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BEGIN:VEVENT
SUMMARY:Morgan Craig (Université de Montréal)
DTSTART:20200619T200000Z
DTEND:20200619T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/1
DESCRIPTION:Title: Quantitative approaches to understanding the immune resp
onse to SARS-CoV-2 infection\nby Morgan Craig (Université de Montréa
l) as part of CRM-ISM Colloque des sciences mathématiques du Québec\n\nL
ecture held in Zoom.\n\nAbstract\nCOVID-19 is typically characterized by a
range of respiratory symptoms that\, in severe cases\, progress to acute
respiratory distress syndrome (ARDS). These symptoms are also frequently a
ccompanied by a range of inflammatory indications\, particularly hyper-rea
ctive and dysregulated inflammatory responses in the form of cytokine stor
ms and severe immunopathology. Much remains to be uncovered about the mech
anisms that lead to disparate outcomes in COVID-19. Here\, quantitative ap
proaches\, especially mechanistic mathematical models\, can be leveraged t
o improve our understanding of the immune response to SARS-CoV-2 infection
. Building upon our prior work modelling the production of innate immune c
ell subsets and the viral dynamics of HIV and oncolytic viruses\, we are d
eveloping a quantitative framework to interrogate open questions about the
innate and adaptive immune reaction in COVID-19. In this talk\, I will ou
tline our recent work modelling SARS-CoV-2 viral dynamics and the ensuing
immune response at both the tissue and systemic levels. A portion of this
work is done as part of an international and multidisciplinary coalition w
orking to establish a comprehensive tissue simulator (physicell.org/covid1
9 [1])\, which I will also discuss in more detail.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lai-Sang Young (Courant Institute of Mathematical Sciences\, New Y
ork University)
DTSTART:20200417T200000Z
DTEND:20200417T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/2
DESCRIPTION:Title: Observable events and typical trajectories in finite and
infinite dimensional dynamical systems\nby Lai-Sang Young (Courant In
stitute of Mathematical Sciences\, New York University) as part of CRM-ISM
Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\
n\nAbstract\nThe terms "observable events" and "typical trajectories" in t
he title should really be between quotation marks\, because what is typica
l and/or observable is a matter of interpretation. For dynamical systems o
n finite dimensional spaces\, one often equates observable events with pos
itive Lebesgue measure sets\, and invariant distributions that reflect the
large-time behaviors of positive Lebesgue measure sets of initial conditi
ons (such as Liouville measure for Hamiltonian systems) are considered to
be especially important. I will begin by introducing these concepts for ge
neral dynamical systems -- including those with attractors -- describing a
simple dynamical picture that one might hope to be true. This picture doe
s not always hold\, unfortunately\, but a small amount of random noise wil
l bring it about. In the second part of my talk I will consider infinite d
imensional systems such as semi-flows arising from dissipative evolutionar
y PDEs. I will discuss the extent to which the ideas above can be generali
zed to infinite dimensions\, and propose a notion of "typical solutions".\
n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Griffiths (Institute for Advanced Study\, Princeton\, USA)
DTSTART:20201009T190000Z
DTEND:20201009T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/3
DESCRIPTION:Title: Hodge Theory and Moduli\nby Phillip Griffiths (Insti
tute for Advanced Study\, Princeton\, USA) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n
The theory of moduli is an important and active area in algebraic geometry
. For varieties of general type the existence of a moduli space with a ca
nonical completion has been proved by Kollar/Shepard-Barron/Alexeev. Asid
e from the classical case of algebraic curves\, very little is known about
the structure of \, especially it’s boundary. The period mapping from H
odge theory provides a tool for studying these issues.\n\nIn this talk\, w
e will discuss some aspects of this topic with emphasis on I-surfaces\, wh
ich provide one of the first examples where the theory has been worked out
in some detail. Particular notice will me made of how the extension data
in the limiting mixed Hodge structures that arise from singular surfaces o
n the boundary of moduli may be used to guide the desingularization of tha
t boundary.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École Normale Supérieure (Paris)\, France)
DTSTART:20201016T190000Z
DTEND:20201016T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/4
DESCRIPTION:Title: Trigonometric functions and modular symbols\nby Nico
las Bergeron (École Normale Supérieure (Paris)\, France) as part of CRM-
ISM Colloque des sciences mathématiques du Québec\n\nLecture held in Zoo
m.\n\nAbstract\nIn his fantastic book « Elliptic functions according to E
isenstein and Kronecker\, » Weil writes:\n\n « As Eisenstein shows\, hi
s method for constructing elliptic functions applies beautifully to the s
impler case of the trigonometric functions. Moreover\, this case provides
[…] the simplest proofs for a series of results\, originally discovered
by Euler. » \n\nThe results Weil alludes to are relations between product
of trigonometric functions. I will first explain how these relations are
quite surprisingly governed by relations between modular symbols (whose el
ementary theory I will sketch). I will then show how this story fits into
a wider picture that relates the topological world of group homology of so
me linear groups to the algebraic world of trigonometric and elliptic func
tions. To conclude I will briefly describe a number theoretical applicati
on. \n\nThis is based on a work-in-progress with Pierre Charollois\, Luis
Garcia and Akshay Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Broderick (Massachusetts Institute of Technology\, USA)
DTSTART:20201113T203000Z
DTEND:20201113T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/5
DESCRIPTION:Title: Approximate Cross-Validation for Large Data and High Dim
ensions\nby Tamara Broderick (Massachusetts Institute of Technology\,
USA) as part of CRM-ISM Colloque des sciences mathématiques du Québec\n\
nLecture held in Zoom.\n\nAbstract\nThe error or variability of statistica
l and machine learning algorithms is often assessed by repeatedly re-fitti
ng a model with different weighted versions of the observed data. The ubiq
uitous tools of cross-validation (CV) and the bootstrap are examples of th
is technique. These methods are powerful in large part due to their model
agnosticism but can be slow to run on modern\, large data sets due to the
need to repeatedly re-fit the model. We use a linear approximation to the
dependence of the fitting procedure on the weights\, producing results tha
t can be faster than repeated re-fitting by orders of magnitude. This line
ar approximation is sometimes known as the "infinitesimal jackknife" (IJ)
in the statistics literature\, where it has mostly been used as a theoreti
cal tool to prove asymptotic results. We provide explicit finite-sample er
ror bounds for the infinitesimal jackknife in terms of a small number of s
imple\, verifiable assumptions. Without further modification\, though\, we
note that the IJ deteriorates in accuracy in high dimensions and incurs a
running time roughly cubic in dimension. We additionally show\, then\, ho
w dimensionality reduction can be used to successfully run the IJ in high
dimensions when data is sparse or low rank. Simulated and real-data experi
ments support our theory.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wieslawa Niziol (CNRS\, Sorbone Université)
DTSTART:20201120T200000Z
DTEND:20201120T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/6
DESCRIPTION:Title: Hodge Theory of p-adic varieties\nby Wieslawa Nizio
l (CNRS\, Sorbone Université) as part of CRM-ISM Colloque des sciences ma
thématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\np-adic Hodge
Theory is one of the most powerful tools in modern Arithmetic Geometry.
