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BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200428T160000Z
DTEND:20200428T170000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/1
DESCRIPTION:Title: Geometric stochastic PDEs\nby Martin Hairer (
Imperial College London) as part of UCLA distinguished lecture series\n\nL
ecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nWe review P
arisi and Wu's stochastic quantisation procedure and apply it to the non-l
inear sigma model as well as the Yang-Mills model. We then review a number
of recent results on the resulting equations. In particular\, this sheds
some new light on an old controversy regarding the interpretation of path
integrals.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200429T160000Z
DTEND:20200429T170000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/2
DESCRIPTION:Title: Introduction to regularity structures 1\nby M
artin Hairer (Imperial College London) as part of UCLA distinguished lectu
re series\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstrac
t\nI will give an introduction to the main concepts behind the theory of r
egularity structures which allows to give meaning to many stochastic PDEs
that were previously thought to be ill-posed. This combines some of the in
sights and tools from (perturbative) QFT with classical PDE theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20200430T160000Z
DTEND:20200430T170000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/3
DESCRIPTION:Title: Introduction to regularity structures 2\nby M
artin Hairer (Imperial College London) as part of UCLA distinguished lectu
re series\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstrac
t\nI will give an introduction to the main concepts behind the theory of r
egularity structures which allows to give meaning to many stochastic PDEs
that were previously thought to be ill-posed. This combines some of the in
sights and tools from (perturbative) QFT with classical PDE theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200512T220000Z
DTEND:20200512T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/4
DESCRIPTION:Title: Knot categorification from mirror symmetry\, I\nby Mina Aganagic (UC Berkeley) as part of UCLA distinguished lecture se
ries\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nIn
the series of lectures\, I will describe two approaches to categorifying
quantum link invariants which work uniformly for all simple Lie algebras\,
and originate from geometry and from string theory. Many ingredients that
go into the story have been found by mathematicians earlier\, but physics
spells out how they should be put together for a uniform framework for th
e knot categorification problem. One of the important aspects of both appr
oaches is that the fact that decategorification gives the quantum link inv
ariants one set out to categorify\, becomes manifest. \n\nThe first approa
ch is based on derived categories of coherent sheaves on resolutions of sl
ices in affine Grassmannians. While some elements of it are familiar to ma
thematicians\, others are new. The second approach is perhaps more surpris
ing. It uses symplectic geometry and is related to the first by two dimens
ional (equivariant) mirror symmetry. Unlike previous symplectic geometry b
ased approaches\, it produces a bi-graded homology theory. In both cases\,
mirror symmetry\, and techniques developed by physicists and mathematicia
ns to understand it play a crucial role. I will also explain the relation
to another string theory based approach\, due to Witten.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200513T220000Z
DTEND:20200513T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/5
DESCRIPTION:Title: Knot categorification from mirror symmetry\, II\nby Mina Aganagic (UC Berkeley) as part of UCLA distinguished lecture s
eries\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\nI
n the series of lectures\, I will describe two approaches to categorifying
quantum link invariants which work uniformly for all simple Lie algebras\
, and originate from geometry and from string theory. Many ingredients tha
t go into the story have been found by mathematicians earlier\, but physic
s spells out how they should be put together for a uniform framework for t
he knot categorification problem. One of the important aspects of both app
roaches is that the fact that decategorification gives the quantum link in
variants one set out to categorify\, becomes manifest. \n\nThe first appro
ach is based on derived categories of coherent sheaves on resolutions of s
lices in affine Grassmannians. While some elements of it are familiar to m
athematicians\, others are new. The second approach is perhaps more surpri
sing. It uses symplectic geometry and is related to the first by two dimen
sional (equivariant) mirror symmetry. Unlike previous symplectic geometry
based approaches\, it produces a bi-graded homology theory. In both cases\
, mirror symmetry\, and techniques developed by physicists and mathematici
ans to understand it play a crucial role. I will also explain the relation
to another string theory based approach\, due to Witten.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mina Aganagic (UC Berkeley)
DTSTART:20200514T220000Z
DTEND:20200514T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/6
DESCRIPTION:Title: Knot categorification from mirror symmetry\, III<
/a>\nby Mina Aganagic (UC Berkeley) as part of UCLA distinguished lecture
series\n\nLecture held in https://ucla.zoom.us/j/9264073849.\n\nAbstract\n
In the series of lectures\, I will describe two approaches to categorifyin
g quantum link invariants which work uniformly for all simple Lie algebras
\, and originate from geometry and from string theory. Many ingredients th
