BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Adam Piggott (Australian National University)
DTSTART:20210408T050000Z
DTEND:20210408T060000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/1
DESCRIPTION:Title: Stubborn conjectures concerning rewriting systems\, geodesic n
ormal forms and geodetic graphs\nby Adam Piggott (Australian National
University) as part of SMRI seminars\n\nLecture held in Quad Oriental Room
S204 (University of Sydney staff\, students and affiliates only).\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murray Elder (University of Technology Sydney)
DTSTART:20210408T060000Z
DTEND:20210408T070000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/2
DESCRIPTION:Title: Which groups have polynomial geodesic growth?\nby Murray E
lder (University of Technology Sydney) as part of SMRI seminars\n\nLecture
held in Quad Oriental Room S204 (University of Sydney staff\, students a
nd affiliates only).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcy Robertson (University of Melbourne)
DTSTART:20210422T053000Z
DTEND:20210422T063000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/3
DESCRIPTION:Title: Expansions\, completions and automorphisms of welded tangled f
oams\nby Marcy Robertson (University of Melbourne) as part of SMRI sem
inars\n\nLecture held in Quad Oriental Room S204 (University of Sydney st
aff\, students and affiliates only).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Tillmann (University of Sydney)
DTSTART:20210520T053000Z
DTEND:20210520T063000Z
DTSTAMP:20260404T111414Z
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\nLectur
e held in Quad S227 (University of Sydney staff\, students and affiliates
only).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Onn (Australian National University)
DTSTART:20210603T053000Z
DTEND:20210603T063000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/5
DESCRIPTION:Title: Base change and representation growth of arithmetic groups
\nby Uri Onn (Australian National University) as part of SMRI seminars\n\n
Lecture held in Quad S227 (University of Sydney staff\, students and affi
liates only).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Bazhanov (Australian National University)
DTSTART:20211026T030000Z
DTEND:20211026T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/6
DESCRIPTION:Title: Quantum geometry of 3-dimensional lattices\nby Vladimir Ba
zhanov (Australian National University) as part of SMRI seminars\n\n\nAbst
ract\nIn this lecture I will explain a relationship between incidence theo
rems in elementary geometry and the theory of integrable systems\, both cl
assical and quantum. We will study geometric consistency relations between
angles of 3-dimensional (3D) circular quadrilateral lattices - lattices w
hose faces are planar quadrilaterals inscribable into a circle. We show th
at these relations generate canonical transformations of a remarkable "ult
ra-local" Poisson bracket algebra defined on discrete 2D surfaces consisti
ng of circular quadrilaterals. Quantization of this structure allowed us t
o obtain new solutions of the tetrahedron equation (the 3D analogue of the
Yang-Baxter equation) as well as reproduce all those that were previously
known. These solutions generate an infinite number of non-trivial solutio
ns of the Yang-Baxter equation and also define integrable 3D models of sta
tistical mechanics and quantum field theory. The latter can be thought of
as describing quantum fluctuations of lattice geometry.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Davydov (Ohio University)
DTSTART:20211213T030000Z
DTEND:20211213T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/7
DESCRIPTION:Title: Condensation of anyons in topological states of matter and str
ucture 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 str
ucture present in both parts of the title. This algebraic story is most pr
onounced for E_2-algebras in the category of 2-vector spaces (also known a
s braided fusion categories). Condensation gives rise to an equivalence re
lation on such E_2-algebras (Witt equivalence) with sets of equivalence cl
asses exhibiting nice properties\, e.g. being abelian groups (Witt groups)
. The Witt group of braided fusion categories is a countably generated abe
