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BEGIN:VEVENT
SUMMARY:Morgan Craig (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20200619T200000Z
DTEND;VALUE=DATE-TIME:20200619T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/1
DESCRIPTION:Title: Quantitative approaches to understanding the immune response to
SARS-CoV-2 infection\nby Morgan Craig (Université de Montréal) as p
art of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLecture
held in Zoom.\n\nAbstract\nCOVID-19 is typically characterized by a range
of respiratory symptoms that\, in severe cases\, progress to acute respira
tory distress syndrome (ARDS). These symptoms are also frequently accompan
ied by a range of inflammatory indications\, particularly hyper-reactive a
nd dysregulated inflammatory responses in the form of cytokine storms and
severe immunopathology. Much remains to be uncovered about the mechanisms
that lead to disparate outcomes in COVID-19. Here\, quantitative approache
s\, especially mechanistic mathematical models\, can be leveraged to impro
ve our understanding of the immune response to SARS-CoV-2 infection. Build
ing upon our prior work modelling the production of innate immune cell sub
sets and the viral dynamics of HIV and oncolytic viruses\, we are developi
ng a quantitative framework to interrogate open questions about the innate
and adaptive immune reaction in COVID-19. In this talk\, I will outline o
ur 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 working
to establish a comprehensive tissue simulator (physicell.org/covid19 [1])\
, which I will also discuss in more detail.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lai-Sang Young (Courant Institute of Mathematical Sciences\, New Y
ork University)
DTSTART;VALUE=DATE-TIME:20200417T200000Z
DTEND;VALUE=DATE-TIME:20200417T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/2
DESCRIPTION:Title: Observable events and typical trajectories in finite and infini
te dimensional dynamical systems\nby Lai-Sang Young (Courant Institute
of Mathematical Sciences\, New York University) as part of CRM-ISM Colloq
ue des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbst
ract\nThe terms "observable events" and "typical trajectories" in the titl
e should really be between quotation marks\, because what is typical and/o
r observable is a matter of interpretation. For dynamical systems on finit
e dimensional spaces\, one often equates observable events with positive L
ebesgue measure sets\, and invariant distributions that reflect the large-
time behaviors of positive Lebesgue measure sets of initial conditions (su
ch as Liouville measure for Hamiltonian systems) are considered to be espe
cially important. I will begin by introducing these concepts for general d
ynamical systems -- including those with attractors -- describing a simple
dynamical picture that one might hope to be true. This picture does not a
lways hold\, unfortunately\, but a small amount of random noise will bring
it about. In the second part of my talk I will consider infinite dimensio
nal systems such as semi-flows arising from dissipative evolutionary PDEs.
I will discuss the extent to which the ideas above can be generalized to
infinite dimensions\, and propose a notion of "typical solutions".\n
LOCATION:https://researchseminars.org/talk/generalmathematics/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Griffiths (Institute for Advanced Study\, Princeton\, USA)
DTSTART;VALUE=DATE-TIME:20201009T190000Z
DTEND;VALUE=DATE-TIME:20201009T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/3
DESCRIPTION:Title: Hodge Theory and Moduli\nby Phillip Griffiths (Institute fo
r Advanced Study\, Princeton\, USA) as part of CRM-ISM Colloque des scienc
es mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nThe the
ory of moduli is an important and active area in algebraic geometry. For v
arieties of general type the existence of a moduli space with a canonical
completion has been proved by Kollar/Shepard-Barron/Alexeev. Aside from
the classical case of algebraic curves\, very little is known about the st
ructure of \, especially it’s boundary. The period mapping from Hodge th
eory provides a tool for studying these issues.\n\nIn this talk\, we will
discuss some aspects of this topic with emphasis on I-surfaces\, which pro
vide one of the first examples where the theory has been worked out in som
e detail. Particular notice will me made of how the extension data in the
limiting mixed Hodge structures that arise from singular surfaces on the b
oundary of moduli may be used to guide the desingularization of that bound
ary.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Bergeron (École Normale Supérieure (Paris)\, France)
DTSTART;VALUE=DATE-TIME:20201016T190000Z
DTEND;VALUE=DATE-TIME:20201016T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/4
DESCRIPTION:Title: Trigonometric functions and modular symbols\nby Nicolas Ber
geron (École Normale Supérieure (Paris)\, France) as part of CRM-ISM Col
loque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nA
bstract\nIn his fantastic book « Elliptic functions according to Eisenste
in and Kronecker\, » Weil writes:\n\n « As Eisenstein shows\, his metho
d for constructing elliptic functions applies beautifully to the simpler
case of the trigonometric functions. Moreover\, this case provides […] t
he simplest proofs for a series of results\, originally discovered by Eule
r. » \n\nThe results Weil alludes to are relations between product of tri
gonometric functions. I will first explain how these relations are quite s
urprisingly governed by relations between modular symbols (whose elementar
y 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 some line
ar groups to the algebraic world of trigonometric and elliptic functions.