at go into the story have been found by mathematicians earlier\, but physi
cs spells out how they should be put together for a uniform framework for
the knot categorification problem. One of the important aspects of both ap
proaches is that the fact that decategorification gives the quantum link i
nvariants one set out to categorify\, becomes manifest. \n\nThe first appr
oach is based on derived categories of coherent sheaves on resolutions of
slices in affine Grassmannians. While some elements of it are familiar to
mathematicians\, others are new. The second approach is perhaps more surpr
ising. It uses symplectic geometry and is related to the first by two dime
nsional (equivariant) mirror symmetry. Unlike previous symplectic geometry
based approaches\, it produces a bi-graded homology theory. In both cases
\, mirror symmetry\, and techniques developed by physicists and mathematic
ians to understand it play a crucial role. I will also explain the relatio
n to another string theory based approach\, due to Witten.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anima Anandkumar (Caltech)
DTSTART:20220413T220000Z
DTEND:20220413T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/7
DESCRIPTION:Title: Heralding Scientific Breakthroughs through AI at
Supercomputing Scale\nby Anima Anandkumar (Caltech) as part of UCLA di
stinguished lecture series\n\n\nAbstract\nMany scientific applications cur
rently rely on the use of brute-force numerical methods performed on high-
performance computing (HPC) infrastructure. However\, these methods have t
heir limits even with the growing hardware capabilities\, e.g. for fine-sc
ale climate prediction and large-molecule quantum chemistry. Can artificia
l intelligence (AI) methods augment or even entirely replace these brute-f
orce calculations to obtain million-x speed-ups? Can we make groundbreakin
g new discoveries because of such speed-ups? I will present exciting recen
t advances that build new foundations in AI that are applicable to a wide
range of problems such as fluid dynamics and quantum chemistry.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anima Anandkumar (Caltech)
DTSTART:20220414T220000Z
DTEND:20220415T001500Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/8
DESCRIPTION:Title: Neural operator: Learning in infinite dimensions
with applications to PDEs\nby Anima Anandkumar (Caltech) as part of UC
LA distinguished lecture series\n\n\nAbstract\nStandard neural networks as
sume finite-dimensional inputs and outputs\, and hence\, are unsuitable fo
r modeling phenomena such as those arising from the solutions of Partial D
ifferential Equations (PDE). We introduce neural operators that can learn
operators\, which are mappings between infinite dimensional spaces. By fra
ming neural operators as non-linear compositions of kernel integrations\,
we establish that they can universally approximate any operator. They are
independent of the resolution or grid of training data and allow for zero-
shot generalization to higher resolution evaluations. We find that the Fou
rier neural operator can solve turbulent fluid flows with a 1000x speedup
compared to numerical solvers. I will outline several applications where n
eural operator has shown orders of magnitude speedup.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220425T220000Z
DTEND:20220425T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/9
DESCRIPTION:Title: From combinatorics to dynamics and back again
\nby Bryna Kra (Northwestern) as part of UCLA distinguished lecture series
\n\n\nAbstract\nA striking example of the interactions between additive co
mbinatorics and ergodic theory is Szemeredi’s Theorem that a set of inte
gers with positive upper density contains arbitrarily long arithmetic prog
ressions. Soon thereafter\, Furstenberg used Ergodic Theory to gave a new
proof of this result\, leading to the development of combinatorial ergodic
theory. These tools have led to uncovering new patterns that must occur i
n sufficiently large sets of integers and an understanding of what types o
f structures control these behaviors. We start with an overview of the typ
es of patterns that occur in any sufficiently large set\, start with the c
lassical setting of the arithmetic progressions in Szemeredi’s seminal r
esult and then turning to the more difficult question of infinite patterns
\, including the recent solution of the Erdos Sumset Conjecture by Moreira
\, Richter\, and Robertson\, and its generalizations.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220426T220000Z
DTEND:20220426T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/10
DESCRIPTION:Title: Translating combinatorial questions into dynamic
al ones\nby Bryna Kra (Northwestern) as part of UCLA distinguished lec
ture series\n\n\nAbstract\nFurstenberg’s proof of Szemeredi’s Theorem
introduced the Correspondence Principle\, a general technique for translat
ing a combinatorial problem into a dynamical one. While the original formu
lation suffices for certain patterns\, including arithmetic progressions a
nd some infinite configurations\, higher order generalizations have requir
ed refinements of these tools.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryna Kra (Northwestern)
DTSTART:20220427T220000Z
DTEND:20220427T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/11
DESCRIPTION:Title: Dynamical structure theorems and infinitary comb
inatorics\nby Bryna Kra (Northwestern) as part of UCLA distinguished l
ecture series\n\n\nAbstract\nIn joint work with Joel Moreira\, Florian Ric
hter\, and Donald Robertson\, we use ergodic methods to prove a k-fold gen
eralization of the Erdos Sumset Conjecture. We give an overview of the dyn
amical structures that are used to prove this result.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220517T220000Z