lian group with the torsion part annihilated by 32.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Guo (Monash University)
DTSTART:20220222T040000Z
DTEND:20220222T050000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/8
DESCRIPTION:Title: Stochastic Optimal Transport in Financial Mathematics\nby
Ivan Guo (Monash University) as part of SMRI seminars\n\n\nAbstract\nAbstr
act: In recent years\, the field of optimal transport has attracted the at
tention of many high-profile mathematicians with a wide range of applicati
ons. In this talk we will discuss some of its recent applications in finan
cial mathematics\, particularly on the problems of model calibration\, rob
ust finance and portfolio optimisation. Classical topological duality resu
lts are extended to probabilistic settings\, connecting stochastic control
problems with non-linear partial differential equations and providing int
eresting practical interpretations in finance. We will also look at how nu
merical methods\, including machine learning algorithms\, can be implement
ed to solve these problems.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Vo (Monash University)
DTSTART:20220308T040000Z
DTEND:20220308T050000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/9
DESCRIPTION:Title: Canards\, Cardiac Cycles\, and Chimeras\nby Theodore Vo (M
onash University) as part of SMRI seminars\n\n\nAbstract\nSMRI Seminar \n'
Canards\, Cardiac Cycles\, and Chimeras’'\nTheodore Vo (Monash Universit
y) \n\nTuesday 8th March\, 3:00-4:00pm (AEDT) \n\nAbstract: Canards are so
lutions of singularly perturbed ODEs that organise the dynamics\nin phase
and parameter space. In this talk\, we explore two aspects of canard theo
ry:\ntheir applications in the life sciences and their ability to generate
new phenomena.\nMore specifically\, we will use canard theory to analyse
a canonical model of the\nelectrical activity in a heart muscle cell. We
demonstrate that pathological heart\nrhythms\, called early afterdepolaris
ations\, are canard-induced phenomena. We use this\nknowledge to explain
the rich set of model behaviours\, some of which have also been\nobserved
in experiments. Then\, we explore a new class of canard-induced patterns
in\nreaction-diffusion PDEs which exhibit coexisting domains of mutually s
ynchronised\noscillators and complementary domains of decoherent (asynchro
nous) oscillators. \n\nNote: This seminar will be recorded\, including pa
rticipant questions (participants only\nwhen asking questions)\, and uploa
ded to the SMRI YouTube Channel\nhttps://www.youtube.com/c/SydneyMathemati
calResearchInstituteSMRI \n\nOther upcoming SMRI events can be found here:
\nhttps://mathematical-research-institute.sydney.edu.au/news-events/\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Grazian (University of Sydney)
DTSTART:20220510T050000Z
DTEND:20220510T060000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/10
DESCRIPTION:Title: Finding structures in observations: consistent(?) clustering
analysis\nby Clara Grazian (University of Sydney) as part of SMRI semi
nars\n\n\nAbstract\nAbstract: Clustering is an important task in almost ev
ery area of knowledge: medicine\nand epidemiology\, genomics\, environment
al science\, economics\, visual sciences\, among\nothers. Methodologies t
o perform inference on the number of clusters have often been\nproved to b
e inconsistent and introducing a dependence structure among the clusters\n
implies additional difficulties in the estimation process. In a Bayesian
setting\,\nclustering in the situation where the number of clusters is unk
nown is often performed\nby using Dirichlet process priors or finite mixtu
re models. However\, the posterior\ndistributions on the number of groups
have been recently proved to be inconsistent.\nThis seminar aims at revie
wing the Bayesian approaches available to perform via mixture\nmodels and
give some new insights.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henri Guenancia (Paul Sabatier University)
DTSTART:20220826T040000Z
DTEND:20220826T060000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/11
DESCRIPTION:Title: On the invariance of plurigenera\nby Henri Guenancia (Pau
l Sabatier University) as part of SMRI seminars\n\nLecture held in Quad S2
27 (for University of Sydney staff\, students & affiliates only) & Online.
