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BEGIN:VEVENT
SUMMARY:Adam Piggott (Australian National University)
DTSTART:20210408T050000Z
DTEND:20210408T060000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/1
DESCRIPTION:Title: Stubborn conjectures concerning rewriting systems\, geodesic normal f
orms and geodetic graphs\nby Adam Piggott (Australian National Univers
ity) as part of SMRI seminars\n\nLecture held in Quad Oriental Room S204
(University of Sydney staff\, students and affiliates only).\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murray Elder (University of Technology Sydney)
DTSTART:20210408T060000Z
DTEND:20210408T070000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/2
DESCRIPTION:Title: Which groups have polynomial geodesic growth?\nby Murray Elder (U
niversity of Technology Sydney) as part of SMRI seminars\n\nLecture held i
n Quad Oriental Room S204 (University of Sydney staff\, students and affi
liates only).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcy Robertson (University of Melbourne)
DTSTART:20210422T053000Z
DTEND:20210422T063000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/3
DESCRIPTION:Title: Expansions\, completions and automorphisms of welded tangled foams\nby Marcy Robertson (University of Melbourne) as part of SMRI seminars\n
\nLecture held in Quad Oriental Room S204 (University of Sydney staff\, s
tudents and affiliates only).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Tillmann (University of Sydney)
DTSTART:20210520T053000Z
DTEND:20210520T063000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/4
DESCRIPTION:Title: On the space of properly convex projective structures\nby Stephan
Tillmann (University of Sydney) as part of SMRI seminars\n\nLecture held
in Quad S227 (University of Sydney staff\, students and affiliates only).
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Onn (Australian National University)
DTSTART:20210603T053000Z
DTEND:20210603T063000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/5
DESCRIPTION:Title: Base change and representation growth of arithmetic groups\nby Ur
i Onn (Australian National University) as part of SMRI seminars\n\nLecture
held in Quad S227 (University of Sydney staff\, students and affiliates
only).\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Bazhanov (Australian National University)
DTSTART:20211026T030000Z
DTEND:20211026T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/6
DESCRIPTION:Title: Quantum geometry of 3-dimensional lattices\nby Vladimir Bazhanov
(Australian National University) as part of SMRI seminars\n\n\nAbstract\nI
n this lecture I will explain a relationship between incidence theorems in
elementary geometry and the theory of integrable systems\, both classical
and quantum. We will study geometric consistency relations between angles
of 3-dimensional (3D) circular quadrilateral lattices - lattices whose fa
ces are planar quadrilaterals inscribable into a circle. We show that thes
e relations generate canonical transformations of a remarkable "ultra-loca
l" Poisson bracket algebra defined on discrete 2D surfaces consisting of c
ircular quadrilaterals. Quantization of this structure allowed us to obtai
n new solutions of the tetrahedron equation (the 3D analogue of the Yang-B
axter equation) as well as reproduce all those that were previously known.
These solutions generate an infinite number of non-trivial solutions of t
he Yang-Baxter equation and also define integrable 3D models of statistica
l mechanics and quantum field theory. The latter can be thought of as desc
ribing quantum fluctuations of lattice geometry.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Davydov (Ohio University)
DTSTART:20211213T030000Z
DTEND:20211213T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/7
DESCRIPTION:Title: Condensation of anyons in topological states of matter and structure
theory of E_2-algebras\nby Alexei Davydov (Ohio University) as part of
SMRI seminars\n\n\nAbstract\nThe talk will be on the algebraic structure
present in both parts of the title. This algebraic story is most pronounce
d for E_2-algebras in the category of 2-vector spaces (also known as braid
ed fusion categories). Condensation gives rise to an equivalence relation
on such E_2-algebras (Witt equivalence) with sets of equivalence classes e
xhibiting nice properties\, e.g. being abelian groups (Witt groups). The W
itt group of braided fusion categories is a countably generated abelian gr
oup with the torsion part annihilated by 32.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Guo (Monash University)
DTSTART:20220222T040000Z
DTEND:20220222T050000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/8
DESCRIPTION:Title: Stochastic Optimal Transport in Financial Mathematics\nby Ivan Gu
o (Monash University) as part of SMRI seminars\n\n\nAbstract\nAbstract: In
recent years\, the field of optimal transport has attracted the attention
of many high-profile mathematicians with a wide range of applications. In
this talk we will discuss some of its recent applications in financial ma
thematics\, particularly on the problems of model calibration\, robust fin
