it is a
symmetric tensor category (shortly\, STC) which uniquely determines G. A S
TC is a natural home for studying any kind of linear algebraic structures
(commutative algebras\, Lie algebras\, Hopf algebras\, modules over them\,
etc.)\; for instance\, doing so in Rep(G) amounts to studying such struct
ures with a G-symmetry. It is therefore natural to ask: does the study of
STC reduce to group representation theory\, or is it more general? In othe
r words\, do there exist STC other than Rep(G)? If so\, this would be inte
resting\, since algebra in such STC would be a new kind of algebra\, one
“without vector spaces”. Luckily\, the answer turns out to be “yes
”. I will discuss examples in characteristic zero and p>0\, and also Del
igne’s theorem\, which puts restrictions on the kind of examples one can
have.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240117T230000Z
DTEND:20240118T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/22
DESCRIPTION:Title: Representation theory in non-integral rank\nby Pave
l Etingof (MIT) as part of UCLA distinguished lecture series\n\n\nAbstract
\nExamples of symmetric tensor categories over complex numbers which are n
ot representation categories of supergroups were given by Deligne-Milne in
1981. These very interesting categories are interpolations of representat
ion categories of classical groups GL(n)\, O(n)\, Sp(n) to arbitrary compl
ex values of n. Deligne later generalized them to symmetric groups and als
o to characteristic p\, where\, somewhat unexpectedly\, one needs to inter
polate n to p-adic integer values rather than elements of the ground field
. I will review some of the recent results on these categories and discuss
algebra and representation theory in them.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240118T001500Z
DTEND:20240118T011500Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/23
DESCRIPTION:Title: Symmetric tensor categories of moderate growth and modu
lar representation theory\nby Pavel Etingof (MIT) as part of UCLA dist
inguished lecture series\n\n\nAbstract\nDeligne categories discussed in Le
cture 2 violate an obvious necessary condition for a symmetric tensor cate
gory (STC) to have any realization by finite dimensional vector spaces (an
d in particular to be of the form Rep(G)): for each object X the length of
the n-th tensor power of X grows at most exponentially with n. We call th
is property “moderate growth”. So it is natural to ask if there exist
STC of moderate growth other than Rep(G). In characteristic zero\, the neg
ative answer is given by the remarkable theorem of Deligne (2002)\, discus
sed in Lecture 1. Namely Deligne’s theorem says that a STC of moderate g
rowth can always be realized in supervector spaces. However\, in character
istic p the situation is much more interesting. Namely\, Deligne’s theor
em is known to fail in any characteristic p>0. The simplest exotic symmetr
ic tensor category of moderate growth (i.e.\, not of the form Rep(G)) for
p>3 is the semisimplification of the category of representations of Z/p\,
called the Verlinde category. For example\, for p=5\, this category has an
object X such that X^2=X+1\, so X cannot be realized by a vector space (a
s its dimension would have to equal the golden ratio). I will discuss some
aspects of algebra in these categories\, in particular failure of the PBW
theorem for Lie algebras (and how to fix it) and a generalization of Deli
gne’s theorem in characteristic p due to Kevin Coulembier\, Victor Ostri
k and myself. This generalization allows one to prove new properties of mo
dular representations of finite groups (and\, more generally\, affine grou
p schemes) which were previously out of reach. I will also discuss a famil
y of non-semisimple exotic categories in characteristic p constructed in m
y joint work with Dave Benson and Victor Ostrik\, and their relation to th
e representation theory of groups (Z/p)^n over a field of characteristic p
.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240507T220000Z
DTEND:20240507T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/24
DESCRIPTION:Title: The Mathematics of Artificial Intelligence\nby Gitt
a Kutyniok as part of UCLA distinguished lecture series\n\n\nAbstract\nThe
new wave of artificial intelligence is impacting industry\, public life\,
and the sciences in an unprecedented manner. A similarly strong impact ca
n currently be witnessed within mathematics on areas such as inverse probl
ems and numerical analysis of partial differential equations. However\, on
e major drawback worldwide\, in particular\, in light of regulations such
as the EU AI Act and the G7 Hiroshima AI Process\, is the lack of reliabil
ity of such methodologies.\n\nThe goal of this first lecture is to first p
rovide an introduction into this new vibrant research area. We will then s
urvey recent advances on a profound mathematical understanding of deep neu
ral networks\, in particular\, concerning their expressive power\, the lea
rning process\, and overall performance guarantees. Due to the importance
of explainability for reliability\, we will also touch upon this area by h
ighlighting an explainability approach which is itself reliable due to its