\n\nAbstract\nAbstract: In this mini-course\, I will talk about a celebrat
ed theorem of Yum-Tong Siu asserting that given a smooth projective family
f:X->Y of complex manifolds over an irreducible base and given any positi
ve integer 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 histori
cal context\, I will mention the Ohsawa-Takegoshi extension theorem which
plays a central role of the proof. Finally\, I will sketch the main steps
following Mihai Paun's streamlined proof of the theorem.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jana de Wiljes (University of Potsdam)
DTSTART:20220908T030000Z
DTEND:20220908T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/12
DESCRIPTION:Title: Sequential Bayesian Learning\nby Jana de Wiljes (Universi
ty of Potsdam) as part of SMRI seminars\n\nLecture held in Quad S223 (for
University of Sydney staff\, students & affiliates only) & Online.\n\nAbst
ract\nIn various application areas it is crucial to make predictions or de
cisions based on sequentially incoming observations and previous existing
knowledge on the system of interest. The prior knowledge is often given in
the form of evolution equations (e.g.\, ODEs derived via first principles
or fitted based on previously collected data)\, from here on referred to
as model. Despite the available observation and prior model information\,
accurate predictions of the „true“ reference dynamics can be very diff
icult. Common reasons that make this problem so challenging are: (i) the u
nderlying system is extremely complex (e.g.\, highly nonlinear) and chaoti
c (i.e.\, crucially dependent on the initial conditions)\, (ii) the associ
ate state and/or parameter space is very high dimensional (e.g.\, worst ca
se 10^8) (iii) Observations are noisy\, partial in space and discrete in t
ime.\n\nIn practice these obstacles are combated with a series of approxim
ations (the most important ones being based on assuming Gaussian densities
and using Monte Carlo type estimations) and numerical tools that work sur
prisingly well in some settings. Yet the mathematical understanding of the
signal tracking ability of a lot of these methods is still lacking. Addit
ionally\, solutions of some of the more complicated problems that require
simultaneous state and parameter estimation (including control parameters
that can be understood as decisions/actions performed) can still not be ap
proximated in a computationally feasible fashion. Here we will try to addr
ess the first layer of these issues step by step and discuss the next adva
nces that need to be made in these many layered problems. More specificall
y a stability and accuracy analysis of a family of the most popular sequen
tial data assimilation methods typically used in practice is presented. Th
en we will discuss how techniques from the world of machine learning can a
id to overcome some of the computational challenges.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafał Kulik (University of Ottawa)
DTSTART:20221110T020000Z
DTEND:20221110T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/13
DESCRIPTION:Title: Disjoint and sliding blocks estimators for heavy tailed time
series\nby Rafał Kulik (University of Ottawa) as part of SMRI seminar
s\n\nLecture held in Quad S223 (for University of Sydney staff\, students
& affiliates only) & Online.\n\nAbstract\nExtreme value theory deals with
large values and rare events. These large\nvalues tend to cluster in case
of temporal dependence. This clustering behaviour is\nwidely observed in
practice. \n\nI will start with a mild introduction to extreme value the
ory\, discussing probabilistic\nand statistical issues. This part will be
accessible to a broader audience. \n\nThen\, I will talk about a more sp
ecific problem of statistical theory for cluster\nfunctionals and rare eve
nts. Two types of estimators are of a primary importance:\ndisjoint and s
liding blocks estimators. It has been conjectured that sliding blocks\nes
timators are "better" (to be made precise in the talk). We proved in a re
cent\nseries of papers that this is not the case and in fact both disjoint
and sliding blocks\nestimators are asymptotically equivalent. This part
will be aimed at probabilistic and\nstatisticians. \n\nI will conclude wi
th recent directions in extreme value theory\, such as extremes in high\nd
imension\, extremes of graphs and networks.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Conder (University of Auckland)
DTSTART:20221110T040000Z
DTEND:20221110T050000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/14
DESCRIPTION:Title: Discrete two-generator subgroups of PSL(2\,Q_p)\nby Matth
ew Conder (University of Auckland) as part of SMRI seminars\n\nLecture hel
d in Quad S223 (for University of Sydney staff\, students & affiliates onl
y) & Online.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeroen Schillewaert (University of Auckland)
DTSTART:20221117T000000Z
DTEND:20221117T010000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/15
DESCRIPTION:Title: Constructing highly regular expanders from hyperbolic Coxeter
groups\nby Jeroen Schillewaert (University of Auckland) as part of SM
RI seminars\n\nLecture held in Quad S223 & Online.\n\nAbstract\nGiven a st
ring Coxeter system (W\,S)\, we construct highly regular quotients of the
1-skeleton of its universal polytope P\, which form an infinite family of
expander graphs when (W\,S) is indefinite and P has finite vertex links. T
he regularity of the graphs in this family depends on the Coxeter diagram
of (W\,S). The expansion stems from superapproximation applied to (W\,S).