ance and portfolio optimisation. Classical topological duality results are
extended to probabilistic settings\, connecting stochastic control proble
ms with non-linear partial differential equations and providing interestin
g practical interpretations in finance. We will also look at how numerical
methods\, including machine learning algorithms\, can be implemented to s
olve these problems.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Vo (Monash University)
DTSTART:20220308T040000Z
DTEND:20220308T050000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/9
DESCRIPTION:Title: Canards\, Cardiac Cycles\, and Chimeras\nby Theodore Vo (Monash U
niversity) as part of SMRI seminars\n\n\nAbstract\nSMRI Seminar \n'Canards
\, Cardiac Cycles\, and Chimeras’'\nTheodore Vo (Monash University) \n\n
Tuesday 8th March\, 3:00-4:00pm (AEDT) \n\nAbstract: Canards are solutions
of singularly perturbed ODEs that organise the dynamics\nin phase and par
ameter space. In this talk\, we explore two aspects of canard theory:\nth
eir applications in the life sciences and their ability to generate new ph
enomena.\nMore specifically\, we will use canard theory to analyse a canon
ical model of the\nelectrical activity in a heart muscle cell. We demonst
rate that pathological heart\nrhythms\, called early afterdepolarisations\
, are canard-induced phenomena. We use this\nknowledge to explain the ric
h set of model behaviours\, some of which have also been\nobserved in expe
riments. Then\, we explore a new class of canard-induced patterns in\nrea
ction-diffusion PDEs which exhibit coexisting domains of mutually synchron
ised\noscillators and complementary domains of decoherent (asynchronous) o
scillators. \n\nNote: This seminar will be recorded\, including participa
nt questions (participants only\nwhen asking questions)\, and uploaded to
the SMRI YouTube Channel\nhttps://www.youtube.com/c/SydneyMathematicalRese
archInstituteSMRI \n\nOther upcoming SMRI events can be found here:\nhttps
://mathematical-research-institute.sydney.edu.au/news-events/\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Grazian (University of Sydney)
DTSTART:20220510T050000Z
DTEND:20220510T060000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/10
DESCRIPTION:Title: Finding structures in observations: consistent(?) clustering analysi
s\nby Clara Grazian (University of Sydney) as part of SMRI seminars\n\
n\nAbstract\nAbstract: Clustering is an important task in almost every are
a of knowledge: medicine\nand epidemiology\, genomics\, environmental scie
nce\, economics\, visual sciences\, among\nothers. Methodologies to perfo
rm inference on the number of clusters have often been\nproved to be incon
sistent and introducing a dependence structure among the clusters\nimplies
additional difficulties in the estimation process. In a Bayesian setting
\,\nclustering in the situation where the number of clusters is unknown is
often performed\nby using Dirichlet process priors or finite mixture mode
ls. However\, the posterior\ndistributions on the number of groups have b
een recently proved to be inconsistent.\nThis seminar aims at reviewing th
e Bayesian approaches available to perform via mixture\nmodels and give so
me new insights.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henri Guenancia (Paul Sabatier University)
DTSTART:20220826T040000Z
DTEND:20220826T060000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/11
DESCRIPTION:Title: On the invariance of plurigenera\nby Henri Guenancia (Paul Sabat
ier University) as part of SMRI seminars\n\nLecture held in Quad S227 (for
University of Sydney staff\, students & affiliates only) & Online.\n\nAbs
tract\nAbstract: In this mini-course\, I will talk about a celebrated theo
rem of Yum-Tong Siu asserting that given a smooth projective family f:X->Y
of complex manifolds over an irreducible base and given any positive inte
ger m\, the dimension of the space of pluricanonical forms H^0(X_y\, mK_{X
_y}) is independent of Y. After recasting the result in its historical con
text\, I will mention the Ohsawa-Takegoshi extension theorem which plays a
central role of the proof. Finally\, I will sketch the main steps followi
ng Mihai Paun's streamlined proof of the theorem.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jana de Wiljes (University of Potsdam)
DTSTART:20220908T030000Z
DTEND:20220908T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/12
DESCRIPTION:Title: Sequential Bayesian Learning\nby Jana de Wiljes (University of P
otsdam) as part of SMRI seminars\n\nLecture held in Quad S223 (for Univers
ity of Sydney staff\, students & affiliates only) & Online.\n\nAbstract\nI
n various application areas it is crucial to make predictions or decisions
based on sequentially incoming observations and previous existing knowled
ge on the system of interest. The prior knowledge is often given in the fo
rm of evolution equations (e.g.\, ODEs derived via first principles or fit
ted based on previously collected data)\, from here on referred to as mode
l. Despite the available observation and prior model information\, accurat
e predictions of the „true“ reference dynamics can be very difficult.