In this talk\, I will review p-adic Hodge Theory of algebraic varieties\,
present current developments in p-adic Hodge Theory of analytic varieties\
, and discuss some of its applications to problems in Number Theory.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART:20201127T200000Z
DTEND:20201127T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/7
DESCRIPTION:Title: Moduli of unstable objects in algebraic geometry\nby
Frances Kirwan (University of Oxford) as part of CRM-ISM Colloque des sci
ences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nModu
li spaces arise naturally in classification problems in geometry. The stud
y of the moduli spaces of nonsingular complex projective curves (or equiva
lently of compact Riemann surfaces) goes back to Riemann himself in the ni
neteenth century. The construction of the moduli spaces of stable curves o
f fixed genus is one of the classical applications of Mumford's geometric
invariant theory (GIT)\, developed in the 1960s\; many other moduli spaces
of 'stable' objects can be constructed using GIT and in other ways. A pro
jective curve is stable if it has only very mild singularities (nodes) and
its automorphism group is finite\; similarly in other contexts stable obj
ects are usually better behaved than unstable ones. \n\nThe aim of this ta
lk is to explain how recent methods from a version of GIT for non-reductiv
e group actions can help us to classify singular curves in such a way that
we can construct moduli spaces of unstable curves (of fixed type). More g
enerally our aim is to use suitable 'stability conditions' to stratify oth
er moduli stacks into locally closed strata with coarse moduli spaces. The
talk is based on joint work with Gergely Berczi\, Vicky Hoskins and Joshu
a Jackson.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Haslhofer (Université de Toronto)
DTSTART:20210122T200000Z
DTEND:20210122T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/9
DESCRIPTION:Title: Mean curvature flow through neck-singularities\nby R
obert Haslhofer (Université de Toronto) as part of CRM-ISM Colloque des s
ciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nA
family of surfaces moves by mean curvature flow if the velocity at each po
int is given by the mean curvature vector. Mean curvature flow first arose
as a model of evolving interfaces and has been extensively studied over t
he last 40 years.\n\nIn this talk\, I will give an introduction and overvi
ew for a general mathematical audience. To gain some intuition we will fir
st consider the one-dimensional case of evolving curves. We will then disc
uss Huisken’s classical result that the flow of convex surfaces always c
onverges to a round point. On the other hand\, if the initial surface is n
ot convex we will see that the flow typically encounters singularities. Ge
tting a hold of these singularities is crucial for most striking applicati
ons in geometry\, topology and physics. Specifically\, singularities can b
e either of neck-type or conical-type. We will discuss examples from the 9
0s\, which show\, both experimentally and theoretically\, that flow throug
h conical singularities is utterly non-unique.\n\nIn the last part of the
talk\, I will report on recent work with Kyeongsu Choi\, Or Hershkovits an
d Brian White\, where we proved that mean curvature flow through neck-sing
ularities is unique. The key for this is a classification result for ancie
nt asymptotically cylindrical flows that describes all possible blowup lim
its near a neck-singularity. In particular\, this confirms the mean-convex
neighborhood conjecture. Assuming Ilmanen’s multiplicity-one conjecture
\, we conclude that for embedded two-spheres mean curvature flow through s
ingularities is well-posed.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (Université de Montréal)
DTSTART:20210205T200000Z
DTEND:20210205T210000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/10
DESCRIPTION:Title: Symmetry\, barcodes\, and Hamiltonian dynamics\nby
Egor Shelukhin (Université de Montréal) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nI
n the early 60s Arnol'd has conjectured that Hamiltonian diffeomorphisms\,
the motions of classical mechanics\, often possess more fixed points than
required by classical topological considerations. In the late 80s and ea
rly 90s Floer has developed a powerful theory to approach this conjecture\
, considering fixed points as critical points of a certain functional. Re
cently\, in joint work with L. Polterovich\, we observed that Floer theor
y filtered by the values of this functional fits into the framework of per
sistence modules and their barcodes\, originating in data sciences. I wil
l review these developments and their applications\, which arise from a na
tural time-symmetry of Hamiltonians. This includes new constraints on one
-parameter subgroups of Hamiltonian diffeomorphisms\, as well as my recent
solution of the Hofer-Zehnder periodic points conjecture. The latter com
bines barcodes with equivariant cohomological operations in Floer theory r
ecently introduced by Seidel to form a new method with further consequence
s.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Wakefield (University of Washington)
DTSTART:20210129T203000Z
DTEND:20210129T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/11
DESCRIPTION:Title: Small Area Estimation in Low- and Middle-Income Countri
es\nby Jon Wakefield (University of Washington) as part of CRM-ISM Col
loque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nA
bstract\nThe under-five mortality rate (U5MR) is a key barometer of the he
alth of a nation. Unfortunately\, many people living in low- and middle-in
come countries are not covered by civil registration systems. This makes e
stimation of the U5MR\, particularly at the subnational level\, difficult.
In this talk\, I will describe models that have been developed to produce
the official United Nations (UN) subnational U5MR estimates in 22 countri
es. Estimation is based on household surveys\, which use stratified\, two-
stage cluster sampling. I will describe a range of area- and unit-level mo
dels and describe the rationale for the modeling we carry out. Data sparsi
ty in time and space is a key challenge\, and smoothing models are vital.
I will discuss the advantages and disadvantages of discrete and continuous
spatial models\, in the context of estimation at the scale at which healt
h interventions are made. Other issues that will be touched upon include:
design-based versus model-based inference\; adjustments for HIV epidemics\
; the inclusion of so-called indirect (summary birth history) data\; repro
ducibility through software availability\; benchmarking\; how to deal with
incomplete geographical data\; and working with the UN to produce estimat
es.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikael Kuusela (Carnegie Mellon University)
DTSTART:20210212T203000Z
DTEND:20210212T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/12
DESCRIPTION:Title: Spatio-temporal methods for estimating subsurface ocean
thermal response to tropical cyclones\nby Mikael Kuusela (Carnegie Me
llon University) as part of CRM-ISM Colloque des sciences mathématiques d
u Québec\n\nLecture held in Zoom.\n\nAbstract\nTropical cyclones (TCs)\,
driven by heat exchange between the air and sea\, pose a substantial risk
to many communities around the world. Accurate characterization of the su
bsurface ocean thermal response to TC passage is crucial for accurate TC i
ntensity forecasts and for understanding the role TCs play in the global c
limate system\, yet that characterization is complicated by the high-noise
ocean environment\, correlations inherent in spatio-temporal data\, relat
ive scarcity of in situ observations and the entanglement of the TC-induce
d signal with seasonal signals. We present a general methodological frame
work that addresses these difficulties\, integrating existing techniques i
n seasonal mean field estimation\, Gaussian process modeling\, and nonpara
metric regression into a functional ANOVA model. Importantly\, we improve
upon past work by properly handling seasonality\, providing rigorous unce
rtainty quantification\, and treating time as a continuous variable\, rath
er than producing estimates that are binned in time. This functional ANOV
A model is estimated using in situ subsurface temperature profiles from th
e Argo fleet of autonomous floats through a multi-step procedure\, which (
1) characterizes the upper ocean seasonal shift during the TC season\; (2)
models the variability in the temperature observations\; (3) fits a thin
plate spline using the variability estimates to account for heteroskedasti
city and correlation between the observations. This spline fit reveals th
e ocean thermal response to TC passage. Through this framework\, we obtai
n new scientific insights into the interaction between TCs and the ocean o
n a global scale\, including a three-dimensional characterization of the n
ear-surface and subsurface cooling along the TC storm track and the mixing
-induced subsurface warming on the track's right side. Joint work with Ad
dison Hu\, Ann Lee\, Donata Giglio and Kimberly Wood.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Breidt (Colorado State University)
DTSTART:20210312T203000Z
DTEND:20210312T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/13
DESCRIPTION:Title: Nonparametric Tests for Informative Selection in Comple
x Surveys\nby Jay Breidt (Colorado State University) as part of CRM-IS
M Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom.