This construction is also extended to cover Wythoffian polytopes. As a dir
ect application\, we obtain several notable families of expander graphs wi
th high levels of regularity\, answering in particular a question posed by
Chapman\, Linial and Peled positively.\n\nThis talk is based on joint wor
k with Marston Conder\, Alexander Lubotzky and Francois Thilmany.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changfeng Gui (University of Texas at San Antonio)
DTSTART:20221117T020000Z
DTEND:20221117T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/16
DESCRIPTION:Title: Some New Inequalities in Analysis and Geometry\nby Changf
eng Gui (University of Texas at San Antonio) as part of SMRI seminars\n\nL
ecture held in Quad S223 & Online.\n\nAbstract\nThe classical Trudinger-Mo
ser inequality is a borderline case of Sobolev inequalities and plays an i
mportant role in geometric analysis and PDEs in general. Aubin in 1979 sho
wed that the best constant in the Trudinger-Moser inequality can be improv
ed by reducing to one half if the functions are restricted to the compleme
nt of a three dimensional subspace of the Sobolev space $H^1$\, while Onof
ri in 1982 discovered an elegant optimal form of Trudinger-Moser inequalit
y on sphere. In this talk\, I will present new sharp inequalities which ar
e variants of Aubin and Onofri inequalities on the sphere with or without
mass center constraints.\n\nOne such inequality\, for example\, incorporat
es the mass center deviation (from the origin) into the optimal inequality
of Aubin on the sphere\, which is for functions with mass centered at the
origin. The main ingredient leading to the above inequalities is a novel
geometric inequality: Sphere Covering Inequality.\n\nEfforts have also bee
n made to show similar inequalities in higher dimensions. Among the prelim
inary results\, we have improved Beckner's inequality for axially symmetri
c functions when the dimension $n=4\, 6\, 8$. Many questions remain open.\
n\nThe talk is based on collaborations with Amir Moradifam\, Sun-Yung Alic
e Chang\, Yeyao Hu and Weihong Xie.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Crespo (Universidad del Bío-Bío)
DTSTART:20221201T020000Z
DTEND:20221201T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/17
DESCRIPTION:Title: Relative equilibria in the full N-body problem\nby Franci
sco Crespo (Universidad del Bío-Bío) as part of SMRI seminars\n\nLecture
held in Quad S223 & Online.\n\nAbstract\nSMRI Seminar\n'Relative equilibr
ia in the full N-body problem'\nFrancisco Crespo (Universidad del Bío-Bí
o)\n\nThursday 1st December\nQuad S223 & Online\n\nAbstract: The full N-bo
dy problem addresses the dynamics of N rigid bodies under mutual gravitati
onal interactions. This physical system has powered the fabric of science
and especially mathematics for centuries\, having a decisive role in devel
oping geometric mechanics\, qualitative theory of dynamical systems\, or K
AM theory. In this talk\, we briefly survey this problem and focus on anal
yzing special solutions called relative equilibria.\n\nAfter determining t
he hamiltonian equations of motion\, our approach identifies and uses the
existence of translational and rotational symmetries of the N-body problem
. In particular\, we provide very compact equations characterizing relativ
e equilibria solutions\, which become linear by fixing the values of the i
nvariants associated with the action of the symmetry group.\n\nIn the exis
ting literature\, relative equilibria have been classified into Lagrangian
and non-Lagrangian\, respectively\, corresponding to whether the center o
f mass of all bodies is in the same plane. Our analysis determines what ki
nd of configurations allow for each type of equilibrium and provides neces
sary conditions for non-Lagrangian equilibria.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Foucart (Texas A&M University)
DTSTART:20230302T020000Z
DTEND:20230302T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/18
DESCRIPTION:Title: Nonstatistical Learning Theory: the View from Optimal Recover
y\nby Simon Foucart (Texas A&M University) as part of SMRI seminars\n\
nLecture held in Quad S249 & Online.\n\nAbstract\nFor a function observed
through point evaluations\, is there an optimal way to recover it or merel
y to estimate a dependent quantity? I will give affirmative answers to var
iations of this data-focused question\, especially under the assumption th
at the function belongs to a model set defined by approximation capabiliti
es. In fact\, I will uncover computationally implementable linear recovery
maps that are optimal in the worst-case setting. I will present some rece
nt and ongoing works extending the theory in several directions\, with par
ticular emphasis put on observations that are inexact---adversarially or r
andomly.\n\nThis seminar will not be recorded.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Yang (Microsoft Research in Redmond\, Washington)
DTSTART:20230323T020000Z
DTEND:20230323T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/19
DESCRIPTION:Title: The unreasonable effectiveness of mathematics in large scale
deep learning\nby Greg Yang (Microsoft Research in Redmond\, Washingto
n) as part of SMRI seminars\n\nLecture held in Quad S249 & Online.\n\nAbst
ract\nRecently\, the theory of infinite-width neural networks led to the f