mathematical foundation.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240508T220000Z
DTEND:20240508T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/25
DESCRIPTION:Title: Artificial Intelligence for Mathematics\nby Gitta K
utyniok as part of UCLA distinguished lecture series\n\n\nAbstract\nNovel
approaches based on artificial intelligence have already shown their impre
ssive potential in mathematical research areas such as imaging sciences or
numerical analysis of partial differential equations\, sometimes by far o
utperforming classical mathematical approaches for particular problem clas
ses.\n\nIn this second lecture\, we will focus on optimal combinations of
traditional model-based methods with AI-based approaches in the sense of t
rue hybrid algorithms for imaging sciences. In this realm\, we will presen
t some recent advances for the ill-posed problems of (limited-angle) compu
ted tomography and shape reconstruction. Finally\, we will also touch upon
mathematical insights into the ability of deep neural networks to circumv
ent the curse of dimensionality for high-dimensional partial differential
equations and their benefits as solvers.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240509T220000Z
DTEND:20240509T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/26
DESCRIPTION:Title: Overcoming the Boundaries of Artificial Intelligence: A
Mathematical Approach\nby Gitta Kutyniok as part of UCLA distinguishe
d lecture series\n\n\nAbstract\nClassical approaches of artificial intelli
gence typically employ digital hardware. However\, it turns out that such
computing platforms impose serious restrictions to AI-based algorithms in
terms of computability\, reliability\, legal requirements\, and energy req
uirements.\n\nIn this third lecture\, we will first discuss current mathem
atical limitations of artificial intelligence imposed by digital hardware
modeled as a Turing machine. We will then show how those boundaries can be
overcome by embracing analog computing approaches\, modeled by the Blum-S
hub-Smale machine. This will reveal the tremendous importance of novel com
puting hardware such as neuromorphic hardware for future AI computing. Fin
ally\, we will discuss mathematical aspects of spiking neural networks\, w
hich mimic natural neural networks much closer than classical artificial n
eural networks and are perfectly adapted to neuromorphic hardware.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241008T220000Z
DTEND:20241008T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/27
DESCRIPTION:Title: The optimal paper Moebius band\nby Rick Schwartz (B
rown) as part of UCLA distinguished lecture series\n\nLecture held in MS 6
627.\n\nAbstract\nSuppose you take a 1 x L strip of paper\, twist it aroun
d in space\, and tape the length-1 ends together to make a Moebius band. I
f L is very large this is easy and if L is very small this is impossible.
What is the cutoff? In this talk I will prove that you can do it if and on
ly if L>sqrt(3)\, and moreoever if L is near sqrt(3) the Moebius band you
make must be very close to a certain limiting example that is shaped like
an equilateral triangle. This answers a question that goes back to a paper
of W. Wunderlich in the 60s\, and more specifically confirms the 1977 con
jecture of B. Halpern and C. Weaver about this. The proof is pretty elemen
tary and I will explain it all in the talk.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241009T220000Z
DTEND:20241009T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/28
DESCRIPTION:Title: Outer billiards on kites\nby Rick Schwartz (Brown)
as part of UCLA distinguished lecture series\n\n\nAbstract\nOuter billiard
s is a billiards-like dynamical system that moves points around in the pla
ne on the outside of a convex shape. B. Neumann introduced this game in th
e late 1950s and in the 70s J. Moser (somewhat) popularized the game as a
toy model for planetary motion. One of the central questions about outer b
illiards\, called the Moser-Neumann problem\, is the question of whether o
ne can pick a convex shape and a point with an unbounded orbit. In this ta
lk I will sketch some ideas in my solution of this problem: Outer billiard
s has unbounded orbits with respect to any irrational kite -- i.e.\, a qua
drilateral having a diagonal of symmetry whose other diagonal divides the
shape into two irrationally related areas. My proof was inspired by comput
er experimentation\, and I will show computer demos which illustrate the r
ich combinatorial phenomena that underly the unbounded orbits result.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241010T220000Z
DTEND:20241010T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/29
DESCRIPTION:Title: Five Points on a Sphere\nby Rick Schwartz (Brown) a
s part of UCLA distinguished lecture series\n\n\nAbstract\nThomson's probl
em asks which configurations of points on the sphere (considered as electr
ons) minimize the total electrostatic potential. Computer simulations done
by physicists Melnyk\, Knop\, and Smith in the 70s suggested that the tri
angular bi-pyramid minimizers the potential with respect to a power-law po
tential of exponent s provided that s<15.048077... and then there is a pha