\n\nAbstract\nInformative selection\, in which the distribution of respons
e variables given that they are sampled is different from their distributi
on in the population\, is pervasive in complex surveys. Failing to take s
uch informativeness into account can produce severe inferential errors\, i
ncluding biased and inconsistent estimation of population parameters. Whi
le several parametric procedures exist to test for informative selection\,
these methods are limited in scope and their parametric assumptions are d
ifficult to assess. We consider two classes of nonparametric tests of inf
ormative selection. The first class is motivated by classic nonparametri
c two-sample tests. We compare weighted and unweighted empirical distribu
tion functions and obtain tests for informative selection that are analogo
us to Kolmogorov-Smirnov and Cramer-von Mises. For the second class of te
sts\, we adapt a kernel-based learning method that compares distributions
based on their maximum mean discrepancy. The asymptotic distributions of
the test statistics are established under the null hypothesis of noninform
ative selection. Simulation results show that our tests have power compet
itive with existing parametric tests in a correctly specified parametric s
etting\, and better than those tests under model misspecification. A rec
reational angling application illustrates the methodology. \nThis is join
t work with Teng Liu\, Colorado State University.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Guth (MIT)
DTSTART:20210219T203000Z
DTEND:20210219T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/14
DESCRIPTION:Title: Local smoothing for the wave equation\nby Larry Gut
h (MIT) as part of CRM-ISM Colloque des sciences mathématiques du Québec
\n\nLecture held in Zoom.\n\nAbstract\nThe local smoothing problem asks ab
out how much solutions to the wave equation can focus. It was formulated
by Chris Sogge in the early 90s. Hong Wang\, Ruixiang Zhang\, and I rec
ently proved the conjecture in two dimensions. In the talk\, we will buil
d up some intuition about waves to motivate the conjecture\, and then disc
uss some of the obstacles and some ideas from the proof.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Dubois (Le CNAM - Paris\, Member of IRL-CRM CNRS)
DTSTART:20210319T190000Z
DTEND:20210319T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/16
DESCRIPTION:Title: ABCD asymptotic expansion for lattice Boltzmann schemes
and application to compressible Navier Stokes equations\nby François
Dubois (Le CNAM - Paris\, Member of IRL-CRM CNRS) as part of CRM-ISM Coll
oque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAb
stract\nWe first recall some elements of history of the construction of la
ttice Boltzmann schemes. Then we present our "ABCD" approach\, founded on
the property that the numerical scheme is exact for the advection equatio
n with the velocities of the lattice. This asymptotic analysis allows to
write at several orders the conservative partial differential equations eq
uivalent to the numerical scheme. A fit of parameters permits in favorabl
e cases a precise approximation of compressible fluids equations.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Cornell University)
DTSTART:20210409T190000Z
DTEND:20210409T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/17
DESCRIPTION:Title: Insect Flight from Newton’s law to Neurons\nby Ja
ne Wang (Cornell University) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nWhy do animals
move the way they do? Bacteria\, insects\, birds\, and fish share with us
the necessity to move so as to live. Although each organism follows its
own evolutionary course\, it also obeys a set of common laws. At the very
least\, the movement of animals\, like that of planets\, is governed by N
ewton’s law: All things fall. On Earth\, most things fall in air or wat
er\, and their motions are thus subject to the laws of hydrodynamics. Thr
ough trial and error\, animals have found ways to interact with fluid so t
hey can float\, drift\, swim\, sail\, glide\, soar\, and fly. This elemen
tary struggle to escape the fate of falling shapes the development of moto
rs\, sensors\, and mind. Perhaps we can deduce parts of their neural comp
utations by understanding what animals must do so as not to fall. We have
been seeking mechanistic explanations of the complex movement of insect f
light. Starting from the Navier-Stokes equations governing the unsteady a
erodynamics of flapping flight\, we worked to build a theoretical framewor
k for computing flight and for studying the control of flight. I will dis
cuss our recent computational and experimental studies of the balancing ac
t of dragonflies and fruit flies: how a dragonfly recovers from falling up
side-down and how a fly balances in air. In each case\, the physics of fl
ight informs us about the neural feedback circuitries underlying their fas
t reflexes.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kilian Raschel (CNRS - Université de Tours)
DTSTART:20210416T190000Z
DTEND:20210416T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/18
DESCRIPTION:Title: Reflected Brownian motion in a wedge: from probability
theory to Galois theory of difference equations\nby Kilian Raschel (C
NRS - Université de Tours) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nWe consider a
reflected Brownian motion in a two-dimensional wedge. Under standard assu
mptions on the parameters of the model (opening of the wedge\, angles of
the reflections on the axes\, drift)\, we study the algebraic and differe
ntial nature of the Laplace transform of its stationary distribution. We
derive necessary and sufficient conditions for this Laplace transform to
be rational\, algebraic\, differentially finite or more generally differe
ntially algebraic. These conditions are explicit linear dependencies amon
g the angles involved in the definition of the model.\n\nTo prove these r
esults\, we start from a functional equation that the Laplace transform s
atisfies\, to which we apply tools from diverse horizons. To establish di
fferential algebraicity\, a key ingredient is Tutte's invariant approach\
, which originates in enumerative combinatorics. To establish differentia
l transcendence\, we turn the functional equation into a difference equat
ion and apply Galoisian results on the nature of the solutions to such eq
uations.\n\nThis is a joint work with M. Bousquet-Mélou\, A. Elvey Price\
, S. Franceschi and C. Hardouin (https://arxiv.org/abs/2101.01562).\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Lewis (Cornell University)
DTSTART:20210423T190000Z
DTEND:20210423T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/19
DESCRIPTION:Title: Generalized gradients\, conservative fields\, tame pote
ntials\, and deep learning\nby Adrian Lewis (Cornell University) as pa
rt of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLecture h
eld in Zoom.\n\nAbstract\nTo the dismay and irritation of the variational
analysis community\, practitioners of deep learning often implement gradie
nt-based optimization via automatic differentiation and blithely apply the
result to nonsmooth objectives. Worse\, they then gleefully point out nu
merical convergence. In fact\, as elegantly remarked by Bolte and Pauwels
\, automatic differentiation produces a novel generalized gradient: a con
servative field with enough calculus to prove convergence of stochastic su
bgradient descent\, as practiced in deep learning. I will sketch this int
erplay of analytic and algorithmic ideas\, and explain how\, for concrete
objectives (typically semi-algebraic)\, this novel generalized gradient ju
st slightly modifies Clarke's original notion.\n \nJoint work with Tonghua
Tian\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Bayer-Fluckiger (École Polytechnique Fédérale de Lausanne)
DTSTART:20210430T190000Z
DTEND:20210430T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/20
DESCRIPTION:Title: Knots\, polynomials and signatures\nby Eva Bayer-Fl
uckiger (École Polytechnique Fédérale de Lausanne) as part of CRM-ISM C
olloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\
nAbstract\nAfter a historical introduction to knot theory\, the talk will
be centered around two knot invariants\, the Alexander polynomial and the
signature. The aim is to introduce a finite abelian group that controls t
heir relationship\, and to illustrate this by several examples. Using Sei
fert matrices\, the geometric questions are translated into arithmetic one
s.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART:20211119T203000Z
DTEND:20211119T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/21
DESCRIPTION:Title: (André Aisenstatd Prize) Exploring string vacua throug
h geometric transitions\nby Tristan Collins (MIT) as part of CRM-ISM C
olloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\
nAbstract\nLauréat 2021 du prix de mathématiques André-Aisenstadt\n\nA
fundamental problem in string theory is the multitude of distinct geometri
es which give rise to consistent solutions of the vacuum equations of moti
on. \n\nOne possible resolution of this "vacuum degeneracy" problem is the
"fantasy" that the moduli space of string vacua is connected through the
process of "geometric transitions". \n\nI will discuss some geometric prob
lems associated to this fantasy and their applications.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20211015T193000Z
DTEND:20211015T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/22
DESCRIPTION:Title: (André Aisenstatd Prize) Entropy along the Mandelbrot
set\nby Giulio Tiozzo (University of Toronto) as part of CRM-ISM Collo
que des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbs
tract\nThe notion of topological entropy\, arising from information theory
\, is a fundamental tool to understand the complexity of a dynamical syste
m. When the dynamical system varies in a family\, the natural question ar
ises of how the entropy changes with the parameter. In the last decade\
, W. Thurston introduced these ideas in the context of complex dynamics b