irst technology\, muTransfer\, for tuning enormous neural networks that ar
e too expensive to train more than once. For example\, this allowed us to
tune the 6.7 billion parameter version of GPT-3 using only 7% of its pretr
aining compute budget\, and with some asterisks\, we get a performance com
parable to the original GPT-3 model with twice the parameter count. In thi
s talk\, I will explain the core insight behind this theory. In fact\, thi
s is an instance of what I call the *Optimal Scaling Thesis*\, which conne
cts infinite-size limits for general notions of “size” to the optimal
design of large models in practice\, illustrating a way for theory to reli
ably guide the future of AI. I'll end with several concrete key mathematic
al research questions whose resolutions will have incredible impact on how
practitioners scale up their NNs.\n\n\nBiography: Greg Yang is a research
er at Microsoft Research in Redmond\, Washington.\nHe joined MSR after he
obtained Bachelor's in Mathematics and Master's degrees in Computer Scienc
e from Harvard University\, respectively advised by ST Yau and Alexander R
ush. He won the Hoopes prize at Harvard for best undergraduate thesis as w
ell as Honorable Mention for the AMS-MAA-SIAM Morgan Prize\, the highest h
onor in the world for an undergraduate in mathematics. He gave an invited
talk at the International Congress of Chinese Mathematicians 2019.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Kovács (University of Washington)
DTSTART:20230420T030000Z
DTEND:20230420T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/20
DESCRIPTION:Title: Tricking the Devil\nby Sándor Kovács (University of Was
hington) as part of SMRI seminars\n\nLecture held in Quad S249.\n\nAbstrac
t\nMax Noether said that algebraic curves were created by God and algebrai
c surfaces 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 resul
ts of the moduli theory of curves to that of surfaces and then discuss how
one may resolve the arising issue. Time permitting\, I will also explain
the various stability conditions this problem and its resolution led to.\n
\nBiography: Sándor Kovács is a Professor of Mathematics at the Universi
ty of Washington. He received his BS degree at Eötvös University (Hungar
y)\, and his PhD at the University of Utah. He held positions at MIT and t
he University of Chicago before moving to the University of Washington. Hi
s awards include the American Mathematical Society's Centennial Research F
ellowship\, Alfred P. Sloan Foundation Research Fellowship\, and two Simon
s Foundation Fellowships. He is a Fellow of the American Mathematical Soci
ety.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan James Wylie (City University of Hong Kong)
DTSTART:20230427T030000Z
DTEND:20230427T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/21
DESCRIPTION:Title: Unexpected Behaviour in Dilute Granular Materials\nby Jon
athan James Wylie (City University of Hong Kong) as part of SMRI seminars\
n\nLecture held in Quad S249.\n\nAbstract\nThe phrase 'granular material'
is used to describe a large number of discrete solid\, macroscopic particl
es that lose energy whenever the particles collide. One might naively imag
ine that such systems would exhibit similar behaviour to traditional fluid
and solid mechanics. However\, we present two problems that superficially
appear to be extremely simple but yield surprisingly rich dynamics that h
ave no analogue in traditional mechanics. Firstly\, we consider a dilute s
tream of particles that collides with an oblique planar wall. Secondly\, w
e show several surprising phenomena that occur in an extremely simple syst
em of a single frictionless\, inelastic\, spherical particle falling under
gravity through a symmetric funnel.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Gray (University of East Anglia)
DTSTART:20230504T030000Z
DTEND:20230504T040000Z
DTSTAMP:20260404T111414Z
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 se
minars\n\nLecture held in Quad S249 & Online.\n\nAbstract\nIn the 1960's H
igman was able to characterize the finitely generated subgroups of finitel
y presented groups\, that is\, groups defined using a finite set of genera
tors and finite set of defining relations. His result\, which is called th
e Higman Embedding Theorem\, is a key result in combinatorial group theory
which makes precise the connection between group presentations and logic.
In this talk I will present a result of a similar flavour\, proved in rec
ent joint work with Mark Kambites (Manchester)\, in which we characterise
the groups of units of inverse monoids defined by presentation where all t
he defining relators are of the form w=1. I will explain what an inverse m
onoid is\, the motivation for studying this class of inverse monoids\, and
also outline some of the geometric ideas that we developed in order to pr
ove our results.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Rink (Vrije Universiteit Amsterdam)
DTSTART:20230511T030000Z
DTEND:20230511T040000Z
DTSTAMP:20260404T111414Z
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\nLe
cture held in Quad S249 & Online.\n\nAbstract\nThe parametrization method
is a tool to compute invariant manifolds in dynamical systems\, such as pe
riodic orbits\, (un-)stable manifolds\, slow manifolds and invariant tori.