Common reasons that make this problem so challenging are: (i) the underlyi
ng system is extremely complex (e.g.\, highly nonlinear) and chaotic (i.e.
\, crucially dependent on the initial conditions)\, (ii) the associate sta
te and/or parameter space is very high dimensional (e.g.\, worst case 10^8
) (iii) Observations are noisy\, partial in space and discrete in time.\n\
nIn practice these obstacles are combated with a series of approximations
(the most important ones being based on assuming Gaussian densities and us
ing Monte Carlo type estimations) and numerical tools that work surprising
ly well in some settings. Yet the mathematical understanding of the signal
tracking ability of a lot of these methods is still lacking. Additionally
\, solutions of some of the more complicated problems that require simulta
neous state and parameter estimation (including control parameters that ca
n be understood as decisions/actions performed) can still not be approxima
ted in a computationally feasible fashion. Here we will try to address the
first layer of these issues step by step and discuss the next advances th
at need to be made in these many layered problems. More specifically a sta
bility and accuracy analysis of a family of the most popular sequential da
ta assimilation methods typically used in practice is presented. Then we w
ill discuss how techniques from the world of machine learning can aid to o
vercome some of the computational challenges.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafał Kulik (University of Ottawa)
DTSTART:20221110T020000Z
DTEND:20221110T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/13
DESCRIPTION:Title: Disjoint and sliding blocks estimators for heavy tailed time series<
/a>\nby Rafał Kulik (University of Ottawa) as part of SMRI seminars\n\nLe
cture held in Quad S223 (for University of Sydney staff\, students & affil
iates only) & Online.\n\nAbstract\nExtreme value theory deals with large v
alues and rare events. These large\nvalues tend to cluster in case of tem
poral dependence. This clustering behaviour is\nwidely observed in practi
ce. \n\nI will start with a mild introduction to extreme value theory\, d
iscussing probabilistic\nand statistical issues. This part will be access
ible to a broader audience. \n\nThen\, I will talk about a more specific
problem of statistical theory for cluster\nfunctionals and rare events. T
wo types of estimators are of a primary importance:\ndisjoint and sliding
blocks estimators. It has been conjectured that sliding blocks\nestimator
s are "better" (to be made precise in the talk). We proved in a recent\ns
eries of papers that this is not the case and in fact both disjoint and sl
iding blocks\nestimators are asymptotically equivalent. This part will be
aimed at probabilistic and\nstatisticians. \n\nI will conclude with rece
nt directions in extreme value theory\, such as extremes in high\ndimensio
n\, extremes of graphs and networks.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART:20221110T040000Z
DTEND:20221110T050000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/14
DESCRIPTION:Title: Discrete two-generator subgroups of PSL(2\,Q_p)\nby Matthew Cond
er (University of Auckland) as part of SMRI seminars\n\nLecture held in Qu
ad S223 (for University of Sydney staff\, students & affiliates only) & On
line.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeroen Schillewaert (University of Auckland)
DTSTART:20221117T000000Z
DTEND:20221117T010000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/15
DESCRIPTION:Title: Constructing highly regular expanders from hyperbolic Coxeter groups
\nby Jeroen Schillewaert (University of Auckland) as part of SMRI semi
nars\n\nLecture held in Quad S223 & Online.\n\nAbstract\nGiven a string Co
xeter system (W\,S)\, we construct highly regular quotients of the 1-skele
ton of its universal polytope P\, which form an infinite family of expande
r graphs when (W\,S) is indefinite and P has finite vertex links. The regu
larity of the graphs in this family depends on the Coxeter diagram of (W\,
S). The expansion stems from superapproximation applied to (W\,S). This co
nstruction is also extended to cover Wythoffian polytopes. As a direct app
lication\, we obtain several notable families of expander graphs with high
levels of regularity\, answering in particular a question posed by Chapma
n\, Linial and Peled positively.\n\nThis talk is based on joint work with
Marston Conder\, Alexander Lubotzky and Francois Thilmany.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changfeng Gui (University of Texas at San Antonio)
DTSTART:20221117T020000Z
DTEND:20221117T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/16
DESCRIPTION:Title: Some New Inequalities in Analysis and Geometry\nby Changfeng Gui
(University of Texas at San Antonio) as part of SMRI seminars\n\nLecture
held in Quad S223 & Online.\n\nAbstract\nThe classical Trudinger-Moser ine
quality is a borderline case of Sobolev inequalities and plays an importan