y defining the "core entropy" of a quadratic polynomials as the entropy of
a certain forward-invariant set of the Julia set (the Hubbard tree). As
we shall see\, the core entropy is a purely topological/combinatorial qua
ntity which nonetheless captures the richness of the fractal structure of
the Mandelbrot set. In particular\, we will relate the variation of such
a function to the geometry of the Mandelbrot set. We will also prove that
the core entropy on the space of polynomials of a given degree varies con
tinuously\, answering a question of Thurston. Finally\, we will provide
a new interpretation of core entropy in terms of measured laminations\, an
d discuss its finer regularity properties such as its Holder exponent.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Hill (NYU Steinhardt)
DTSTART:20210924T190000Z
DTEND:20210924T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/23
DESCRIPTION:Title: Deep down\, everyone wants to be causal\nby Jennife
r Hill (NYU Steinhardt) as part of CRM-ISM Colloque des sciences mathémat
iques du Québec\n\nLecture held in Zoom.\n\nAbstract\nMost researchers in
the social\, behavioral\, and health sciences are taught to be extremely
cautious in making causal claims. However\, causal inference is a necessa
ry goal in research for addressing many of the most pressing questions aro
und policy and practice. In the past decade\, causal methodologists have
increasingly been using and touting the benefits of more complicated machi
ne learning algorithms to estimate causal effects. These methods can take
some of the guesswork out of analyses\, decrease the opportunity for “p
-hacking\,” and may be better suited for more fine-tuned tasks such as i
dentifying varying treatment effects and generalizing results from one pop
ulation to another. However\, should these more advanced methods change o
ur fundamental views about how difficult it is to infer causality? In this
talk I will discuss some potential advantages and disadvantages of using
machine learning for causal inference and emphasize ways that we can all b
e more transparent in our inferences and honest about their limitations.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bo'az Klartag (Weizmann Institute of Science)
DTSTART:20211001T150000Z
DTEND:20211001T160000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/24
DESCRIPTION:Title: (Nirenberg Lecture) Convexity and High-Dimensional Phen
omena\nby Bo'az Klartag (Weizmann Institute of Science) as part of CRM
-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in Zo
om.\n\nAbstract\nHigh-dimensional problems with a geometric flavor appear
in a number of branches of mathematics and mathematical physics. A priori
\, it seems that the immense diversity observed in high dimensions would m
ake it impossible to formulate general\, interesting theorems that apply t
o large classes of high-dimensional geometric objects. In this talk we wi
ll discuss situations in which high dimensionality\, when viewed correctly
\, induces remarkable order and simplicity rather than complication. For
example\, Dvoretzky's theorem demonstrates that any high-dimensional conve
x body possesses nearly-Euclidean sections of large dimension. Another ex
ample is the central limit theorem for convex bodies\, according to which
any high-dimensional convex body has approximately-Gaussian marginals. Th
ere are strong motifs in high-dimensional geometry\, such as the concentra
tion of measure\, which appear to compensate for the large number of diffe
rent configurations. Convexity allows us to harness these motifs in order
to formulate elegant and non-trivial theorems.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuansi Chen (Duke University)
DTSTART:20211008T150000Z
DTEND:20211008T160000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/25
DESCRIPTION:Title: (Nirenberg Lecture) Recent progress on the Kannan-Lovas
z-Simonovits (KLS) conjecture and Bourgain's slicing problem II\nby Yu
ansi Chen (Duke University) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn recent work
\, Chen (2020) improved Eldan's stochastic localization proof technique\,
which was deployed in Lee and Vempala (2017)\, to prove an almost constant
Cheeger isoperimetric coefficient in the KLS conjecture with dimension de
pendency d^o(1). Consequently\, his proof also provides a substantial adv
ance toward the resolution of Bourgain's slicing conjecture and the thin-s
hell conjecture. After getting conformable with Eldan's stochastic locali
zation technique\, in this talk we navigate through how to refine the tech
nique to provide the current best bound. We will complete the self-contai
ned proof of Chen (2020) and highlight the new ideas involved. Finally\,
we will discuss some extensions and provide an outlook for future research
directions.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Bonner (U of Western Ontario)
DTSTART:20211126T203000Z
DTEND:20211126T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/26
DESCRIPTION:Title: Adventures with Partial Identifications in Studies of M
arked Individuals\nby Simon Bonner (U of Western Ontario) as part of C
RM-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in
Zoom.\n\nAbstract\nMonitoring marked individuals is a common strategy in s
tudies of wild animals (referred to as mark-recapture or capture-recapture
experiments) and hard to track human populations (referred to as multi-li
st methods or multiple-systems estimation). A standard assumption of thes
e techniques is that individuals can be identified uniquely and without e
rror\, but this can be violated in many ways. In some cases\, it may not
be possible to identify individuals uniquely because of the study design o
r the choice of marks. Other times\, errors may occur so that individuals
are incorrectly identified. I will discuss work with my collaborators ov
er the past 10 years developing methods to account for problems that arise
when are only individuals are only partially identified. I will present
theoretical aspects of this research\, including an introduction to the la
tent multinomial model and algebraic statistics\, and also describe applic
ations to studies of species ranging from the golden mantella (an endanger
ed frog endemic to Madagascar measuring only 20 mm) to the whale shark (th
e largest known species of sh measuring up to 19 m).\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiffany Timbers (University of British Columbia)
DTSTART:20211029T193000Z
DTEND:20211029T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/27
DESCRIPTION:Title: Opinionated practices for teaching reproducibility: mot
ivation\, guided instruction and practice\nby Tiffany Timbers (Univers
ity of British Columbia) as part of CRM-ISM Colloque des sciences mathéma
tiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn the data scienc
e courses at the University of British Columbia\, we define data science a
s the study\, development and practice of reproducible and auditable proce
sses to obtain insight from data. While reproducibility is core to our def
inition\, most data science learners enter the field with other aspects of
data science in mind\, for example predictive modelling\, which is often
one of the most interesting topic to novices. This fact\, along with the h
ighly technical nature of the industry standard reproducibility tools curr
ently employed in data science\, present out-ofthe gate challenges in teac
hing reproducibility in the data science classroom. Put simply\, students
are not as intrinsically motivated to learn this topic\, and it is not an
easy one for them to learn. What can a data science educator do? Over seve
ral iterations of teaching courses focused on reproducible data science to
ols and workflows\, we have found that providing extra motivation\, guided
instruction and lots of practice are key to effectively teaching this cha
llenging\, yet important subject. Here we present examples of how we deepl
y motivate\, effectively guide and provide ample practice opportunities to
data science students to effectively engage them in learning about this t
opic.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louise Poirier (Université de Montréal)
DTSTART:20211105T193000Z
DTEND:20211105T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/28
DESCRIPTION:Title: Les mathématiques ont une histoire et une géographie<
/a>\nby Louise Poirier (Université de Montréal) as part of CRM-ISM Collo
que des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbs
tract\nLa présentation se divise en deux temps. Dans un premier temps\,
les principaux résultats de notre étude sur le « portrait mathématique
» des étudiants du Québec effectué dans le cadre du projet En avant m
ath! (projet conjoint CRM-CIRANO soutenu par le Ministère des finances) s
eront présentés. Ce rapport se fonde d’une part sur les résultats de
s tests internationaux TIMS et PISA pour les élèves québécois du prima
ire et du secondaire et d’autre part\, sur la situation des mathématiqu
es dans les universités québécoises dégagée des données du Bureau de
coopération interuniversitaire (BCI) ( évolution des inscriptions étud
iantes et portrait des étudiants tant en genre qu’en statut). Les donn
ées du BCI montrent que l'étudiant typique inscrit en maths dans les uni
versités québécoises est citoyen canadien\, blanc et masculin. Et le no
mbre total d'inscrits baisse à chaque année (sauf\, peut-être au doctor
at). Où sont les filles? Où sont les étudiants issus de l'immigration r
écente? Et pourtant aux tests PISA et TIMMS les élèves issus de l'immig
ration performent mieux au Canada que les élèves canadiens (c'est l'inve
rse pour la moyenne des pays de l'OCDE).\n\nPuis\, dans un deuxième temps
\, à la lumière des résultats du portrait des étudiants\, nous discute
rons des enjeux sociaux pour des mathématiques plus inclusives. Une reche
rche collaborative avec les communautés inuit du Nunavik viendra illustre
r nos propos. \n\nNote : Denis Gued m’excusera l’emprunt de ce titre.