The idea behind the method is simple: it works by (algorithmically) findi
ng an embedding of the invariant manifold together with a representation o
f its dynamics in a coordinate chart. De La Llave et al realized that the
method can nicely be combined with ideas from rigorous numerics\, to provi
de computer-assisted proofs for the existence of invariant manifolds. Othe
rs\, including myself\, have used the method to compute high-precision app
roximations of the dynamics on the invariant manifolds. I will discuss bot
h approaches\, starting with the basics and finishing with an unpublished
result on high-order phase reduction.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20230720T030000Z
DTEND:20230720T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/24
DESCRIPTION:Title: Nonlocal Aggregation-Diffusion Equations: fast diffusion and
partial concentration\nby Jose A. Carrillo (University of Oxford) as p
art of SMRI seminars\n\nLecture held in Carslaw 375 & Online.\n\nAbstract\
nWe will discuss several recent results for aggregation-diffusion equation
s related to partial concentration of the density of particles. Nonlinear
diffusions with homogeneous kernels will be reviewed quickly in the case o
f degenerate diffusions to have a full picture of the problem. Most of the
talk will be devoted to discuss the less explored case of fast diffusion
with homogeneous kernels with positive powers. We will first concentrate i
n the case of stationary solutions by looking at minimisers of the associa
ted free energy showing that the minimiser must consist of a regular smoot
h solution with singularity at the origin plus possibly a partial concentr
ation of the mass at the origin. We will give necessary conditions for thi
s partial mass concentration to and not to happen. We will then look at th
e related evolution problem and show that for a given confinement potentia
l this concentration happens in infinite time under certain conditions. We
will briefly discuss the latest developments when we introduce the aggreg
ation term. This talk is based on a series of works in collaboration with
M. Delgadino\, J. Dolbeault\, A. Fernández\, R. Frank\, D. Gómez-Castro\
, F. Hoffmann\, M. Lewin\, and J. L. Vázquez\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Lu (University of Oregon)
DTSTART:20230810T030000Z
DTEND:20230810T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/25
DESCRIPTION:Title: Conformal Bach flow\nby Peng Lu (University of Oregon) as
part of SMRI seminars\n\nLecture held in Carslaw 375 & Online.\n\nAbstrac
t\nWe introduce conformal Bach flow and establish its well-posedness on cl
osed \nmanifolds. We also obtain its backward uniqueness. To give an atte
mpt to study the \nlong-time behavior of conformal Bach flow\, assuming t
hat the curvature and the pressure \nfunction are bounded\, global and loc
al 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 o
n high order \nparabolic curvature flow. This is a joint work with Jiaqi C
hen of Xiamen University and \nJie Qing of UCSC.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franz Pedit (University of Massachusetts\, Amherst)
DTSTART:20230824T030000Z
DTEND:20230824T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/26
DESCRIPTION:Title: Minimal Lagrangian surfaces of high genus in $CP^2$\nby F
ranz Pedit (University of Massachusetts\, Amherst) as part of SMRI seminar
s\n\nLecture held in Carslaw 375 & Online.\n\nAbstract\nThe study of prope
rties of surfaces in space has historically been a fertile ground for adva
nces in topology\, analysis\, geometry\, Lie theory\, and mathematical phy
sics. The most important surface classes are those which arise form variat
ional problems\, for example\, minimal surfaces which are critical points
of the area functional. The Euler Lagrange equations are PDEs which serve
as model cases for developments in geometric analysis. Often these equatio
ns exhibit large (sometimes infinite dimensional) symmetry groups which pu
ts the theory into the realm of “integrable systems”\, that is\, PDEs
which allow for an infinte hierarchy of conserved quantities. This theory
has been studied extensively over the past 40 years and led to significant
advances in the classification of (minimal\, constant mean curvature\, Wi
llmore etc.) surfaces of genus one. The higher genus case has been more il
lusive and examples are usually constructed using non-linear perturbation
theory and gluing techniques.\n\nIn this talk I will explain how one can u
se ideas from integrable systems to construct examples of high genus minma
l Lagrangian surfaces without recourse to hard analysis.\n\nThis approach
is more explicit than PDE existence results and one is able to obtain more
quantitative information about the constructed examples\, for instance\,
asymptotic area/energy estimates. I will also give a brief overview of the