To conclude I will briefly describe a number theoretical application. \n\
nThis is based on a work-in-progress with Pierre Charollois\, Luis Garcia
and Akshay Venkatesh.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Broderick (Massachusetts Institute of Technology\, USA)
DTSTART;VALUE=DATE-TIME:20201113T203000Z
DTEND;VALUE=DATE-TIME:20201113T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/5
DESCRIPTION:Title: Approximate Cross-Validation for Large Data and High Dimensions
\nby Tamara Broderick (Massachusetts Institute of Technology\, USA) as
part of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLectur
e held in Zoom.\n\nAbstract\nThe error or variability of statistical and m
achine learning algorithms is often assessed by repeatedly re-fitting a mo
del with different weighted versions of the observed data. The ubiquitous
tools of cross-validation (CV) and the bootstrap are examples of this tech
nique. These methods are powerful in large part due to their model agnosti
cism 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 depende
nce of the fitting procedure on the weights\, producing results that can b
e faster than repeated re-fitting by orders of magnitude. This linear appr
oximation is sometimes known as the "infinitesimal jackknife" (IJ) in the
statistics literature\, where it has mostly been used as a theoretical too
l to prove asymptotic results. We provide explicit finite-sample error bou
nds for the infinitesimal jackknife in terms of a small number of simple\,
verifiable assumptions. Without further modification\, though\, we note t
hat the IJ deteriorates in accuracy in high dimensions and incurs a runnin
g time roughly cubic in dimension. We additionally show\, then\, how dimen
sionality reduction can be used to successfully run the IJ in high dimensi
ons when data is sparse or low rank. Simulated and real-data experiments s
upport our theory.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wieslawa Niziol (CNRS\, Sorbone Université)
DTSTART;VALUE=DATE-TIME:20201120T200000Z
DTEND;VALUE=DATE-TIME:20201120T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/6
DESCRIPTION:Title: Hodge Theory of p-adic varieties\nby Wieslawa Niziol (CNRS
\, Sorbone Université) as part of CRM-ISM Colloque des sciences mathémat
iques 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 d
iscuss some of its applications to problems in Number Theory.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART;VALUE=DATE-TIME:20201127T200000Z
DTEND;VALUE=DATE-TIME:20201127T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/7
DESCRIPTION:Title: Moduli of unstable objects in algebraic geometry\nby France
s Kirwan (University of Oxford) as part of CRM-ISM Colloque des sciences m
athématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nModuli spac
es arise naturally in classification problems in geometry. The study of th
e moduli spaces of nonsingular complex projective curves (or equivalently
of compact Riemann surfaces) goes back to Riemann himself in the nineteent
h century. The construction of the moduli spaces of stable curves of fixed
genus is one of the classical applications of Mumford's geometric invaria
nt theory (GIT)\, developed in the 1960s\; many other moduli spaces of 'st
able' objects can be constructed using GIT and in other ways. A projective
curve is stable if it has only very mild singularities (nodes) and its au
tomorphism group is finite\; similarly in other contexts stable objects ar
e usually better behaved than unstable ones. \n\nThe aim of this talk is t
o explain how recent methods from a version of GIT for non-reductive 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 generall
y our aim is to use suitable 'stability conditions' to stratify other modu
li stacks into locally closed strata with coarse moduli spaces. The talk i
s based on joint work with Gergely Berczi\, Vicky Hoskins and Joshua Jacks
on.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Haslhofer (Université de Toronto)
DTSTART;VALUE=DATE-TIME:20210122T200000Z
DTEND;VALUE=DATE-TIME:20210122T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/9
DESCRIPTION:Title: Mean curvature flow through neck-singularities\nby Robert H
aslhofer (Université de Toronto) as part of CRM-ISM Colloque des sciences
mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nA family
of surfaces moves by mean curvature flow if the velocity at each point is