Ces propos se retrouvent dans son entrevue « Rendons les mathématiques a
imables » accordée à L’express. https://www.lexpress.fr/informations
/rendons-les-mathematiques-aimables_640643.html\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Lugosi (UPF and BSE)
DTSTART:20211112T203000Z
DTEND:20211112T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/29
DESCRIPTION:Title: Estimating the mean of a random vector\nby Gabor Lu
gosi (UPF and BSE) as part of CRM-ISM Colloque des sciences mathématiques
du Québec\n\nLecture held in Zoom.\n\nAbstract\nOne of the most basic pr
oblems in statistics is the estimation of the mean of a random vector\, ba
sed on independent observations. This problem has received renewed attent
ion in the last few years\, both from statistical and computational points
of view. In this talk\, we review some recent results on the statistical
performance of mean estimators that allow heavy tails and adversarial con
tamination in the data. In particular\, we are interested in estimators t
hat have a near-optimal error in all directions in which the variance of t
he one dimensional marginal of the random vector is not too small. The ma
terial of this talk is based on a series of joint papers with Shahar Mende
lson.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Tosatti (McGill University)
DTSTART:20211203T203000Z
DTEND:20211203T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/30
DESCRIPTION:Title: K3 surfaces: geometry and dynamics\nby Valentino To
satti (McGill University) as part of CRM-ISM Colloque des sciences mathém
atiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nK3 surfaces are a
class of compact complex manifolds that enjoys many special properties an
d play an important role in several areas of mathematics. In this colloqui
um I will discuss a new interplay between complex geometry and analysis on
K3 surfaces equipped with their Calabi-Yau metrics\, and dynamics of holo
morphic diffeomorphisms of these surfaces\, that Simion Filip and I have b
een investigating recently.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke University)
DTSTART:20211210T190000Z
DTEND:20211210T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/31
DESCRIPTION:Title: Stark's Conjectures and Hilbert's 12th Problem\nby
Samit Dasgupta (Duke University) as part of CRM-ISM Colloque des sciences
mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn this ta
lk we will discuss two central problems in algebraic number theory and the
ir interconnections: explicit class field theory and the special values of
L-functions. The goal of explicit class field theory is to describe the
abelian extensions of a ground number field via analytic means intrinsic t
o the ground field\; this question lies at the core of Hilbert's 12th Prob
lem. Meanwhile\, there is an abundance of conjectures on the values of L-
functions at certain special points. Of these\, Stark's Conjecture has re
levance toward explicit class field theory. I will describe two recent jo
int results with Mahesh Kakde on these topics. The first is a proof of th
e Brumer-Stark conjecture away from p=2. This conjecture states the existe
nce of certain canonical elements in abelian extensions of totally real fi
elds. The second is a proof of an exact formula for Brumer-Stark units th
at has been developed over the last 15 years. We show that these units to
gether with other easily written explicit elements generate the maximal ab
elian extension of a totally real field\, thereby giving a p-adic solution
to the question of explicit class field theory for these fields.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-Tsung Huang (Institute of Statistical Science\, Academia Sinic
a)
DTSTART:20211217T150000Z
DTEND:20211217T160000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/32
DESCRIPTION:Title: Nonparametric causal mediation in a time-to-event setti
ng\nby Yen-Tsung Huang (Institute of Statistical Science\, Academia Si
nica) as part of CRM-ISM Colloque des sciences mathématiques du Québec\n
\nLecture held in Zoom.\n\nAbstract\nA causal mediation model with multipl
e time-to-event mediators is exemplified by the natural course of human di
sease marked by sequential milestones with a time-to-event nature. For ex
ample\, from hepatitis B infection to death\, patients may experience inte
rmediate events such as liver cirrhosis and liver cancer. The sequential
events of hepatitis\, cirrhosis\, cancer\, and death are susceptible to ri
ght censoring\; moreover\, the latter events may preclude the former event
s. Casting the natural course of human diseases in the framework of causa
l mediation modeling\, we establish a model with intermediate and terminal
events as the mediators and outcomes\, respectively. We define the inter
ventional analog of path-specific effects (iPSEs) as the effect of an expo
sure on a terminal event mediated (or not mediated) by any combination of
intermediate events without parametric models. The expression of a counti
ng process-based counterfactual hazard is derived under the sequential ign
orability assumption. We employ composite nonparametric likelihood estima
tion to obtain maximum likelihood estimators for the counterfactual hazard
and iPSEs. Our proposed estimators achieve asymptotic unbiasedness\, uni
form consistency\, and weak convergence. Applying the proposed method\, w
e show that hepatitis B induced mortality is mostly mediated through liver
cancer and/or cirrhosis whereas hepatitis C induced mortality may be thro
ugh extrahepatic diseases.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Stupfler (ENSAI)
DTSTART:20220128T203000Z
DTEND:20220128T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/33
DESCRIPTION:Title: Risk assessment\, heavy tails\, and asymmetric least sq
uares techniques\nby Gilles Stupfler (ENSAI) as part of CRM-ISM Colloq
ue des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbst
ract\nStatistical risk assessment\, in particular in finance and insurance
\, requires estimating simple indicators to summarize the risk incurred in
a given situation. Of most interest is to infer extreme levels of risk s
o as to be able to manage high-impact rare events such as extreme climate
episodes or stock market crashes. A standard procedure in this context\,
whether in the academic\, industrial or regulatory circles\, is to estimat
e a well-chosen single quantile (or Value-at-Risk). One drawback of quant
iles is that they only take into account the frequency of an extreme event
\, and in particular do not give an idea of what the typical magnitude of
such an event would be. Another issue is that they do not induce a cohere
nt risk measure\, which is a serious concern in actuarial and financial ap
plications. In this talk\, after giving a leisurely tour of extreme quant
ile estimation\, I will explain how\, starting from the formulation of a q
uantile as the solution of an optimization problem\, one may come up with
two alternative families of risk measures\, called expectiles and extremil
es\, in order to address these two drawbacks. I will give a broad overvie
w of their properties\, as well as of their estimation at extreme levels i
n heavy-tailed models\, and explain why they constitute sensible alternati
ves for risk assessment using real data applications. This is based on jo
int work with Abdelaati Daouia\, Irène Gijbels\, Stéphane Girard\, Simon
e Padoan and Antoine Usseglio-Carleve.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (Polytechnic University of Catalonia)
DTSTART:20220114T160000Z
DTEND:20220114T170000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/34
DESCRIPTION:Title: Looking at hydrodynamics through a contact mirror: From
Euler to Turing and beyond\nby Eva Miranda (Polytechnic University of
Catalonia) as part of CRM-ISM Colloque des sciences mathématiques du Qu
ébec\n\nLecture held in Zoom.\n\nAbstract\nWhat physical systems can be n
on-computational? (Roger Penrose\, 1989). Is hydrodynamics capable of cal
culations? (Cris Moore\, 1991). Can a mechanical system (including the tra
jectory of a fluid) simulate a universal Turing machine? (Terence Tao\, 20
17).\n\nThe movement of an incompressible fluid without viscosity is gover
ned by Euler equations. Its viscid analogue is given by the Navier-Stokes
equations whose regularity is one of the open problems in the list of prob
lems for the Millenium by\nthe Clay Foundation. The trajectories of a flui
d are complex. Can we measure its levels of complexity (computational\, lo
gical and dynamical)?\n\nIn this talk\, we will address these questions. I
n particular\, we will show how to construct a 3-dimensional Euler flow wh
ich is Turing complete. Undecidability of fluid paths is then a consequenc
e of the classical undecidability of the halting\n\nproblem proved by Alan
Turing back in 1936. This is another manifestation of complexity in hydro
dynamics which is very different from the theory of chaos.\n\nOur solution
of Euler equations corresponds to a stationary solution or Beltrami field
. To address this problem\, we will use a mirror [5] reflecting Beltrami f
ields as Reeb vector fields of a contact\n\nstructure. Thus\, our solution
s import techniques from geometry to solve a problem in fluid dynamics. Bu
t how general are Euler flows? Can we represent any dynamics as an Euler f
low? We will address this universality problem using the Beltrami/Reeb mir
ror again and Gromov's h-principle. We will also consider the non-stationa
ry case. These universality features illustrate the complexity of Euler fl
ows. However\, this construction is not "physical" in the sense that the a
ssociated metric is not the euclidean metric. We will announce an euclide
an construction and its implications to complexity and undecidability.\n\n
These constructions [1\,2\,3\,4] are motivated by Tao's approach to the
problem of Navier-Stokes [7\,8\,9] which we will also explain.\n\n[1] R.
Cardona\, E. Miranda\, D. Peralta-Salas\, F. Presas. Universality of Euler
flows and flexibility of Reeb\nembeddings. https://arxiv.org/abs/1911.019
63.\n[2] R. Cardona\, E. Miranda\, D. Peralta-Salas\, F. Presas. Construct
ing Turing complete Euler flows in\ndimension 3. Proc. Natl. Acad. Sci. 11
8 (2021) e2026818118.\n[3] R. Cardona\, E. Miranda\, D. Peralta-Salas. Tur
ing universality of the incompressible Euler equations\nand a conjecture o
f Moore. Int. Math. Res. Notices\, \, 2021\;\, rnab233\,\nhttps://doi.org/
10.1093/imrn/rnab233\n[4] R. Cardona\, E. Miranda\, D. Peralta-Salas. Comp
utability and Beltrami fields in Euclidean space.\nhttps://arxiv.org/abs/2
111.03559 \n[5] J. Etnyre\, R. Ghrist. Contact topology and hydrodynamics
I. Beltrami fields and the Seifert conjecture.\nNonlinearity 13 (2000) 441
–458.\n[6] C. Moore. Generalized shifts: unpredictability and undecidabi
lity in dynamical systems. Nonlinearity\n4 (1991) 199–230.\n\n[7] T. Tao
. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219
–238.\n[8] T. Tao. On the universality of the incompressible Euler equat
ion on compact manifolds. Discrete\nCont. Dyn. Sys. A 38 (2018) 1553–156
5.\n[9] T. Tao. Searching for singularities in the Navier-Stokes equations
. Nature Rev. Phys. 1 (2019) 418–419.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Hynd (University of Pennsylvania)
DTSTART:20220211T203000Z
DTEND:20220211T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/35
DESCRIPTION:Title: Sticky particle dynamics\nby Ryan Hynd (University
of Pennsylvania) as part of CRM-ISM Colloque des sciences mathématiques d
u Québec\n\nLecture held in Zoom.\n\nAbstract\nI will discuss the time ev
olution of a collection of particles that interact primarily through perfe
ctly inelastic collisions. I will explain why this problem is tractable if
the particles are constrained to lie on a line versus if they are allowe
d to move freely in space. In particular\, I'll also describe an equatio
n at the heart of this difficulty which some researchers believe has bee
n solved and others do not. This topic has motivations in astronomy and
connections with optimal mass transportation which I will touch upon if t
ime permits.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell University)
DTSTART:20220121T190000Z
DTEND:20220121T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/37
DESCRIPTION:Title: The commuting variety and generic pipe dreams\nby A
llen Knutson (Cornell University) as part of CRM-ISM Colloque des sciences
mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nNobody kn
ows whether the scheme "pairs of commuting nxn matrices" is reduced. I'll
show how this scheme relates to matrix Schubert varieties\, and give a for
mula for its equivariant cohomology class (and that of many other varietie
s) using "generic pipe dreams" that I'll introduce. These interpolate betw
een ordinary and bumpless pipe dreams. With those\, I'll rederive both for
mulae (ordinary and bumpless) for double Schubert polynomials. This work i
s joint with Paul Zinn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Zerbes (ETH Zurich)
DTSTART:20220204T170000Z
DTEND:20220204T180000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/38
DESCRIPTION:Title: Euler systems and the Birch—Swinnerton-Dyer conjectur
e\nby Sarah Zerbes (ETH Zurich) as part of CRM-ISM Colloque des scienc
es mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nL-funct
ions are one of the central objects of study in number theory. There are m
any beautiful theorems and many more open conjectures linking their values
to arithmetic problems. The most famous example is the conjecture of Birc
h and Swinnerton-Dyer\, which is one of the Clay Millenium Prize Problems.