t role in geometric analysis and PDEs in general. Aubin in 1979 showed tha
t the best constant in the Trudinger-Moser inequality can be improved by r
educing to one half if the functions are restricted to the complement of a
three dimensional subspace of the Sobolev space $H^1$\, while Onofri in 1
982 discovered an elegant optimal form of Trudinger-Moser inequality on sp
here. In this talk\, I will present new sharp inequalities which are varia
nts of Aubin and Onofri inequalities on the sphere with or without mass ce
nter constraints.\n\nOne such inequality\, for example\, incorporates the
mass center deviation (from the origin) into the optimal inequality of Aub
in on the sphere\, which is for functions with mass centered at the origin
. The main ingredient leading to the above inequalities is a novel geometr
ic inequality: Sphere Covering Inequality.\n\nEfforts have also been made
to show similar inequalities in higher dimensions. Among the preliminary r
esults\, we have improved Beckner's inequality for axially symmetric funct
ions when the dimension $n=4\, 6\, 8$. Many questions remain open.\n\nThe
talk is based on collaborations with Amir Moradifam\, Sun-Yung Alice Chang
\, Yeyao Hu and Weihong Xie.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Crespo (Universidad del Bío-Bío)
DTSTART:20221201T020000Z
DTEND:20221201T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/17
DESCRIPTION:Title: Relative equilibria in the full N-body problem\nby Francisco Cre
spo (Universidad del Bío-Bío) as part of SMRI seminars\n\nLecture held i
n Quad S223 & Online.\n\nAbstract\nSMRI Seminar\n'Relative equilibria in t
he full N-body problem'\nFrancisco Crespo (Universidad del Bío-Bío)\n\nT
hursday 1st December\nQuad S223 & Online\n\nAbstract: The full N-body prob
lem addresses the dynamics of N rigid bodies under mutual gravitational in
teractions. This physical system has powered the fabric of science and esp
ecially mathematics for centuries\, having a decisive role in developing g
eometric mechanics\, qualitative theory of dynamical systems\, or KAM theo
ry. In this talk\, we briefly survey this problem and focus on analyzing s
pecial solutions called relative equilibria.\n\nAfter determining the hami
ltonian equations of motion\, our approach identifies and uses the existen
ce of translational and rotational symmetries of the N-body problem. In pa
rticular\, we provide very compact equations characterizing relative equil
ibria solutions\, which become linear by fixing the values of the invarian
ts associated with the action of the symmetry group.\n\nIn the existing li
terature\, relative equilibria have been classified into Lagrangian and no
n-Lagrangian\, respectively\, corresponding to whether the center of mass
of all bodies is in the same plane. Our analysis determines what kind of c
onfigurations allow for each type of equilibrium and provides necessary co
nditions for non-Lagrangian equilibria.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Foucart (Texas A&M University)
DTSTART:20230302T020000Z
DTEND:20230302T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/18
DESCRIPTION:Title: Nonstatistical Learning Theory: the View from Optimal Recovery\n
by Simon Foucart (Texas A&M University) as part of SMRI seminars\n\nLectur
e held in Quad S249 & Online.\n\nAbstract\nFor a function observed through
point evaluations\, is there an optimal way to recover it or merely to es
timate a dependent quantity? I will give affirmative answers to variations
of this data-focused question\, especially under the assumption that the
function belongs to a model set defined by approximation capabilities. In
fact\, I will uncover computationally implementable linear recovery maps t
hat are optimal in the worst-case setting. I will present some recent and
ongoing works extending the theory in several directions\, with particular
emphasis put on observations that are inexact---adversarially or randomly
.\n\nThis seminar will not be recorded.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Yang (Microsoft Research in Redmond\, Washington)
DTSTART:20230323T020000Z
DTEND:20230323T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/19
DESCRIPTION:Title: The unreasonable effectiveness of mathematics in large scale deep le
arning\nby Greg Yang (Microsoft Research in Redmond\, Washington) as p
art of SMRI seminars\n\nLecture held in Quad S249 & Online.\n\nAbstract\nR
ecently\, the theory of infinite-width neural networks led to the first te
chnology\, muTransfer\, for tuning enormous neural networks that are too e
xpensive to train more than once. For example\, this allowed us to tune th
e 6.7 billion parameter version of GPT-3 using only 7% of its pretraining
compute budget\, and with some asterisks\, we get a performance comparable
to the original GPT-3 model with twice the parameter count. In this talk\
, I will explain the core insight behind this theory. In fact\, this is an
instance of what I call the *Optimal Scaling Thesis*\, which connects inf