DTEND:20220517T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/12
DESCRIPTION:Title: Contractibility as uniqueness\nby Emily Rieh
l (Johns Hopkins) as part of UCLA distinguished lecture series\n\n\nAbstra
ct\nWhat does it mean for something to exist uniquely? Classically\, to sa
y 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 encodes the statement that the space is contractible\, i.e.\, that A
is continuously deformable to a point. This talk will explore this notion
of contractibility as uniqueness and its role in generalizing from ordina
ry categories to infinite-dimensional categories.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220518T220000Z
DTEND:20220518T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/13
DESCRIPTION:Title: Path induction and the indiscernibility of ident
icals\nby Emily Riehl (Johns Hopkins) as part of UCLA distinguished le
cture series\n\n\nAbstract\nMathematics students learn a powerful techniqu
e for proving theorems about an arbitrary natural number: the principle of
mathematical induction. This talk introduces a closely related proof tech
nique called “path induction\,” which can be thought of as an expressi
on of Leibniz’s “indiscernibility of identicals”: if x and y are ide
ntified\, then they must have the same properties\, and conversely. What m
akes this interesting is that the notion of identification referenced here
is given by Per Martin-Löf’s intensional identity types\, which encode
a more flexible notion of sameness than the traditional equality predicat
e in that an identification can carry data\, for instance of an explicit i
somorphism or equivalence. The nickname “path induction” for the elimi
nation rule for identity types derives from a new homotopical interpretati
on of type theory\, in which the terms of a type define the points of a sp
ace and identifications correspond to paths. In this homotopical context\,
indiscernibility of identicals is a consequence of the path lifting prope
rty of fibrations. Path induction is then justified by the fact that based
path spaces are contractible.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Riehl (Johns Hopkins)
DTSTART:20220519T220000Z
DTEND:20220519T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/14
DESCRIPTION:Title: Arrow induction and the dependent Yoneda lemma\nby Emily Riehl (Johns Hopkins) as part of UCLA distinguished lecture s
eries\n\n\nAbstract\nArguably the least straightforward theorem of 1-categ
ory theory to extend to ∞-categories is the Yoneda lemma. The aim of thi
s talk will be to present a few new perspectives on this result that can b
e used both to generalize its statement and provide a model-independent pr
oof. Because we work at a level of abstraction in which an ∞-category is
simply an object in a suitable “∞-cosmos\,” no prior acquaintance w
ith ∞-categories will be required. We show that Ross Street’s “Cheva
lley criterion” gives rise to two model-independent characterizations of
“cartesian fibrations” of ∞-categories in terms of the presence of
certain right adjoints. In fact\, cartesian arrows can be characterized si
milarly in terms of the presence of certain “relative” right adjoints\
, from which the characterization of cartesian fibrations follows by consi
dering the generic cartesian lift of the universal arrow. These notions ca
n then be used to state and prove a fibrational form of the Yoneda lemma.
By an analogy in which arrows in an ∞-category are thought of as directe
d paths\, there is a principle of “arrow induction” that categorifies
the principle of “path induction.” We explain how this unravels to a
“dependent” generalization of the Yoneda lemma. This involves joint wo
rk with Dominic Verity and Mike Shulman.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230509T220000Z
DTEND:20230509T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/15
DESCRIPTION:Title: The UCLA origins of viscosity solutions\nby
Craig Evans (UC Berkeley) as part of UCLA distinguished lecture series\n\n
\nAbstract\nI will present a motivated introduction to the notion of visco
sity solutions\, a huge breakthrough in nonlinear PDE\ntheory. The history
and prehistory here is strongly tied to the UCLA Mathematics Department.\
n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230510T220000Z
DTEND:20230510T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/16
DESCRIPTION:Title: Passing to limits\, lots of examples\nby Cra
ig Evans (UC Berkeley) as part of UCLA distinguished lecture series\n\n\nA
bstract\nThis talk will be an overview of the many applications of viscosi
ty solutions\, focussing upon some highlights\, both past and recent.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Evans (UC Berkeley)
DTSTART:20230511T220000Z
DTEND:20230511T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/17
DESCRIPTION:Title: Recent developments: successes and failures\
nby Craig Evans (UC Berkeley) as part of UCLA distinguished lecture series
\n\n\nAbstract\nI will conclude my overview by explaining new perspectives
\, new research opportunities and some really important (but really\nintra
ctable) open questions.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231128T230000Z
DTEND:20231129T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/18
DESCRIPTION:Title: Unique continuation for discrete harmonic functi
ons\nby Eugenia Malinnikova (Stanford) as part of UCLA distinguished l
ecture series\n\n\nAbstract\nWe discuss a surprising version of the classi
cal Liouville theorem. It says that a harmonic function bounded on a large
portion of the standard square lattice is bounded. The corresponding sta
tement fails on higher dimensional lattices. The main result was obtained
in a joint work with Lev Buhovsky\, Alexander Logunov\, and Mikhail Sodin.