given by the mean curvature vector. Mean curvature flow first arose as a m
odel of evolving interfaces and has been extensively studied over the last
40 years.\n\nIn this talk\, I will give an introduction and overview for
a general mathematical audience. To gain some intuition we will first cons
ider the one-dimensional case of evolving curves. We will then discuss Hui
sken’s classical result that the flow of convex surfaces always converge
s to a round point. On the other hand\, if the initial surface is not conv
ex we will see that the flow typically encounters singularities. Getting a
hold of these singularities is crucial for most striking applications in
geometry\, topology and physics. Specifically\, singularities can be eithe
r of neck-type or conical-type. We will discuss examples from the 90s\, wh
ich show\, both experimentally and theoretically\, that flow through conic
al singularities is utterly non-unique.\n\nIn the last part of the talk\,
I will report on recent work with Kyeongsu Choi\, Or Hershkovits and Brian
White\, where we proved that mean curvature flow through neck-singulariti
es is unique. The key for this is a classification result for ancient asym
ptotically cylindrical flows that describes all possible blowup limits nea
r a neck-singularity. In particular\, this confirms the mean-convex neighb
orhood conjecture. Assuming Ilmanen’s multiplicity-one conjecture\, we c
onclude that for embedded two-spheres mean curvature flow through singular
ities is well-posed.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20210205T200000Z
DTEND;VALUE=DATE-TIME:20210205T210000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/10
DESCRIPTION:Title: Symmetry\, barcodes\, and Hamiltonian dynamics\nby Egor Sh
elukhin (Université de Montréal) as part of CRM-ISM Colloque des science
s mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn the e
arly 60s Arnol'd has conjectured that Hamiltonian diffeomorphisms\, the mo
tions of classical mechanics\, often possess more fixed points than requir
ed by classical topological considerations. In the late 80s and early 90s
Floer has developed a powerful theory to approach this conjecture\, consi
dering fixed points as critical points of a certain functional. Recently\
, in joint work with L. Polterovich\, we observed that Floer theory filte
red by the values of this functional fits into the framework of persistenc
e modules and their barcodes\, originating in data sciences. I will revie
w these developments and their applications\, which arise from a natural t
ime-symmetry of Hamiltonians. This includes new constraints on one-parame
ter subgroups of Hamiltonian diffeomorphisms\, as well as my recent soluti
on of the Hofer-Zehnder periodic points conjecture. The latter combines b
arcodes with equivariant cohomological operations in Floer theory recently
introduced by Seidel to form a new method with further consequences.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Wakefield (University of Washington)
DTSTART;VALUE=DATE-TIME:20210129T203000Z
DTEND;VALUE=DATE-TIME:20210129T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/11
DESCRIPTION:Title: Small Area Estimation in Low- and Middle-Income Countries\
nby Jon Wakefield (University of Washington) as part of CRM-ISM Colloque d
es sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract
\nThe under-five mortality rate (U5MR) is a key barometer of the health of
a nation. Unfortunately\, many people living in low- and middle-income co
untries are not covered by civil registration systems. This makes estimati
on of the U5MR\, particularly at the subnational level\, difficult. In thi
s talk\, I will describe models that have been developed to produce the of
ficial United Nations (UN) subnational U5MR estimates in 22 countries. Est
imation is based on household surveys\, which use stratified\, two-stage c
luster sampling. I will describe a range of area- and unit-level models an
d describe the rationale for the modeling we carry out. Data sparsity in t
ime and space is a key challenge\, and smoothing models are vital. I will
discuss the advantages and disadvantages of discrete and continuous spatia
l models\, in the context of estimation at the scale at which health inter
ventions are made. Other issues that will be touched upon include: design-
based versus model-based inference\; adjustments for HIV epidemics\; the i
nclusion of so-called indirect (summary birth history) data\; reproducibil