historical developments and the significance of minimal Lagrangian surfac
es in mathematical physics.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Wyatt (University of Cambridge)
DTSTART:20230831T030000Z
DTEND:20230831T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/27
DESCRIPTION:Title: Stability problems in general relativity\nby Zoe Wyatt (U
niversity of Cambridge) as part of SMRI seminars\n\nLecture held in Carsla
w 375 & Online.\n\nAbstract\nEinstein's theory of general relativity makes
spectacular 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 mat
hematics to general relativity\, highlighting a recent joint work showing
the stability of Kaluza-Klein spacetimes. These are important models in su
pergravity and their stability is connected to claims of Penrose and Witte
n.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daryl Cooper (University of California\, Santa Barbara)
DTSTART:20240222T020000Z
DTEND:20240222T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/28
DESCRIPTION:Title: Symmetry\, old and new\nby Daryl Cooper (University of Ca
lifornia\, Santa Barbara) as part of SMRI seminars\n\nLecture held in Univ
ersity of Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAbstract\nI
will discuss symmetry from a combinatorial perspective. Examples include w
allpaper groups\, 4-valent graphs\, regular languages\, molecules\, Penr
ose tilings\, and geometric 3-manifolds. It turns out that for each of the
se classes there is a finite universal geometric object that encodes all t
he possibilities.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Elvira (University of Edinburgh)
DTSTART:20240229T020000Z
DTEND:20240229T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/29
DESCRIPTION:Title: State-space models as graphs\nby Victor Elvira (Universit
y of Edinburgh) as part of SMRI seminars\n\nLecture held in University of
Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAbstract\nModeling and
inference in multivariate time series is central in statistics\,\nsignal
processing\, and machine learning. A fundamental question when analyzing\
nmultivariate sequences is the search for relationships between their entr
ies (or the\nmodeled hidden states)\, especially when the inherent structu
re is a directed (causal)\ngraph. In such context\, graphical modeling co
mbined with sparsity constraints allows to\nlimit the proliferation of par
ameters and enables a compact data representation which is\neasier to inte
rpret in applications\, e.g.\, in inferring causal relationships of physic
al\nprocesses in a Granger sense. In this talk\, we present a novel persp
ective consisting\non state-space models being interpreted as graphs. The
n\, we propose novel algorithms\nthat exploit this new perspective for the
estimation of the linear matrix operator and\nalso the covariance matrix
in the state equation of a linear-Gaussian state-space\nmodel. Finally\,
we discuss the extension of this perspective for the estimation of\nother
model parameters in more complicated models.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shane G. Henderson (Cornell University)
DTSTART:20240307T020000Z
DTEND:20240307T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/30
DESCRIPTION:Title: A Tutorial and Perspectives on Monte Carlo Simulation Optimiz
ation\nby Shane G. Henderson (Cornell University) as part of SMRI semi
nars\n\nLecture held in University of Sydney\, Law Annex Lecture Theatre 0
26 & Online.\n\nAbstract\nI provide a tutorial and some perspectives on si
mulation optimization\, in which one wishes to minimize an objective funct
ion that can only be evaluated with noise through a stochastic computer si
mulation. First\, I'll give a few examples and intuitively explain some ce
ntral issues in the area. Second\, I'll explain why so-called sample-path
functions can exhibit extremely complex behavior that is well worth unders
tanding. Third\, I'll argue that more attention should be devoted to the f
inite-time performance of solvers than on ensuring convergence properties
that may only arise in asymptotic time scales that may never be reached in
practice. I'll outline an approach for obtaining such results analyticall
y (through Lyapunov functions) and introduce a framework and code for comp
utational experiments that can further this goal. Fourth (if time permits\
, though I doubt it will)\, I'll advocate the use of a layered approach to
formulating and solving optimization problems\, whereby a sequence of mod
els are built and optimized\, rather than first building a simulation mode
l and only later “bolting on” optimization\, partly through an example
of my work involving bike sharing with the organization Citi Bike in New
York city.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Su (Harvey Mudd College)
DTSTART:20240314T020000Z