inite-size limits for general notions of “size” to the optimal design
of large models in practice\, illustrating a way for theory to reliably gu
ide the future of AI. I'll end with several concrete key mathematical rese
arch questions whose resolutions will have incredible impact on how practi
tioners scale up their NNs.\n\n\nBiography: Greg Yang is a researcher at M
icrosoft Research in Redmond\, Washington.\nHe joined MSR after he obtaine
d Bachelor's in Mathematics and Master's degrees in Computer Science from
Harvard University\, respectively advised by ST Yau and Alexander Rush. He
won the Hoopes prize at Harvard for best undergraduate thesis as well as
Honorable Mention for the AMS-MAA-SIAM Morgan Prize\, the highest honor in
the world for an undergraduate in mathematics. He gave an invited talk at
the International Congress of Chinese Mathematicians 2019.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Kovács (University of Washington)
DTSTART:20230420T030000Z
DTEND:20230420T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/20
DESCRIPTION:Title: Tricking the Devil\nby Sándor Kovács (University of Washington
) as part of SMRI seminars\n\nLecture held in Quad S249.\n\nAbstract\nMax
Noether said that algebraic curves were created by God and algebraic surfa
ces by the Devil. Unfortunately\, that description seems to be also valid
for the moduli theory of these objects respectively. I will recall one of
the first obstacles one faces when trying to extend the basic results of t
he moduli theory of curves to that of surfaces and then discuss how one ma
y resolve the arising issue. Time permitting\, I will also explain the var
ious stability conditions this problem and its resolution led to.\n\nBiogr
aphy: Sándor Kovács is a Professor of Mathematics at the University of W
ashington. He received his BS degree at Eötvös University (Hungary)\, an
d his PhD at the University of Utah. He held positions at MIT and the Univ
ersity of Chicago before moving to the University of Washington. His award
s include the American Mathematical Society's Centennial Research Fellowsh
ip\, Alfred P. Sloan Foundation Research Fellowship\, and two Simons Found
ation Fellowships. He is a Fellow of the American Mathematical Society.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan James Wylie (City University of Hong Kong)
DTSTART:20230427T030000Z
DTEND:20230427T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/21
DESCRIPTION:Title: Unexpected Behaviour in Dilute Granular Materials\nby Jonathan J
ames Wylie (City University of Hong Kong) as part of SMRI seminars\n\nLect
ure held in Quad S249.\n\nAbstract\nThe phrase 'granular material' is used
to describe a large number of discrete solid\, macroscopic particles that
lose energy whenever the particles collide. One might naively imagine tha
t such systems would exhibit similar behaviour to traditional fluid and so
lid mechanics. However\, we present two problems that superficially appear
to be extremely simple but yield surprisingly rich dynamics that have no
analogue in traditional mechanics. Firstly\, we consider a dilute stream o
f particles that collides with an oblique planar wall. Secondly\, we show
several surprising phenomena that occur in an extremely simple system of a
single frictionless\, inelastic\, spherical particle falling under gravit
y through a symmetric funnel.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Gray (University of East Anglia)
DTSTART:20230504T030000Z
DTEND:20230504T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/22
DESCRIPTION:Title: Subgroups of inverse monoids via the geometry of their Cayley graphs
\nby Robert Gray (University of East Anglia) as part of SMRI seminars\
n\nLecture held in Quad S249 & Online.\n\nAbstract\nIn the 1960's Higman w
as able to characterize the finitely generated subgroups of finitely prese
nted groups\, that is\, groups defined using a finite set of generators an
d finite set of defining relations. His result\, which is called the Higma
n Embedding Theorem\, is a key result in combinatorial group theory which
makes precise the connection between group presentations and logic. In thi
s talk I will present a result of a similar flavour\, proved in recent joi
nt work with Mark Kambites (Manchester)\, in which we characterise the gro
ups of units of inverse monoids defined by presentation where all the defi
ning relators are of the form w=1. I will explain what an inverse monoid i
s\, the motivation for studying this class of inverse monoids\, and also o
utline some of the geometric ideas that we developed in order to prove our
results.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Rink (Vrije Universiteit Amsterdam)
DTSTART:20230511T030000Z
DTEND:20230511T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/23
DESCRIPTION:Title: What is the parametrization method in dynamical systems?\nby Bob
Rink (Vrije Universiteit Amsterdam) as part of SMRI seminars\n\nLecture h
eld in Quad S249 & Online.\n\nAbstract\nThe parametrization method is a to