We will survey some applications\, describe a recent interesting general
ization by Bon-Rabee\, Cooperman\, and Ganguly\, and list some open proble
ms.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231129T230000Z
DTEND:20231130T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/19
DESCRIPTION:Title: Remez-type inequality for solutions of elliptic
equations\nby Eugenia Malinnikova (Stanford) as part of UCLA distingui
shed lecture series\n\n\nAbstract\nThe classical Remez inequality for poly
nomials gives a precise bound on the supremum of a polynomial over an inte
rval in terms of its supremum over a subset of the interval of fixed measu
re and the degree of the polynomial. We show that a similar result holds f
or solutions of elliptic PDEs\, where the role of the degree is played by
Almgren’s frequency function. The inequality has applications to nodal
geometry of Laplace eigenfunctions. The talk is based on a joint work wit
h Alexander Logunov.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford)
DTSTART:20231130T230000Z
DTEND:20231201T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/20
DESCRIPTION:Title: Decay of solutions to real Schrodinger equations
on the plane\nby Eugenia Malinnikova (Stanford) as part of UCLA disti
nguished lecture series\n\n\nAbstract\nWe consider solutions of Schröding
er equations with bounded real-valued potentials. In the 1960s Landis aske
d if such solutions decay at most exponentially. We answer the question in
dimension two\, where one of the tools is a quasi-conformal change of va
riables. The talk is based on a joint work with Alexander Logunov\, Nikola
i Nadirashvili\, and Fedya Nazarov.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240116T230000Z
DTEND:20240117T000000Z
DTSTAMP:20260424T153137Z
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 study not just of individual representations (say\, finite dimensional
representations of an affine group or\, more generally\, supergroup scheme
G over an algebraically closed field k) but also of the category Rep(G) f
ormed by them. The properties of Rep(G) can be summarized by saying that i
t is a symmetric tensor category (shortly\, STC) which uniquely determines
G. A STC is a natural home for studying any kind of linear algebraic stru
ctures (commutative algebras\, Lie algebras\, Hopf algebras\, modules over
them\, etc.)\; for instance\, doing so in Rep(G) amounts to studying such
structures with a G-symmetry. It is therefore natural to ask: does the st
udy of STC reduce to group representation theory\, or is it more general?
In other words\, do there exist STC other than Rep(G)? If so\, this would
be interesting\, 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 al
so Deligne’s theorem\, which puts restrictions on the kind of examples o
ne can have.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240117T230000Z
DTEND:20240118T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/22
DESCRIPTION:Title: Representation theory in non-integral rank\n
by Pavel Etingof (MIT) as part of UCLA distinguished lecture series\n\n\nA
bstract\nExamples of symmetric tensor categories over complex numbers whic
h are not representation categories of supergroups were given by Deligne-M
ilne in 1981. These very interesting categories are interpolations of repr
esentation categories of classical groups GL(n)\, O(n)\, Sp(n) to arbitrar
y complex values of n. Deligne later generalized them to symmetric groups
and also to characteristic p\, where\, somewhat unexpectedly\, one needs t
o interpolate n to p-adic integer values rather than elements of the groun
d field. I will review some of the recent results on these categories and
discuss algebra and representation theory in them.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20240118T001500Z
DTEND:20240118T011500Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/23
DESCRIPTION:Title: Symmetric tensor categories of moderate growth a
nd modular representation theory\nby Pavel Etingof (MIT) as part of UC
LA distinguished lecture series\n\n\nAbstract\nDeligne categories discusse
d in Lecture 2 violate an obvious necessary condition for a symmetric tens
or category (STC) to have any realization by finite dimensional vector spa
ces (and in particular to be of the form Rep(G)): for each object X the le
ngth of the n-th tensor power of X grows at most exponentially with n. We
call this property “moderate growth”. So it is natural to ask if there
exist STC of moderate growth other than Rep(G). In characteristic zero\,
the negative answer is given by the remarkable theorem of Deligne (2002)\,
discussed in Lecture 1. Namely Deligne’s theorem says that a STC of mod
erate growth can always be realized in supervector spaces. However\, in ch
aracteristic p the situation is much more interesting. Namely\, Deligne’
s theorem is known to fail in any characteristic p>0. The simplest exotic
symmetric 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 s
pace (as its dimension would have to equal the golden ratio). I will discu
ss 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 Deligne’s theorem in characteristic p due to Kevin Coulembier\, Victo
r Ostrik and myself. This generalization allows one to prove new propertie
s of modular representations of finite groups (and\, more generally\, affi
ne group schemes) which were previously out of reach. I will also discuss
a family of non-semisimple exotic categories in characteristic p construct
ed in my joint work with Dave Benson and Victor Ostrik\, and their relatio
n to the representation theory of groups (Z/p)^n over a field of character
istic p.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240507T220000Z
DTEND:20240507T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/24