DTEND:20240314T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/31
DESCRIPTION:Title: Sperner's Lemma: a generalization with surprising application
s\nby Francis Su (Harvey Mudd College) as part of SMRI seminars\n\nLec
ture held in University of Sydney\, Law Annex Lecture Theatre 026 & Online
.\n\nAbstract\nWho doesn't like one of these three: geometry\, topology\,
and combinatorics? And even if you don't\, you will still love Sperner's l
emma\, which is a combinatorial statement that is equivalent to the Brouwe
r fixed point theorem in topology. I'll explain what it is\, why it's so a
mazing\, give heartwarming old and new proofs\, and present a recent gener
alization tio polytopes that has surprised me with diverse applications: t
o the study of triangulations\, to fair division problems\, and the Game o
f Hex.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salil Vadhan (Harvard University)
DTSTART:20240321T020000Z
DTEND:20240321T030000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/32
DESCRIPTION:Title: Derandomizing Algorithms via Spectral Graph Theory\nby Sa
lil Vadhan (Harvard University) as part of SMRI seminars\n\nLecture held i
n University of Sydney\, Law Annex Lecture Theatre 026 & Online.\n\nAbstra
ct\nRandomization is a powerful tool for algorithms\; it is often easier t
o design efficient algorithms if we allow the algorithms to "toss coins" a
nd output a correct answer with high probability. However\, a longstanding
conjecture in theoretical computer science is that every randomized algor
ithm can be efficiently "derandomized" --- converted into a deterministic
algorithm (which always outputs the correct answer) with only a polynomial
increase in running time and only a constant-factor increase in space (i.
e. memory usage). In this talk\, I will describe an approach to proving th
e space (as opposed to time) part of this conjecture via spectral graph th
eory. Specifically\, I will explain how randomized space-bounded algorithm
s are described by random walks on directed graphs\, and techniques in alg
orithmic spectral graph theory (e.g. solving Laplacian systems) have yield
ed deterministic space-efficient algorithms for approximating the behavior
of such random walks on undirected graphs and Eulerian directed graphs (w
here every vertex has the same in-degree as out-degree). If these algorith
ms can be extended to general directed graphs\, then the aforementioned co
njecture about derandomizing space-efficient algorithms will be resolved.
These problems also lead us to explore new notions of what it means for tw
o directed graphs to "spectrally approximate" each other\, which may be of
independent interest.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Donovan (Tsinghua University)
DTSTART:20240411T030000Z
DTEND:20240411T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/33
DESCRIPTION:Title: McKay correspondence and toric geometry\nby Will Donovan
(Tsinghua University) as part of SMRI seminars\n\nLecture held in Universi
ty of Sydney\, Law Annex Lecture Theatre 026.\n\nAbstract\nFinite subgroup
s of the matrix group SU(2) may be studied algebraically via \ntheir repre
sentations. They may also be studied geometrically via two-dimensional \nc
omplex manifolds naturally associated to them. The McKay correspondence is
a general \nphenomenon which\, in particular\, explains how these two app
roaches relate. I’ll \nintroduce this using diagramatics from toric geom
etry\, indicate how the correspondence \ngeneralizes to higher dimensions\
, and discuss open questions and current projects.\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dave Futer (Temple University\, Philadelphia)
DTSTART:20240502T030000Z
DTEND:20240502T040000Z
DTSTAMP:20260404T111414Z
UID:SMRIseminars/34
DESCRIPTION:Title: The generalized knot complement problem\nby Dave Futer (T
emple University\, Philadelphia) as part of SMRI seminars\n\nLecture held
in University of Sydney\, Law Annex Lecture Theatre 026.\n\nAbstract\nIn 1
908\, Tietze posed the provocative question of whether a mathematical knot
\n- a knotted rope\, with its ends spliced together - is completely deter
mined by the \ntopological shape of the empty space that surrounds the kno
t. After being open for 80 \nyears\, this question was solved in 1988\, an
d we know the answer is Yes.\n\nSince that time\, mathematicians have stud
ied the open question of whether the same \nproperty holds for knots in ge
neral 3-dimensional spaces. Given a 3-dimensional manifold \nM\, is a knot
in M entirely determined by the space that surrounds it in M? I will \ndi
scuss some recent work on this question using hyperbolic (negatively curve
d) geometry. \nThis is joint work with Jessica Purcell and Saul Schleimer.
\n
LOCATION:https://stable.researchseminars.org/talk/SMRIseminars/34/
END:VEVENT
END:VCALENDAR