ol to compute invariant manifolds in dynamical systems\, such as periodic
orbits\, (un-)stable manifolds\, slow manifolds and invariant tori. The id
ea behind the method is simple: it works by (algorithmically) finding an e
mbedding of the invariant manifold together with a representation of its d
ynamics in a coordinate chart. De La Llave et al realized that the method
can nicely be combined with ideas from rigorous numerics\, to provide comp
uter-assisted proofs for the existence of invariant manifolds. Others\, in
cluding myself\, have used the method to compute high-precision approximat
ions of the dynamics on the invariant manifolds. I will discuss both appro
aches\, starting with the basics and finishing with an unpublished result
on high-order phase reduction.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20230720T030000Z
DTEND:20230720T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/24
DESCRIPTION:Title: Nonlocal Aggregation-Diffusion Equations: fast diffusion and partial
concentration\nby Jose A. Carrillo (University of Oxford) as part of
SMRI seminars\n\nLecture held in Carslaw 375 & Online.\n\nAbstract\nWe wil
l discuss several recent results for aggregation-diffusion equations relat
ed to partial concentration of the density of particles. Nonlinear diffusi
ons with homogeneous kernels will be reviewed quickly in the case of degen
erate diffusions to have a full picture of the problem. Most of the talk w
ill be devoted to discuss the less explored case of fast diffusion with ho
mogeneous kernels with positive powers. We will first concentrate in the c
ase of stationary solutions by looking at minimisers of the associated fre
e energy showing that the minimiser must consist of a regular smooth solut
ion with singularity at the origin plus possibly a partial concentration o
f the mass at the origin. We will give necessary conditions for this parti
al mass concentration to and not to happen. We will then look at the relat
ed evolution problem and show that for a given confinement potential this
concentration happens in infinite time under certain conditions. We will b
riefly discuss the latest developments when we introduce the aggregation t
erm. This talk is based on a series of works in collaboration with M. Delg
adino\, J. Dolbeault\, A. Fernández\, R. Frank\, D. Gómez-Castro\, F. Ho
ffmann\, M. Lewin\, and J. L. Vázquez\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Lu (University of Oregon)
DTSTART:20230810T030000Z
DTEND:20230810T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/25
DESCRIPTION:Title: Conformal Bach flow\nby Peng Lu (University of Oregon) as part o
f SMRI seminars\n\nLecture held in Carslaw 375 & Online.\n\nAbstract\nWe i
ntroduce conformal Bach flow and establish its well-posedness on closed \n
manifolds. We also obtain its backward uniqueness. To give an attempt to
study the \nlong-time behavior of conformal Bach flow\, assuming that the
curvature and the pressure \nfunction are bounded\, global and local Shi
’s type $L^2$ estimate of derivatives of \ncurvatures are derived.\n\nTo
make the talk more accessible\, we will spend some time to survey on high
order \nparabolic curvature flow. This is a joint work with Jiaqi Chen of
Xiamen University and \nJie Qing of UCSC.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Pedit (University of Massachusetts\, Amherst)
DTSTART:20230824T030000Z
DTEND:20230824T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/26
DESCRIPTION:Title: Minimal Lagrangian surfaces of high genus in $CP^2$\nby Franz Pe
dit (University of Massachusetts\, Amherst) as part of SMRI seminars\n\nLe
cture held in Carslaw 375 & Online.\n\nAbstract\nThe study of properties o
f surfaces in space has historically been a fertile ground for advances in
topology\, analysis\, geometry\, Lie theory\, and mathematical physics. T
he most important surface classes are those which arise form variational p
roblems\, for example\, minimal surfaces which are critical points of the
area functional. The Euler Lagrange equations are PDEs which serve as mode
l cases for developments in geometric analysis. Often these equations exhi
bit large (sometimes infinite dimensional) symmetry groups which puts the
theory into the realm of “integrable systems”\, that is\, PDEs which a
llow for an infinte hierarchy of conserved quantities. This theory has bee
n studied extensively over the past 40 years and led to significant advanc
es in the classification of (minimal\, constant mean curvature\, Willmore
etc.) surfaces of genus one. The higher genus case has been more illusive
and examples are usually constructed using non-linear perturbation theory
and gluing techniques.\n\nIn this talk I will explain how one can use idea
s from integrable systems to construct examples of high genus minmal Lagra
ngian surfaces without recourse to hard analysis.\n\nThis approach is more
explicit than PDE existence results and one is able to obtain more quanti
tative information about the constructed examples\, for instance\, asympto