ity through software availability\; benchmarking\; how to deal with incomp
lete geographical data\; and working with the UN to produce estimates.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikael Kuusela (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20210212T203000Z
DTEND;VALUE=DATE-TIME:20210212T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/12
DESCRIPTION:Title: Spatio-temporal methods for estimating subsurface ocean therma
l response to tropical cyclones\nby Mikael Kuusela (Carnegie Mellon Un
iversity) as part of CRM-ISM Colloque des sciences mathématiques du Québ
ec\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 subsurfac
e ocean thermal response to TC passage is crucial for accurate TC intensit
y forecasts and for understanding the role TCs play in the global climate
system\, yet that characterization is complicated by the high-noise ocean
environment\, correlations inherent in spatio-temporal data\, relative sca
rcity of in situ observations and the entanglement of the TC-induced signa
l with seasonal signals. We present a general methodological framework th
at addresses these difficulties\, integrating existing techniques in seaso
nal mean field estimation\, Gaussian process modeling\, and nonparametric
regression into a functional ANOVA model. Importantly\, we improve upon p
ast work by properly handling seasonality\, providing rigorous uncertainty
quantification\, and treating time as a continuous variable\, rather than
producing estimates that are binned in time. This functional ANOVA model
is estimated using in situ subsurface temperature profiles from the Argo
fleet of autonomous floats through a multi-step procedure\, which (1) char
acterizes the upper ocean seasonal shift during the TC season\; (2) models
the variability in the temperature observations\; (3) fits a thin plate s
pline using the variability estimates to account for heteroskedasticity an
d correlation between the observations. This spline fit reveals the ocean
thermal response to TC passage. Through this framework\, we obtain new s
cientific insights into the interaction between TCs and the ocean on a glo
bal scale\, including a three-dimensional characterization of the near-sur
face and subsurface cooling along the TC storm track and the mixing-induce
d subsurface warming on the track's right side. Joint work with Addison H
u\, Ann Lee\, Donata Giglio and Kimberly Wood.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Breidt (Colorado State University)
DTSTART;VALUE=DATE-TIME:20210312T203000Z
DTEND;VALUE=DATE-TIME:20210312T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/13
DESCRIPTION:Title: Nonparametric Tests for Informative Selection in Complex Surve
ys\nby Jay Breidt (Colorado State University) as part of CRM-ISM Collo
que des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbs
tract\nInformative selection\, in which the distribution of response varia
bles given that they are sampled is different from their distribution in t
he population\, is pervasive in complex surveys. Failing to take such inf
ormativeness into account can produce severe inferential errors\, includin
g biased and inconsistent estimation of population parameters. While seve
ral parametric procedures exist to test for informative selection\, these
methods are limited in scope and their parametric assumptions are difficul
t to assess. We consider two classes of nonparametric tests of informativ
e selection. The first class is motivated by classic nonparametric two-s
ample tests. We compare weighted and unweighted empirical distribution fu
nctions and obtain tests for informative selection that are analogous to K
olmogorov-Smirnov and Cramer-von Mises. For the second class of tests\, w
e adapt a kernel-based learning method that compares distributions based o
n their maximum mean discrepancy. The asymptotic distributions of the tes
t statistics are established under the null hypothesis of noninformative s
election. Simulation results show that our tests have power competitive w
ith existing parametric tests in a correctly specified parametric setting\
, and better than those tests under model misspecification. A recreation
al angling application illustrates the methodology. \nThis is joint work
with Teng Liu\, Colorado State University.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Guth (MIT)
DTSTART;VALUE=DATE-TIME:20210219T203000Z