I will discuss this conjecture and some related open problems\, and I wil
l describe some recent progress on these conjectures\, using tools called
`Euler systems’.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Forrest Crawford (Yale University)
DTSTART:20220429T193000Z
DTEND:20220429T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/39
DESCRIPTION:Title: COVID-19 transmission models in the real world: models\
, data\, and policy\nby Forrest Crawford (Yale University) as part of
CRM-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in
Zoom.\n\nAbstract\nSimple mathematical models of COVID-19 transmission ga
ined prominence in the early days of the pandemic. These models provided r
esearchers and policymakers with qualitative insight into the dynamics of
transmission and quantitative predictions of disease incidence. More sop
histicated models incorporated new information about the natural history o
f COVID-19 disease and the interaction of infected individuals with the he
althcare system\, to predict diagnosed cases\, hospitalization\, ventilato
r usage\, and death. Models also provided intuition for discussions about
outbreaks\, vaccination\, and the effects of non-pharmaceutical interventi
ons like social distancing guidelines and stay-at-home orders. But as the
pandemic progressed\, complex real-world interventions took effect\, peopl
e everywhere changed their behavior\, and the usefulness of simple mathema
tical models of COVID-19 transmission diminished. This challenge forced
researchers to think more broadly about empirical data sources that could
help predictive models regain their utility for guiding public policy. In
this presentation\, I will describe my view of the successes and failures
of population-level transmission models in the context of the COVID-19 pan
demic. I will outline the evolution of a project to predict COVID-19 inc
idence in the state of Connecticut\, from development of a transmission mo
del to engagement with public health policymakers and initiation of a new
data collection effort. I argue that a new data source – passive measure
ment of close interpersonal contact via mobile device location data – is
a promising way to overcome many of the shortcomings of traditional trans
mission models. I conclude with a summary of the impact this work has ha
d on the COVID-19 response in Connecticut and beyond.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stanislav Volgushev (University of Toronto)
DTSTART:20220218T203000Z
DTEND:20220218T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/40
DESCRIPTION:Title: Structure learning for Extremal graphical models\nb
y Stanislav Volgushev (University of Toronto) as part of CRM-ISM Colloque
des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstrac
t\nExtremal graphical models are sparse statistical models for multivariat
e extreme events. The underlying graph encodes conditional independencies
and enables a visual interpretation of the complex extremal dependence st
ructure. For the important case of tree models\, we provide a data-driven
methodology for learning the graphical structure. We show that sample ve
rsions of the extremal correlation and a new summary statistic\, which we
call the extremal variogram\, can be used as weights for a minimum spannin
g tree to consistently recover the true underlying tree. Remarkably\, thi
s implies that extremal tree models can be learned in a completely non-par
ametric fashion by using simple summary statistics and without the need to
assume discrete distributions\, existence of densities\, or parametric mo
dels for marginal or bivariate distributions. Extensions to more general
graphs are also discussed.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Gorksy (UC Davis)
DTSTART:20220311T203000Z
DTEND:20220311T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/41
DESCRIPTION:Title: Algebra\, geometry and combinatorics of link homology\nby Evgeny Gorksy (UC Davis) as part of CRM-ISM Colloque des sciences m
athématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nKhovanov an
d Rozansky defined in 2005 a triply graded link homology theory which gene
ralizes HOMFLY-PT polynomial. In this talk\, I will outline some known res
ults and structures in Khovanov-Rozansky homology\, describe its connectio
n to q\,t-Catalan combinatorics and present several geometric models for s
ome classes of links.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Macbeth (Fordham university)
DTSTART:20220325T193000Z
DTEND:20220325T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/42
DESCRIPTION:Title: Making mathematics computer-checkable\nby Heather M
acbeth (Fordham university) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn the last th
irty years\, computer proof verification became a mature technology\, with
successes including the checking of the Four-Colour Theorem\, the Odd Ord
er Theorem\, and Hales' proof of the Kepler Conjecture. Recent advances s
uch as the "Liquid Tensor Experiment" verifying a recent theorem of Scholz
e have provided further momentum\, as likewise have promising experiments
integrating this technology with machine learning.\n\nI will briefly descr
ibe some of these developments. I will then try to describe\, more genera
lly\, what it *feels* like to carry out research-level computer verificati
ons of mathematics proofs: the level of expression one has access to\, the
ways one finds oneself interrogating and reorganizing a paper proof\, the
kinds of arguments which are more tedious (or less tedious!) than on pape
r.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll (University of Cologne)
DTSTART:20220401T180000Z
DTEND:20220401T190000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/43
DESCRIPTION:Title: Gentle algebras\, surfaces and a glimpse of homological
mirror symmetry\nby Sibylle Schroll (University of Cologne) as part o
f CRM-ISM Colloque des sciences mathématiques du Québec\n\nLecture held
in Zoom.\n\nAbstract\nDerived categories are in general not easy to parse.
However\, in certain cases\, combinatorial models give a good picture of
these categories. One such case are the bounded derived categories of gent
le algebras which can be represented in terms of curves and crossings of c
urves on surfaces. In this talk\, we will give the construction of these s
urface models and briefly explain how they are connected to the homologica
l mirror symmetry programme. We will show how a combination of surface com
binatorics and representation theory can give new insights into the associ
ated categories.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Cardaliaguet (Université Paris-Dauphine)
DTSTART:20220415T190000Z
DTEND:20220415T200000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/44
DESCRIPTION:Title: Some aspects of Mean Field Games\nby Pierre Cardali
aguet (Université Paris-Dauphine) as part of CRM-ISM Colloque des science
s mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nMean Fie
ld Game is the study of the dynamical behavior of a large number of agents
in interaction. For instance\, it can model be the dynamics of a crowd\,
or the production of a renewable resource by a large amount of producers.