tic area/energy estimates. I will also give a brief overview of the histor
ical developments and the significance of minimal Lagrangian surfaces in m
athematical physics.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Wyatt (University of Cambridge)
DTSTART:20230831T030000Z
DTEND:20230831T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/27
DESCRIPTION:Title: Stability problems in general relativity\nby Zoe Wyatt (Universi
ty of Cambridge) as part of SMRI seminars\n\nLecture held in Carslaw 375 &
Online.\n\nAbstract\nEinstein's theory of general relativity makes specta
cular predictions\, like gravitational waves\, about our universe. For the
mathematician\, the analysis of the hyperbolic Einstein equations is one
of the most powerful ways to understand conceptual questions of the theory
.\n\nIn this talk\, I will explain some of the contributions of mathematic
s to general relativity\, highlighting a recent joint work showing the sta
bility of Kaluza-Klein spacetimes. These are important models in supergrav
ity and their stability is connected to claims of Penrose and Witten.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daryl Cooper (University of California\, Santa Barbara)
DTSTART:20240222T020000Z
DTEND:20240222T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/28
DESCRIPTION:Title: Symmetry\, old and new\nby Daryl Cooper (University of Californi
a\, Santa Barbara) as part of SMRI seminars\n\nLecture held in University
of Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAbstract\nI will di
scuss symmetry from a combinatorial perspective. Examples include wallpape
r groups\, 4-valent graphs\, regular languages\, molecules\, Penrose til
ings\, and geometric 3-manifolds. It turns out that for each of these clas
ses there is a finite universal geometric object that encodes all the poss
ibilities.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Elvira (University of Edinburgh)
DTSTART:20240229T020000Z
DTEND:20240229T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/29
DESCRIPTION:Title: State-space models as graphs\nby Victor Elvira (University of Ed
inburgh) as part of SMRI seminars\n\nLecture held in University of Sydney\
, Law Annex Lecture Theatre 026 & Online.\n\nAbstract\nModeling and infere
nce in multivariate time series is central in statistics\,\nsignal process
ing\, and machine learning. A fundamental question when analyzing\nmultiv
ariate sequences is the search for relationships between their entries (or
the\nmodeled hidden states)\, especially when the inherent structure is a
directed (causal)\ngraph. In such context\, graphical modeling combined
with sparsity constraints allows to\nlimit the proliferation of parameters
and enables a compact data representation which is\neasier to interpret i
n applications\, e.g.\, in inferring causal relationships of physical\npro
cesses in a Granger sense. In this talk\, we present a novel perspective
consisting\non state-space models being interpreted as graphs. Then\, we
propose novel algorithms\nthat exploit this new perspective for the estima
tion of the linear matrix operator and\nalso the covariance matrix in the
state equation of a linear-Gaussian state-space\nmodel. Finally\, we disc
uss the extension of this perspective for the estimation of\nother model p
arameters in more complicated models.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shane G. Henderson (Cornell University)
DTSTART:20240307T020000Z
DTEND:20240307T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/30
DESCRIPTION:Title: A Tutorial and Perspectives on Monte Carlo Simulation Optimization\nby Shane G. Henderson (Cornell University) as part of SMRI seminars\n\
nLecture held in University of Sydney\, Law Annex Lecture Theatre 026 & On
line.\n\nAbstract\nI provide a tutorial and some perspectives on simulatio
n optimization\, in which one wishes to minimize an objective function tha
t can only be evaluated with noise through a stochastic computer simulatio
n. First\, I'll give a few examples and intuitively explain some central i
ssues in the area. Second\, I'll explain why so-called sample-path functio
ns can exhibit extremely complex behavior that is well worth understanding
. Third\, I'll argue that more attention should be devoted to the finite-t
ime performance of solvers than on ensuring convergence properties that ma
y only arise in asymptotic time scales that may never be reached in practi
ce. I'll outline an approach for obtaining such results analytically (thro
ugh Lyapunov functions) and introduce a framework and code for computation
al experiments that can further this goal. Fourth (if time permits\, thoug
h I doubt it will)\, I'll advocate the use of a layered approach to formul
ating and solving optimization problems\, whereby a sequence of models are
built and optimized\, rather than first building a simulation model and o
nly later “bolting on” optimization\, partly through an example of my
work involving bike sharing with the organization Citi Bike in New York ci