DTEND;VALUE=DATE-TIME:20210219T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/14
DESCRIPTION:Title: Local smoothing for the wave equation\nby Larry Guth (MIT)
as part of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLec
ture held in Zoom.\n\nAbstract\nThe local smoothing problem asks about how
much solutions to the wave equation can focus. It was formulated by Chr
is Sogge in the early 90s. Hong Wang\, Ruixiang Zhang\, and I recently p
roved the conjecture in two dimensions. In the talk\, we will build up so
me intuition about waves to motivate the conjecture\, and then discuss som
e of the obstacles and some ideas from the proof.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Dubois (Le CNAM - Paris\, Member of IRL-CRM CNRS)
DTSTART;VALUE=DATE-TIME:20210319T190000Z
DTEND;VALUE=DATE-TIME:20210319T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/16
DESCRIPTION:Title: ABCD asymptotic expansion for lattice Boltzmann schemes and ap
plication to compressible Navier Stokes equations\nby François Dubois
(Le CNAM - Paris\, Member of IRL-CRM CNRS) as part of CRM-ISM Colloque de
s sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\
nWe first recall some elements of history of the construction of lattice B
oltzmann schemes. Then we present our "ABCD" approach\, founded on the pr
operty that the numerical scheme is exact for the advection equation with
the velocities of the lattice. This asymptotic analysis allows to write a
t several orders the conservative partial differential equations equivalen
t to the numerical scheme. A fit of parameters permits in favorable cases
a precise approximation of compressible fluids equations.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Cornell University)
DTSTART;VALUE=DATE-TIME:20210409T190000Z
DTEND;VALUE=DATE-TIME:20210409T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/17
DESCRIPTION:Title: Insect Flight from Newton’s law to Neurons\nby Jane Wang
(Cornell University) as part of CRM-ISM Colloque des sciences mathématiq
ues du Québec\n\nLecture held in Zoom.\n\nAbstract\nWhy do animals move t
he way they do? Bacteria\, insects\, birds\, and fish share with us the ne
cessity to move so as to live. Although each organism follows its own evo
lutionary course\, it also obeys a set of common laws. At the very least\
, the movement of animals\, like that of planets\, is governed by Newton
’s law: All things fall. On Earth\, most things fall in air or water\,
and their motions are thus subject to the laws of hydrodynamics. Through
trial and error\, animals have found ways to interact with fluid so they c
an float\, drift\, swim\, sail\, glide\, soar\, and fly. This elementary
struggle to escape the fate of falling shapes the development of motors\,
sensors\, and mind. Perhaps we can deduce parts of their neural computati
ons by understanding what animals must do so as not to fall. We have been
seeking mechanistic explanations of the complex movement of insect flight
. Starting from the Navier-Stokes equations governing the unsteady aerody
namics of flapping flight\, we worked to build a theoretical framework for
computing flight and for studying the control of flight. I will discuss
our recent computational and experimental studies of the balancing act of
dragonflies and fruit flies: how a dragonfly recovers from falling upside-
down and how a fly balances in air. In each case\, the physics of flight
informs us about the neural feedback circuitries underlying their fast ref
lexes.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kilian Raschel (CNRS - Université de Tours)
DTSTART;VALUE=DATE-TIME:20210416T190000Z
DTEND;VALUE=DATE-TIME:20210416T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/18
DESCRIPTION:Title: Reflected Brownian motion in a wedge: from probability theory
to Galois theory of difference equations\nby Kilian Raschel (CNRS -
Université de Tours) as part of CRM-ISM Colloque des sciences mathématiq
ues du Québec\n\nLecture held in Zoom.\n\nAbstract\nWe consider a reflect
ed Brownian motion in a two-dimensional wedge. Under standard assumptions
on the parameters of the model (opening of the wedge\, angles of the ref
lections on the axes\, drift)\, we study the algebraic and differential n
ature of the Laplace transform of its stationary distribution. We derive
necessary and sufficient conditions for this Laplace transform to be rati
onal\, algebraic\, differentially finite or more generally differentially