The analysis of these models\, first introduced in the economic literature
under the terminology of “heterogenous agent models\, has known a spect
acular development with the pioneering woks of Lasry and Lions and of Cain
es\, Huang and Malhamé. The aim of the talk will be to illustrate the the
ory through a few models and present some of the main results and open que
stions.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20220422T193000Z
DTEND:20220422T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/45
DESCRIPTION:Title: Cactus groups and monodromy\nby Joel Kamnitzer (Uni
versity of Toronto) as part of CRM-ISM Colloque des sciences mathématique
s du Québec\n\nLecture held in Zoom.\n\nAbstract\nThe cactus group is a c
ousin of the braid group and shares many of its beautiful properties. It
is the fundamental group of the moduli space of points on RP^1. It also
acts on many collections of combinatorial objects. I will explain how w
e use the cactus group to understand monodromy of eigenvectors for Gaudin
algebras.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Derrida ((École Normale Supérieure\, Paris\, France))
DTSTART:20220318T193000Z
DTEND:20220318T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/46
DESCRIPTION:Title: The importance of large deviations in non-equilibrium s
ystems\nby Bernard Derrida ((École Normale Supérieure\, Paris\, Fran
ce)) as part of CRM-ISM Colloque des sciences mathématiques du Québec\n\
nLecture held in Zoom.\n\nAbstract\n2022 Aisenstadt Chair recipient\n\nSta
tistical Physics allowed to unify\, at the end of the 19th century\, Newto
n's mechanics and thermodynamics. It gave a way to predict the amplitude o
f fluctuations around the physical laws which were known at that time. Ein
stein\, in his very first works\, showed that the measurement of these flu
ctuations allowed to estimate the size of atoms. His reasoning\, which was
at the origin of the linear response theory\, applied to the black body g
ave one of the first evidences of the duality wave-particle in Quantum Mec
hanics. Statistical Physics gives also a framework to predict large deviat
ions for systems at equilibrium. In the last two decades\, major efforts w
ere devoted to extend our understanding of the statistical laws of fluctua
tions and large deviations to non-equilibrium systems. This talk will try
to present some of the recent progresses.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (Ecole Normale Supérieure)
DTSTART:20220520T193000Z
DTEND:20220520T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/47
DESCRIPTION:Title: Mathematical analysis of dilute gases : derivation of t
he Boltzmann equation\, fluctuations and large deviations\nby Isabelle
Gallagher (Ecole Normale Supérieure) as part of CRM-ISM Colloque des sci
ences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n2022
Aisenstadt Chair recipient\n\nThe evolution of a gas can be described by
different models depending on the observation scale. A natural question\,
raised by Hilbert in his sixth problem\, is whether these models provide c
onsistent predictions. In particular\, for rarefied gases\, it is expected
that continuum laws of kinetic theory can be obtained directly from molec
ular dynamics governed by the fundamental principles of mechanics. In the
case of hard sphere gases\, Lanford showed in 1975 that the Boltzmann eq
uation emerges as the law of large numbers in the low density limit\, at l
east for very short times. The goal of this talk is to explain the heurist
ics of his proof and present recent progress in the understanding of this
limiting process.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Raussendorf (UBC)
DTSTART:20220408T193000Z
DTEND:20220408T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/48
DESCRIPTION:Title: Hidden Variable Model for Universal Quantum Computation
with Magic States on Qubits\nby Robert Raussendorf (UBC) as part of C
RM-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in
Zoom.\n\nAbstract\n2021 CAP-CRM Prize Recipient\n\nWe show that every qu
antum computation can be described by a probabilistic update of a probabil
ity distribution on a finite phase space. Negativity in a quasiprobability
function is not required in states or operations\, which is a very unusua
l feature. Nonetheless\, our result is consistent with Gleason’s Theorem
and the Pusey-Barrett- Rudolph theorem. \n\nThe reason I have chosen thi
s subject for my talk is two-fold: (i) It gives the audience a glimpse of
the quest to understand the quantum mechanical cause for speed-up in quant
um computation\, which is one of the central questions on the theory side
of the field\, and (ii) Maybe there can be feedback from the audience. The
structures underlying the above probabilistic model are the so-called Lam
bda-polytopes\, which are highly symmetric objects. At present we only k
now very few general facts about them. Help with analysing them would be a
ppreciated!\n\nJoint work with Michael Zurel and Cihan Okay\,\n\nJournal r
eference: Phys. Rev. Lett. 125\, 260404 (2020)\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Solecki (Cornell University)
DTSTART:20220506T193000Z
DTEND:20220506T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/49
DESCRIPTION:Title: Generic measure preserving transformations and Descript
ive Set Theory\nby Slawomir Solecki (Cornell University) as part of CR
M-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in Z
oom.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:test
DTSTART:20220715T193000Z
DTEND:20220715T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/50
DESCRIPTION:by test as part of CRM-ISM Colloque des sciences mathématique
s du Québec\n\nLecture held in Zoom.\n\nAbstract\nA symmetric conference
matrix is an $n \\times n$ symmetric matrix with 0's on the diagonal and $
\\pm 1$ off the diagonal\, such that $C^2 = (n-1)I$. It can be shown that
the following conditions are necessary conditions for the existence of su
ch a matrix: $n = 4k+2$ and $n-1$ must be a sum of two squares. Examples a
re known for $n=q+1$ where $q$ is a prime power congruent to 1 modulo 4\,
and recursively for $n = (4t+1)(4t-1)^2 + 1$ when there is a conference ma
trix of size $4t+2$ and $4t-1$ is a prime power. Apart from the necessary
conditions stated above\, there are no orders where nonexistence is proved
. Until October 2020\, the smallest open case was $n=66$\, when Oleg Grits
enko gave an example. In this talk\, we will discuss Gritsenko's construct
ion and ongoing efforts to generalize it. This is joint work with Bill Ma
rtin (Worcester Polytechnic Institute).\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (Université Laval)
DTSTART:20220902T193000Z
DTEND:20220902T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/51
DESCRIPTION:Title: Algèbres amassées et théorie des noeuds\nby Vér
onique Bazier-Matte (Université Laval) as part of CRM-ISM Colloque des sc
iences mathématiques du Québec\n\nLecture held in HYBRID - SUR PLACE/ ON
-SITE : Pavillon André Aisenstadt Salle/ Room 5340\, 2920\, chemin de la
tour\,.\n\nAbstract\nLes algèbres amassées sont des algèbres de polyn
ômes de Laurent dont les générateurs s’obtiennent par un processus r
écursif appelé mutation. On commence avec une graine\, paire formée d
’un ensemble de n variables\, appelé amas\, et d’un graphe orienté
à n points. La mutation d’une graine remplace une variable à la fois e
t modifie le graphe\, donnant ainsi une nouvelle graine. L’algèbre amas
sée est engendrée par toutes les variables obtenues par mutations succes
sives\, qu’on appelle variables amassées. \n \nLes algèbres amassée
s ont été définies il y a 20 ans\, et depuis\, des liens entre elles et
divers champs de recherche ont été découverts. Récemment\, avec mon c
ollaborateur\, nous avons établi un lien entre la théorie des noeuds et
les algèbres amassées. Cet exposé introduira d'abord les algèbres amas
sées puis présentera la connection entre ces dernières et le polynôme
d'Alexander d'un noeud.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART:20220916T193000Z
DTEND:20220916T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/52
DESCRIPTION:Title: Modularity of Galois representations\, from Ramanujan t
o Serre's conjecture and beyond\nby Chandrashekhar Khare (UCLA) as par
t of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLecture he
ld in Zoom.\n\nAbstract\nRamanujan made a series of influential conjecture
s in his 1916 paper ``On some arithmetical functions’' on what is now ca
lled the Ramanujan $\\tau$ function. A congruence Ramanujan observed for $
\\tau(n)$ modulo 691 in the paper led to Serre and Swinnerton-Dyer develop
ing a geometric theory of mod $p$ modular forms. It was in the context of
the theory of mod $p$ modular forms that Serre made his modularity conject
ure\, which was initially formulated in a letter of Serre to Tate in 1973.