DESCRIPTION:Title: The Mathematics of Artificial Intelligence\n
by Gitta Kutyniok as part of UCLA distinguished lecture series\n\n\nAbstra
ct\nThe new wave of artificial intelligence is impacting industry\, public
life\, and the sciences in an unprecedented manner. A similarly strong im
pact can currently be witnessed within mathematics on areas such as invers
e problems and numerical analysis of partial differential equations. Howev
er\, one major drawback worldwide\, in particular\, in light of regulation
s such as the EU AI Act and the G7 Hiroshima AI Process\, is the lack of r
eliability of such methodologies.\n\nThe goal of this first lecture is to
first provide an introduction into this new vibrant research area. We will
then survey recent advances on a profound mathematical understanding of d
eep neural networks\, in particular\, concerning their expressive power\,
the learning process\, and overall performance guarantees. Due to the impo
rtance of explainability for reliability\, we will also touch upon this ar
ea by highlighting an explainability approach which is itself reliable due
to its mathematical foundation.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240508T220000Z
DTEND:20240508T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/25
DESCRIPTION:Title: Artificial Intelligence for Mathematics\nby
Gitta Kutyniok as part of UCLA distinguished lecture series\n\n\nAbstract\
nNovel approaches based on artificial intelligence have already shown thei
r impressive potential in mathematical research areas such as imaging scie
nces or numerical analysis of partial differential equations\, sometimes b
y far outperforming classical mathematical approaches for particular probl
em classes.\n\nIn this second lecture\, we will focus on optimal combinati
ons of traditional model-based methods with AI-based approaches in the sen
se of true hybrid algorithms for imaging sciences. In this realm\, we will
present some recent advances for the ill-posed problems of (limited-angle
) computed tomography and shape reconstruction. Finally\, we will also tou
ch upon mathematical insights into the ability of deep neural networks to
circumvent the curse of dimensionality for high-dimensional partial differ
ential equations and their benefits as solvers.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok
DTSTART:20240509T220000Z
DTEND:20240509T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/26
DESCRIPTION:Title: Overcoming the Boundaries of Artificial Intellig
ence: A Mathematical Approach\nby Gitta Kutyniok as part of UCLA disti
nguished lecture series\n\n\nAbstract\nClassical approaches of artificial
intelligence typically employ digital hardware. However\, it turns out tha
t such computing platforms impose serious restrictions to AI-based algorit
hms in terms of computability\, reliability\, legal requirements\, and ene
rgy requirements.\n\nIn this third lecture\, we will first discuss current
mathematical limitations of artificial intelligence imposed by digital ha
rdware modeled as a Turing machine. We will then show how those boundaries
can be overcome by embracing analog computing approaches\, modeled by the
Blum-Shub-Smale machine. This will reveal the tremendous importance of no
vel computing hardware such as neuromorphic hardware for future AI computi
ng. Finally\, we will discuss mathematical aspects of spiking neural netwo
rks\, which mimic natural neural networks much closer than classical artif
icial neural networks and are perfectly adapted to neuromorphic hardware.\
n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241008T220000Z
DTEND:20241008T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/27
DESCRIPTION:Title: The optimal paper Moebius band\nby Rick Schw
artz (Brown) as part of UCLA distinguished lecture series\n\nLecture held
in MS 6627.\n\nAbstract\nSuppose you take a 1 x L strip of paper\, twist i
t around in space\, and tape the length-1 ends together to make a Moebius
band. If L is very large this is easy and if L is very small this is impos
sible. What is the cutoff? In this talk I will prove that you can do it if
and only if L>sqrt(3)\, and moreoever if L is near sqrt(3) the Moebius ba
nd you make must be very close to a certain limiting example that is shape
d 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 1
977 conjecture of B. Halpern and C. Weaver about this. The proof is pretty
elementary and I will explain it all in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241009T220000Z
DTEND:20241009T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/28
DESCRIPTION:Title: Outer billiards on kites\nby Rick Schwartz (
Brown) as part of UCLA distinguished lecture series\n\n\nAbstract\nOuter b
illiards is a billiards-like dynamical system that moves points around in
the plane on the outside of a convex shape. B. Neumann introduced this gam
e in the late 1950s and in the 70s J. Moser (somewhat) popularized the gam
e as a toy model for planetary motion. One of the central questions about
outer billiards\, called the Moser-Neumann problem\, is the question of wh
ether one can pick a convex shape and a point with an unbounded orbit. In
this talk I will sketch some ideas in my solution of this problem: Outer b
illiards has unbounded orbits with respect to any irrational kite -- i.e.\
, a quadrilateral having a diagonal of symmetry whose other diagonal divid
es the shape into two irrationally related areas. My proof was inspired by
computer experimentation\, and I will show computer demos which illustrat
e the rich combinatorial phenomena that underly the unbounded orbits resul
t.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schwartz (Brown)
DTSTART:20241010T220000Z
DTEND:20241010T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/29