se transition so that the answer becomes a pyramid with square base. (Thom
son's problem concerns s=1.). In this talk I will sketch my computer-assis
ted proof of this conjecture\, showing demos of the programs running and d
oing their business. I should say that this work has not been published (a
fter some years) and the computer-assisted nature may prevent it from ever
being published. So\, you could interpret this talk as a good story but p
erhaps a cautionary tale aboud computer-assisted proofs.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250520T220000Z
DTEND:20250520T225000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/30
DESCRIPTION:Title: How irrational is an irrational variety?\nby Robert
Lazarsfeld (Stony Brook University) as part of UCLA distinguished lecture
series\n\n\nAbstract\nRecall that an algebraic variety X is said to be ra
tional if it contains a Zariski open subset isomorphic to a Zariski open s
ubset of projective space. There has been a great deal of recent activity
and progress on issues of rationality\, but most varieties aren’t ration
al. I will survey a body of work concerned with a complementary question\,
namely measuring and controlling “how irrational” a non-rational vari
ety might be. The talk will be aimed at a general mathematical audience.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250521T220000Z
DTEND:20250521T225000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/31
DESCRIPTION:Title: Measures of association between algebraic varieties
\nby Robert Lazarsfeld (Stony Brook University) as part of UCLA distinguis
hed lecture series\n\n\nAbstract\nI will discuss some joint work with Oliv
ier Martin that attempts to measure “how far from birationally isomorphi
c” two varieties X and Y of the same dimension may be. The idea is to st
udy the minimal complexity (in various senses) of correspondences between
them.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250522T220000Z
DTEND:20250522T225000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/32
DESCRIPTION:Title: Further developments and open problems\nby Robert L
azarsfeld (Stony Brook University) as part of UCLA distinguished lecture s
eries\n\n\nAbstract\nI will survey some further developments on these matt
ers\, and discuss some of the many open problems that present themselves.\
n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250225T230000Z
DTEND:20250226T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/33
DESCRIPTION:Title: Elliptic curves and modularity\nby Ana Caraiani (Bo
nn) as part of UCLA distinguished lecture series\n\n\nAbstract\nThe goal o
f this talk is to give you a glimpse of the Langlands\nprogram\, a central
topic at the intersection of algebraic number theory\,\nalgebraic geometr
y and representation theory. I will focus on a celebrated\ninstance of the
Langlands correspondence\, namely the modularity of\nelliptic curves. In
the first part of the talk\, I will give an explicit\nexample\, discuss th
e different meanings of modularity for rational\nelliptic curves\, and men
tion applications. In the second part of the talk\,\nI will discuss what i
s known about the modularity of elliptic curves over\nmore general number
fields.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250226T230000Z
DTEND:20250227T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/34
DESCRIPTION:Title: The cohomology of Shimura varieties - a survey of recen
t developments\nby Ana Caraiani (Bonn) as part of UCLA distinguished l
ecture series\n\n\nAbstract\nShimura varieties are highly symmetric algebr
aic varieties that\nplay an important role in the Langlands program. In th
e first part of the\ntalk\, I will try to give you a sense of what they ar
e like\, with a focus\non their different kinds of symmetries. In the seco
nd part of the talk\, I\nwill survey a recent class of results about the v
anishing of the\ncohomology of Shimura varieties with torsion coefficients
. To give you a\nsense of the breadth of the subject\, I will mention conn
ections both to\nthe geometric Langlands program and to the modularity res
ults discussed in\nthe first lecture.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250227T230000Z
DTEND:20250228T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/35
DESCRIPTION:Title: Ordinary p-adic automorphic forms and Eichler-Shimura t
heory\nby Ana Caraiani (Bonn) as part of UCLA distinguished lecture se
ries\n\n\nAbstract\nIn this talk\, I will discuss a conjectural p-adic ana
logue of\nthe kinds of vanishing results for the cohomology of Shimura var
ieties\nthat were featured in the second lecture. This is closely related
to an\nintegral Eichler-Shimura style comparison between two different\nco
nstructions of ordinary p-adic automorphic forms. Both constructions\norig
inate in the work of Hida\, but the first has a more\nrepresentation-theor
etic flavour and uses the Betti / etale cohomology of\nShimura varieties\,
while the second has a more geometric flavour and uses\ncoherent cohomolo
gy. This talk is based on joint work in progress with\nJames Newton and Ju
an Esteban Rodríguez Camargo that aims to compare the\ntwo constructions.