\n\nI will describe the path from Ramanujan's work in 1916\, to the formu
lation of a first version of Serre's conjecture in 1973\, to its resolutio
n in 2009 by Jean-Pierre Wintenberger and myself. I will also try to indic
ate why this subject is very much alive and\, in spite of all the progress
\, still in its infancy.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (Mcgill)
DTSTART:20220923T193000Z
DTEND:20220923T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/53
DESCRIPTION:Title: A story about pointwise ergodic theorems\nby Anush
Tserunyan (Mcgill) as part of CRM-ISM Colloque des sciences mathématiques
du Québec\n\nLecture held in Zoom.\n\nAbstract\nPointwise ergodic theore
ms provide a bridge between the global behaviour of the dynamical system a
nd the local combinatorial statistics of the system at a point. Such theor
em have been proven in different contexts\, but typically for actions of s
emigroups on a probability space. Dating back to Birkhoff (1931)\, the fir
st known pointwise ergodic theorem states that for a measure-preserving er
godic transformation T on a probability space\, the mean of a function (it
s global average) can be approximated by taking local averages of the func
tion at a point x over finite sets in the forward-orbit of x\, namely {x\,
Tx\, ...\, T^n x}. Almost a century later\, we revisit Birkhoff's theorem
and turn it backwards\, showing that the averages along trees of possible
pasts also approximate the global average. This backward theorem for a s
ingle transformation surprisingly has applications to actions of free grou
ps\, which we will also discuss. This is joint work with Jenna Zomback.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengfei Li (University of Waterloo)
DTSTART:20220930T193000Z
DTEND:20220930T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/54
DESCRIPTION:Title: (Prix SSC) Full likelihood inference for abundance from
capture-recapture data: semiparametric efficiency and EM-algorithm\nb
y Pengfei Li (University of Waterloo) as part of CRM-ISM Colloque des scie
nces mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nCaptu
re-recapture experiments are widely used to collect data needed to estimat
e the abundance of a closed population. To account for heterogeneity in t
he capture probabilities\, Huggins (1989) and Alho (1990) proposed a semip
arametric model in which the capture probabilities are modelled parametric
ally and the distribution of individual characteristics is left unspecifie
d. A conditional likelihood method was then proposed to obtain point esti
mates and Wald-type confidence intervals for the abundance. Empirical stu
dies show that the small-sample distribution of the maximum conditional li
kelihood estimator is strongly skewed to the right\, which may produce Wal
d-type confidence intervals with lower limits that are less than the numbe
r of captured individuals or even negative. \n\nIn this talk\, we prese
nt a full likelihood approach based on Huggins and Alho's model. We show
that the null distribution of the empirical likelihood ratio for the abund
ance is asymptotically chi-square with one degree of freedom\, and the max
imum empirical likelihood estimator achieves semiparametric efficiency. W
e further propose an expectation–maximization algorithm to numerically c
alculate the proposed point estimate and empirical likelihood ratio functi
on. Simulation studies show that the empirical-likelihood-based method is
superior to the conditional-likelihood-based method: its confidence inter
val has much better coverage\, and the maximum empirical likelihood estima
tor has a smaller mean square error.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balint Virag (University of Toronto)
DTSTART:20221007T193000Z
DTEND:20221007T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/55
DESCRIPTION:Title: (Prix-CRM-Fields-Pims) Random plane geometry -- a gentl
e introduction\nby Balint Virag (University of Toronto) as part of CRM
-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in Zo
om.\n\nAbstract\nConsider Z^2\, and assign a random length of 1 or 2 to ea
ch edge based on independent fair coin tosses. The resulting random geomet
ry\, first passage percloation\, is conjectured to have a scaling limit.\n
\nMost random plane geometric models (including hidden geometries) should
have the same scaling limit.\n\nI will explain the basics of the limiting
geometry\, the "directed landscape"\, the central object in the class of m
odels named after\nKardar\, Parisi and Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yevgeny Liokumovich (University of Toronto)
DTSTART:20221014T193000Z
DTEND:20221014T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/56
DESCRIPTION:Title: (2022 André Aisenstadt Prize) New isoperimetric inequa
lities and their applications to systolic geometry and minimal surfaces\nby Yevgeny Liokumovich (University of Toronto) as part of CRM-ISM Collo
que des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbs
tract\nI will describe two new isoperimetric inequalities for k-dimensiona
l submanifolds of R^n or a Banach space. As a consequence of one we obtain
a new systolic inequality that was conjectured by Larry Guth. As a conseq
uence of another\, we obtain an asymptotic formula for volumes of minimal
submanifolds that was conjectured by Mikhail Gromov. The talk is based on
joint works with Boris Lishak\, Alexander Nabutovsky and Regina Rotman\; F
ernando Marques and Andre Neves\; Larry Guth.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derek Bingham (Simon Fraser University)
DTSTART:20221028T193000Z
DTEND:20221028T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/57
DESCRIPTION:by Derek Bingham (Simon Fraser University) as part of CRM-ISM
Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bernstein (Johns Hopkins University)
DTSTART:20221104T193000Z
DTEND:20221104T203000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/58
DESCRIPTION:Title: Complexity of Submanifolds and Colding-Minicozzi Entrop
y\nby Jacob Bernstein (Johns Hopkins University) as part of CRM-ISM Co
lloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\n
Abstract\nGiven a submanifold of Euclidean space\, Colding and Minicozzi d
efined its entropy to be the supremum of the Gaussian weighted surface are
as of all of its translations and dilations. While initially introduced to
study singularities of mean curvature flow\, it has proven to be an inter
esting geometric measure of complexity. In this talk I will survey some of
the recent progress made on studying the Colding-Minicozzi entropy of hyp
ersurfaces. In particular\, I will discuss a series of work by Lu Wang and
myself showing closed hypersurfaces with small entropy are simple in vari
ous senses.\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Steorts (Duke University)
DTSTART:20221125T203000Z
DTEND:20221125T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/59
DESCRIPTION:by Rebecca Steorts (Duke University) as part of CRM-ISM Colloq
ue des sciences mathématiques du Québec\n\nLecture held in Zoom.\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Besser (Ben Gurion University)
DTSTART:20221202T203000Z
DTEND:20221202T213000Z
DTSTAMP:20260404T111102Z
UID:generalmathematics/60
DESCRIPTION:by Amnon Besser (Ben Gurion University) as part of CRM-ISM Col
loque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nA
bstract\n\\documentclass[12pt\,a4]{article} \\usepackage{amsmath\,amssymb\
,amstext} \\usepackage{enumerate} \\setlength{\\parindent}{0pt} \\pagestyl
e{empty} \\begin{document} \\begin{center} {\\large Non-selfadjoint spectr
al problems related to self-similar blowup in nonlinear wave equations} \\
end{center} \\begin{center} Michael Plum \\\\Karlsruhe Institute of Techno
logy\, Germany \\end{center} We consider the wave equation with a power no
nlinearity \\begin{equation} u_{tt}-\\Delta u = u^p\, \\nonumber \\end{equ
ation} with initial profiles $u(x\,0)$ and $u_t(x\,0)$\, $x\\in \\mathbb{R
}^3$\, $t\\ge 0$\, and $p>1$ an odd integer. In order to investigate the b
lowup dynamics we look for radial self-similar blowup solutions of the for
m \\begin{equation} u(x\,t)=(T-t)^{-\\frac{2}{p-1}}U\\left(\\frac{|x|}{T-t
}\\right)\,\\quad T>0\, \\nonumber \\end{equation} with a smooth\, radial
profile $U$. In particular\, we are interested in stability properties of
such solutions. This gives rise to analyzing the spectrum of the linearize
d operator\, i.e. to the eigenvalue problem: \\begin{eqnarray*} \\mathcal{
L} {\\bf u}=\\lambda {\\bf u}\, \\label{ep} \\end{eqnarray*} where $D(\\ma
thcal{L})\\subset H^2_{\\rm rad}(B^3)\\times H^1_{\\rm rad}(B^3)$\, $H^k_{
\\rm rad}(B^3):=\\{ {\\bf u}\\in H^k(B^3):{\\bf u}~{\\rm is~radial} \\}$\,
\\begin{eqnarray*} \\mathcal{L} \\begin{pmatrix} u_1 \\cr u_2\\end{pmatri
x}:=\\begin{pmatrix} -\\rho u_1^{\\prime}(\\rho)-\\alpha u_1(\\rho)+u_2(\\
rho) \\cr u_1^{\\prime \\prime}(\\rho)+\\frac{2}{\\rho}u_1^{\\prime}(\\rho
)-\\rho u_2^{\\prime}(\\rho)-(\\alpha+1)u_2(\\rho)+V(\\rho)u_1(\\rho) \\en
d{pmatrix}\, \\label{lp} \\end{eqnarray*} $B^3=\\{ x\\in \\mathbb{R}^3:|x|
\\le 1 \\}$\, $\\rho=\\frac{|x|}{T-t}$\, $V(\\rho)=pU(\\rho)^{p-1}$ and $\
\alpha=\\frac{2}{p-1}$. We are interested in excluding eigenvalues of $\\m
athcal{L}$ in the crucial parts of the right complex half plane\, which is
ongoing work together with K. Nagatou\, M.T. Nakao\, B. Sch\\"orkhuber an
d Y. Watanabe. We first provide a compact set $R \\subset \\mathbb{C}$ suc
h that no eigenvalues can exist in the right half-plane outside this set.
Furthermore\, we derive estimates ensuring that small discs with explicitl
y computable radii and carefully chosen centers are free of eigenvalues. C
overing the set $R$ with such discs gives\, in principle\, the desired non
-existence of eigenvalues\, implying (linear) stability. \\end{document}\n
LOCATION:https://stable.researchseminars.org/talk/generalmathematics/60/
END:VEVENT
END:VCALENDAR