DESCRIPTION:Title: Five Points on a Sphere\nby Rick Schwartz (B
rown) as part of UCLA distinguished lecture series\n\n\nAbstract\nThomson'
s problem asks which configurations of points on the sphere (considered as
electrons) minimize the total electrostatic potential. Computer simulatio
ns done by physicists Melnyk\, Knop\, and Smith in the 70s suggested that
the triangular bi-pyramid minimizers the potential with respect to a power
-law potential of exponent s provided that s<15.048077... and then there i
s a phase transition so that the answer becomes a pyramid with square base
. (Thomson's problem concerns s=1.). In this talk I will sketch my compute
r-assisted proof of this conjecture\, showing demos of the programs runnin
g and doing their business. I should say that this work has not been publi
shed (after some years) and the computer-assisted nature may prevent it fr
om ever being published. So\, you could interpret this talk as a good stor
y but perhaps a cautionary tale aboud computer-assisted proofs.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250520T220000Z
DTEND:20250520T225000Z
DTSTAMP:20260424T153137Z
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 t
o be rational if it contains a Zariski open subset isomorphic to a Zariski
open subset of projective space. There has been a great deal of recent ac
tivity and progress on issues of rationality\, but most varieties aren’t
rational. I will survey a body of work concerned with a complementary que
stion\, namely measuring and controlling “how irrational” a non-ration
al variety might be. The talk will be aimed at a general mathematical audi
ence.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250521T220000Z
DTEND:20250521T225000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/31
DESCRIPTION:Title: Measures of association between algebraic variet
ies\nby Robert Lazarsfeld (Stony Brook University) as part of UCLA dis
tinguished lecture series\n\n\nAbstract\nI will discuss some joint work wi
th Olivier Martin that attempts to measure “how far from birationally is
omorphic” two varieties X and Y of the same dimension may be. The idea i
s to study the minimal complexity (in various senses) of correspondences b
etween them.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART:20250522T220000Z
DTEND:20250522T225000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/32
DESCRIPTION:Title: Further developments and open problems\nby R
obert Lazarsfeld (Stony Brook University) as part of UCLA distinguished le
cture series\n\n\nAbstract\nI will survey some further developments on the
se matters\, and discuss some of the many open problems that present thems
elves.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250225T230000Z
DTEND:20250226T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/33
DESCRIPTION:Title: Elliptic curves and modularity\nby Ana Carai
ani (Bonn) as part of UCLA distinguished lecture series\n\n\nAbstract\nThe
goal of this talk is to give you a glimpse of the Langlands\nprogram\, a
central topic at the intersection of algebraic number theory\,\nalgebraic
geometry and representation theory. I will focus on a celebrated\ninstance
of the Langlands correspondence\, namely the modularity of\nelliptic curv
es. In the first part of the talk\, I will give an explicit\nexample\, dis
cuss the different meanings of modularity for rational\nelliptic curves\,
and mention applications. In the second part of the talk\,\nI will discuss
what is known about the modularity of elliptic curves over\nmore general
number fields.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250226T230000Z
DTEND:20250227T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/34
DESCRIPTION:Title: The cohomology of Shimura varieties - a survey o
f recent developments\nby Ana Caraiani (Bonn) as part of UCLA distingu
ished lecture series\n\n\nAbstract\nShimura varieties are highly symmetric
algebraic varieties that\nplay an important role in the Langlands program
. In the first part of the\ntalk\, I will try to give you a sense of what
they are like\, with a focus\non their different kinds of symmetries. In t
he second part of the talk\, I\nwill survey a recent class of results abou
t the vanishing of the\ncohomology of Shimura varieties with torsion coeff
icients. To give you a\nsense of the breadth of the subject\, I will menti
on connections both to\nthe geometric Langlands program and to the modular
ity results discussed in\nthe first lecture.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Bonn)
DTSTART:20250227T230000Z
DTEND:20250228T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/35
DESCRIPTION:Title: Ordinary p-adic automorphic forms and Eichler-Sh
imura theory\nby Ana Caraiani (Bonn) as part of UCLA distinguished lec
ture series\n\n\nAbstract\nIn this talk\, I will discuss a conjectural p-a
dic analogue of\nthe kinds of vanishing results for the cohomology of Shim
ura varieties\nthat were featured in the second lecture. This is closely r
elated to an\nintegral Eichler-Shimura style comparison between two differ
ent\nconstructions of ordinary p-adic automorphic forms. Both construction
s\noriginate in the work of Hida\, but the first has a more\nrepresentatio
n-theoretic flavour and uses the Betti / etale cohomology of\nShimura vari
eties\, while the second has a more geometric flavour and uses\ncoherent c
ohomology. This talk is based on joint work in progress with\nJames Newton
and Juan Esteban Rodríguez Camargo that aims to compare the\ntwo constru
ctions.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250513T220000Z
DTEND:20250513T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/36
DESCRIPTION:Title: An overview of metric embeddings and metric repa