ty.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Su (Harvey Mudd College)
DTSTART:20240314T020000Z
DTEND:20240314T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/31
DESCRIPTION:Title: Sperner's Lemma: a generalization with surprising applications\n
by Francis Su (Harvey Mudd College) as part of SMRI seminars\n\nLecture he
ld in University of Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAb
stract\nWho doesn't like one of these three: geometry\, topology\, and com
binatorics? And even if you don't\, you will still love Sperner's lemma\,
which is a combinatorial statement that is equivalent to the Brouwer fixed
point theorem in topology. I'll explain what it is\, why it's so amazing\
, give heartwarming old and new proofs\, and present a recent generalizati
on tio polytopes that has surprised me with diverse applications: to the s
tudy of triangulations\, to fair division problems\, and the Game of Hex.\
n
LOCATION:https://researchseminars.org/talk/SMRIseminars/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salil Vadhan (Harvard University)
DTSTART:20240321T020000Z
DTEND:20240321T030000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/32
DESCRIPTION:Title: Derandomizing Algorithms via Spectral Graph Theory\nby Salil Vad
han (Harvard University) as part of SMRI seminars\n\nLecture held in Unive
rsity of Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAbstract\nRan
domization is a powerful tool for algorithms\; it is often easier to desig
n efficient algorithms if we allow the algorithms to "toss coins" and outp
ut a correct answer with high probability. However\, a longstanding conjec
ture in theoretical computer science is that every randomized algorithm ca
n be efficiently "derandomized" --- converted into a deterministic algorit
hm (which always outputs the correct answer) with only a polynomial increa
se in running time and only a constant-factor increase in space (i.e. memo
ry usage). In this talk\, I will describe an approach to proving the space
(as opposed to time) part of this conjecture via spectral graph theory. S
pecifically\, I will explain how randomized space-bounded algorithms are d
escribed by random walks on directed graphs\, and techniques in algorithmi
c spectral graph theory (e.g. solving Laplacian systems) have yielded dete
rministic space-efficient algorithms for approximating the behavior of suc
h random walks on undirected graphs and Eulerian directed graphs (where ev
ery vertex has the same in-degree as out-degree). If these algorithms can
be extended to general directed graphs\, then the aforementioned conjectur
e about derandomizing space-efficient algorithms will be resolved. These p
roblems also lead us to explore new notions of what it means for two direc
ted graphs to "spectrally approximate" each other\, which may be of indepe
ndent interest.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Donovan (Tsinghua University)
DTSTART:20240411T030000Z
DTEND:20240411T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/33
DESCRIPTION:Title: McKay correspondence and toric geometry\nby Will Donovan (Tsingh
ua University) as part of SMRI seminars\n\nLecture held in University of S
ydney\, Law Annex Lecture Theatre 026.\n\nAbstract\nFinite subgroups of th
e matrix group SU(2) may be studied algebraically via \ntheir representati
ons. They may also be studied geometrically via two-dimensional \ncomplex
manifolds naturally associated to them. The McKay correspondence is a gene
ral \nphenomenon which\, in particular\, explains how these two approaches
relate. I’ll \nintroduce this using diagramatics from toric geometry\,
indicate how the correspondence \ngeneralizes to higher dimensions\, and d
iscuss open questions and current projects.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dave Futer (Temple University\, Philadelphia)
DTSTART:20240502T030000Z
DTEND:20240502T040000Z
DTSTAMP:20260422T225922Z
UID:SMRIseminars/34
DESCRIPTION:Title: The generalized knot complement problem\nby Dave Futer (Temple U
niversity\, Philadelphia) as part of SMRI seminars\n\nLecture held in Univ
ersity of Sydney\, Law Annex Lecture Theatre 026.\n\nAbstract\nIn 1908\, T
ietze posed the provocative question of whether a mathematical knot \n- a
knotted rope\, with its ends spliced together - is completely determined b
y the \ntopological shape of the empty space that surrounds the knot. Afte
r being open for 80 \nyears\, this question was solved in 1988\, and we kn
ow the answer is Yes.\n\nSince that time\, mathematicians have studied the
open question of whether the same \nproperty holds for knots in general 3
-dimensional spaces. Given a 3-dimensional manifold \nM\, is a knot in M e
ntirely determined by the space that surrounds it in M? I will \ndiscuss s
ome recent work on this question using hyperbolic (negatively curved) geom
etry. \nThis is joint work with Jessica Purcell and Saul Schleimer.\n
LOCATION:https://researchseminars.org/talk/SMRIseminars/34/
END:VEVENT
END:VCALENDAR