\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250513T220000Z
DTEND:20250513T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/36
DESCRIPTION:Title: An overview of metric embeddings and metric repair (and
why they matter)\nby Anna Gilbert (Yale) as part of UCLA distinguishe
d lecture series\n\n\nAbstract\nIn this first lecture\, I will introduce t
he notion of metric embeddings and explain some basic mathematical and alg
orithmic results. Next\, I will define the metric repair problem which cap
tures the question\, “What happens if we don’t have a metric to begin
with?!” Fortunately and unfortunately\, this problem is both hard and ha
rd to approximate\, making it an interesting algorithmic question in its o
wn right.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250514T220000Z
DTEND:20250514T230000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/37
DESCRIPTION:Title: Project and Forget and its applications\nby Anna Gi
lbert (Yale) as part of UCLA distinguished lecture series\n\n\nAbstract\nI
n the second lecture\, I will describe a general optimization framework fo
r solving metric-constrained problems which arise from metric embeddings a
nd repair problems. This optimization method can be used to solve huge pro
blems\, problems so large that one cannot write down all of the (inequalit
y) constraints. Finally\, I will discuss its application to transfer learn
ing and optimal transport.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250515T230000Z
DTEND:20250516T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/38
DESCRIPTION:Title: Extensions to random weighted graphs and trees\nby
Anna Gilbert (Yale) as part of UCLA distinguished lecture series\n\n\nAbst
ract\nIn the third lecture\, I will discuss on-going work that tries to de
termine how to solve metric repair problems on average graphs. In doing so
\, we develop an interesting family of random graphs and discuss some prel
iminary structural results for this family.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260303T230000Z
DTEND:20260304T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/39
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang Xu (Prin
ceton) as part of UCLA distinguished lecture series\n\n\nAbstract\nK-stabi
lity was first defined in complex geometry by Tian in late 90s and then re
formulated by Donaldson in algebraic terms\, to characterize the existence
of Kähler-Einstein metrics on Fano varieties. In the last decade\, a pur
ely algebro-geometric theory has been developed. The theory combines deep
techniques in higher dimensional algebraic geometry\, with a circle of new
perspectives from K-stability theory. Major outputs then include a modul
i theory for Fano varieties\, a new stability theory of singularities\, as
well as many new examples of Kähler-Einstein Fano varieties etc.. \n\nIn
my first lecture\, I will give a survey of the K-stability theory\, which
is targeted to general audience. The in the two other lectures\, I will d
iscuss more details of various parts of the theory.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260304T230000Z
DTEND:20260305T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/40
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang Xu (Prin
ceton) as part of UCLA distinguished lecture series\n\n\nAbstract\nK-stabi
lity was first defined in complex geometry by Tian in late 90s and then re
formulated by Donaldson in algebraic terms\, to characterize the existence
of Kähler-Einstein metrics on Fano varieties. In the last decade\, a pur
ely algebro-geometric theory has been developed. The theory combines deep
techniques in higher dimensional algebraic geometry\, with a circle of new
perspectives from K-stability theory. Major outputs then include a modul
i theory for Fano varieties\, a new stability theory of singularities\, as
well as many new examples of Kähler-Einstein Fano varieties etc.. \n\nIn
my first lecture\, I will give a survey of the K-stability theory\, which
is targeted to general audience. The in the two other lectures\, I will d
iscuss more details of various parts of the theory.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260305T230000Z
DTEND:20260306T000000Z
DTSTAMP:20260315T014129Z
UID:UCLADistinguishedLectures/41
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang Xu (Prin
ceton) as part of UCLA distinguished lecture series\n\n\nAbstract\nK-stabi
lity was first defined in complex geometry by Tian in late 90s and then re
formulated by Donaldson in algebraic terms\, to characterize the existence
of Kähler-Einstein metrics on Fano varieties. In the last decade\, a pur
ely algebro-geometric theory has been developed. The theory combines deep
techniques in higher dimensional algebraic geometry\, with a circle of new
perspectives from K-stability theory. Major outputs then include a modul
i theory for Fano varieties\, a new stability theory of singularities\, as
well as many new examples of Kähler-Einstein Fano varieties etc.. \n\nIn
my first lecture\, I will give a survey of the K-stability theory\, which
is targeted to general audience. The in the two other lectures\, I will d
iscuss more details of various parts of the theory.\n
LOCATION:https://researchseminars.org/talk/UCLADistinguishedLectures/41/
END:VEVENT
END:VCALENDAR