ir (and why they matter)\nby Anna Gilbert (Yale) as part of UCLA disti
nguished lecture series\n\n\nAbstract\nIn this first lecture\, I will intr
oduce the notion of metric embeddings and explain some basic mathematical
and algorithmic results. Next\, I will define the metric repair problem wh
ich captures the question\, “What happens if we don’t have a metric to
begin with?!” Fortunately and unfortunately\, this problem is both hard
and hard to approximate\, making it an interesting algorithmic question i
n its own right.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250514T220000Z
DTEND:20250514T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/37
DESCRIPTION:Title: Project and Forget and its applications\nby
Anna Gilbert (Yale) as part of UCLA distinguished lecture series\n\n\nAbst
ract\nIn the second lecture\, I will describe a general optimization frame
work for solving metric-constrained problems which arise from metric embed
dings and repair problems. This optimization method can be used to solve h
uge problems\, problems so large that one cannot write down all of the (in
equality) constraints. Finally\, I will discuss its application to transfe
r learning and optimal transport.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (Yale)
DTSTART:20250515T230000Z
DTEND:20250516T000000Z
DTSTAMP:20260424T153137Z
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\nAbstract\nIn the third lecture\, I will discuss on-going work that trie
s to determine how to solve metric repair problems on average graphs. In d
oing so\, we develop an interesting family of random graphs and discuss so
me preliminary structural results for this family.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260303T230000Z
DTEND:20260304T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/39
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang X
u (Princeton) as part of UCLA distinguished lecture series\n\n\nAbstract\n
K-stability was first defined in complex geometry by Tian in late 90s and
then reformulated by Donaldson in algebraic terms\, to characterize the ex
istence of Kähler-Einstein metrics on Fano varieties. In the last decade\
, a purely algebro-geometric theory has been developed. The theory combine
s deep techniques in higher dimensional algebraic geometry\, with a circle
of new perspectives from K-stability theory. Major outputs then include
a moduli theory for Fano varieties\, a new stability theory of singulariti
es\, 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 discuss more details of various parts of the theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260304T230000Z
DTEND:20260305T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/40
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang X
u (Princeton) as part of UCLA distinguished lecture series\n\n\nAbstract\n
K-stability was first defined in complex geometry by Tian in late 90s and
then reformulated by Donaldson in algebraic terms\, to characterize the ex
istence of Kähler-Einstein metrics on Fano varieties. In the last decade\
, a purely algebro-geometric theory has been developed. The theory combine
s deep techniques in higher dimensional algebraic geometry\, with a circle
of new perspectives from K-stability theory. Major outputs then include
a moduli theory for Fano varieties\, a new stability theory of singulariti
es\, 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 discuss more details of various parts of the theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenyang Xu (Princeton)
DTSTART:20260305T230000Z
DTEND:20260306T000000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/41
DESCRIPTION:Title: K-stability of Fano varieties\nby Chenyang X
u (Princeton) as part of UCLA distinguished lecture series\n\n\nAbstract\n
K-stability was first defined in complex geometry by Tian in late 90s and
then reformulated by Donaldson in algebraic terms\, to characterize the ex
istence of Kähler-Einstein metrics on Fano varieties. In the last decade\
, a purely algebro-geometric theory has been developed. The theory combine
s deep techniques in higher dimensional algebraic geometry\, with a circle
of new perspectives from K-stability theory. Major outputs then include
a moduli theory for Fano varieties\, a new stability theory of singulariti
es\, 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 discuss more details of various parts of the theory.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kuske (Georgia Tech)
DTSTART:20260512T220000Z
DTEND:20260512T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/42
DESCRIPTION:Title: Is the world smooth or non-smooth? Can mathemati
cs tell us?\nby Rachel Kuske (Georgia Tech) as part of UCLA distinguis
hed lecture series\n\nInteractive livestream: https://ucla.zoom.us/j/92640
73849\n\nAbstract\nIn modeling different dynamical processes in physics\,
engineering\, and the life\nsciences we often use models that have some ki
nd of smoothness associated\nwith their evolution. Meanwhile\, models with
abrupt changes – non-smoothness\n– have recently seen more frequent d
emand\, application\, and success. These\ncontrasts raise a number of ques
tions\, such as\, which type should we use? Are\nthe non-smooth models dri
ving new mathematics? Has our preference for\ncertain types of mathematica
l properties kept us from considering certain types\nof models? We conside
r some non-smooth models on completely different\nscales\, in the areas cl
imate\, energy transfer\, and neural feedback\, to see what\nthese models
can capture about the systems they describe. These examples also\nprovide
some perspectives about the mathematics that is needed and available\nfor
understanding and applying these models.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/42/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kuske (Georgia Tech)
DTSTART:20260513T220000Z
DTEND:20260513T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/43
DESCRIPTION:Title: Critical scales for tipping captured in non-smoo
th and noisy model features\nby Rachel Kuske (Georgia Tech) as part of
UCLA distinguished lecture series\n\nInteractive livestream: https://ucla
.zoom.us/j/9264073849\n\nAbstract\nWe consider tipping mechanisms facilita
ted by certain model features in the study of dynamic bifurcations or earl
y warning signals.\nWe review two types of multiple scale features appeari
ng in reduced conceptual climate models: (non)-smoothness of bifurcations\
,\nand approximations of fast fluctuations yielding correlated additive an
d multiplicative (CAM) noise. First\, we consider stochastic\nforcing in S
tommel-type models\, where the interplay of noise\, non-smoothness and mul
tiple time scales can substantially advance\ndynamic bifurcations. Also te
rmed tipping\, these transitions are advanced relative to both determinist
ic systems and systems with\ntraditional “smooth” bifurcations. Analyt
ical results identify critical scales in tipping\, dependent on the balanc
e of stochastic forcing\,\nthe (nearly) non-smoothness of the bifurcations
\, and the slow variability of critical physical and environmental process
\, with high and\nlow frequency forcing also contributing. Second\, we rev
iew studies from the last decade that show how CAM noise captures large\nv
ariability in reduced climate models\, and in multiple scale nonlinear sys
tems more generically. This analysis of CAM noise can then\nbe connected t
o key bifurcation characteristics in our study of Stommel-type models\, hi
ghlighting additional model features and\nhidden time scales that can comp
ete or cooperate in facilitating advanced tipping near bifurcations.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/43/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kuske (Georgia Tech)
DTSTART:20260514T220000Z
DTEND:20260514T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/44
DESCRIPTION:Title: Computer-assisted global analysis of energy tran
sfer in vibro-impact configurations\nby Rachel Kuske (Georgia Tech) as
part of UCLA distinguished lecture series\n\nInteractive livestream: http
s://ucla.zoom.us/j/9264073849\n\nAbstract\nWe discuss a novel return map a
pproach for studying the global dynamics developed in the context of a vib
ro-impact (VI) pair\, that\nis\, a ball moving in a harmonically forced ca
psule. Results are relevant for recent designs of VI-based energy harveste
rs and nonlinear\nenergy transfer\, and hold promise for other non-smooth
systems. Computationally efficient short-time realizations are based on\n
“words” that represent key impact sequences and divide the state space
according to different dynamics. The word-based maps\ndefine surfaces who
se characteristics indicate both transients and potential attractors. Thes
e perspectives complement the\nbifurcation structure of the full system an
d inspire auxiliary maps based on the extreme bounds of the maps\, yieldin
g global\ndynamics of energetically favorable states. Beyond the individua
l impact pair\, we show how the framework is valuable in higher\ndimension
al configurations for shaping the energy transfer\, including billiard-typ
e designs\, networks of VI-pairs\, and multi-cavity VI\npairs. In these sy
stems the diagnostics from combined returns maps greatly reduce the number
of parameters and states of interest.\nComputational efficiencies follow
from maps generated by short sequences of the dynamics\, in contrast to tr
aditional dynamical\nquantities obtained from long-time simulations.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/44/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20260504T220000Z
DTEND:20260504T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/45
DESCRIPTION:Title: The sphere packing problem\nby Maryna Viazov
ska (EPFL) as part of UCLA distinguished lecture series\n\nInteractive liv
estream: https://ucla.zoom.us/j/9264073849\n\nAbstract\nI will discuss the
history of the sphere packing problem\, the known upper and lower bounds\
, and its solution in dimensions 8 and 24. I will introduce the magic func
tions and explain how they are constructed.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/45/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20260505T220000Z
DTEND:20260505T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/46
DESCRIPTION:Title: Fourier interpolation formulas\nby Maryna Vi
azovska (EPFL) as part of UCLA distinguished lecture series\n\nInteractive
livestream: https://ucla.zoom.us/j/9264073849\n\nAbstract\nI will discuss
Fourier interpolation formulas and their connection with the magic functi
ons. As an application\, I will show how such an interpolation formula lea
ds to the universal optimality of the E8 and Leech lattices.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/46/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20260506T220000Z
DTEND:20260506T230000Z
DTSTAMP:20260424T153137Z
UID:UCLADistinguishedLectures/47
DESCRIPTION:Title: Formalizing sphere packing\nby Maryna Viazov
ska (EPFL) as part of UCLA distinguished lecture series\n\nInteractive liv
estream: https://ucla.zoom.us/j/9264073849\n\nAbstract\nI will describe th
e path toward formalizing the sphere packing problem in dimensions 8 and 2
4. I will discuss the main milestones reached so far\, the role of AI\, an
d the challenges posed by large-scale formalization projects.\n
LOCATION:https://stable.researchseminars.org/talk/UCLADistinguishedLecture
s/47/
URL:https://ucla.zoom.us/j/9264073849
END:VEVENT
END:VCALENDAR