algebraic. These conditions are explicit linear dependencies among the
angles involved in the definition of the model.\n\nTo prove these results\
, we start from a functional equation that the Laplace transform satisfie
s\, to which we apply tools from diverse horizons. To establish different
ial algebraicity\, a key ingredient is Tutte's invariant approach\, which
originates in enumerative combinatorics. To establish differential trans
cendence\, we turn the functional equation into a difference equation and
apply Galoisian results on the nature of the solutions to such equations
.\n\nThis is a joint work with M. Bousquet-Mélou\, A. Elvey Price\, S. F
ranceschi and C. Hardouin (https://arxiv.org/abs/2101.01562).\n
LOCATION:https://researchseminars.org/talk/generalmathematics/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Lewis (Cornell University)
DTSTART;VALUE=DATE-TIME:20210423T190000Z
DTEND;VALUE=DATE-TIME:20210423T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/19
DESCRIPTION:Title: Generalized gradients\, conservative fields\, tame potentials\
, and deep learning\nby Adrian Lewis (Cornell University) as part of C
RM-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in
Zoom.\n\nAbstract\nTo the dismay and irritation of the variational analysi
s community\, practitioners of deep learning often implement gradient-base
d optimization via automatic differentiation and blithely apply the result
to nonsmooth objectives. Worse\, they then gleefully point out numerical
convergence. In fact\, as elegantly remarked by Bolte and Pauwels\, auto
matic differentiation produces a novel generalized gradient: a conservati
ve field with enough calculus to prove convergence of stochastic subgradie
nt descent\, as practiced in deep learning. I will sketch this interplay
of analytic and algorithmic ideas\, and explain how\, for concrete objecti
ves (typically semi-algebraic)\, this novel generalized gradient just slig
htly modifies Clarke's original notion.\n \nJoint work with Tonghua Tian\n
LOCATION:https://researchseminars.org/talk/generalmathematics/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Bayer-Fluckiger (École Polytechnique Fédérale de Lausanne)
DTSTART;VALUE=DATE-TIME:20210430T190000Z
DTEND;VALUE=DATE-TIME:20210430T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/20
DESCRIPTION:Title: Knots\, polynomials and signatures\nby Eva Bayer-Fluckiger
(École Polytechnique Fédérale de Lausanne) as part of CRM-ISM Colloque
des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstra
ct\nAfter a historical introduction to knot theory\, the talk will be cent
ered around two knot invariants\, the Alexander polynomial and the signatu
re. The aim is to introduce a finite abelian group that controls their re
lationship\, and to illustrate this by several examples. Using Seifert ma
trices\, the geometric questions are translated into arithmetic ones.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART;VALUE=DATE-TIME:20211119T203000Z
DTEND;VALUE=DATE-TIME:20211119T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/21
DESCRIPTION:Title: (André Aisenstatd Prize) Exploring string vacua through geome
tric transitions\nby Tristan Collins (MIT) as part of CRM-ISM Colloque
des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstra
ct\nLauréat 2021 du prix de mathématiques André-Aisenstadt\n\nA fundame
ntal problem in string theory is the multitude of distinct geometries whic
h give rise to consistent solutions of the vacuum equations of motion. \n\
nOne possible resolution of this "vacuum degeneracy" problem is the "fanta
sy" that the moduli space of string vacua is connected through the process
of "geometric transitions". \n\nI will discuss some geometric problems as
sociated to this fantasy and their applications.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART;VALUE=DATE-TIME:20211015T193000Z
DTEND;VALUE=DATE-TIME:20211015T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/22
DESCRIPTION:Title: (André Aisenstatd Prize) Entropy along the Mandelbrot set
\nby Giulio Tiozzo (University of Toronto) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n
The notion of topological entropy\, arising from information theory\, is a
fundamental tool to understand the complexity of a dynamical system. Whe
n the dynamical system varies in a family\, the natural question arises of
how the entropy changes with the parameter. In the last decade\, W. T
hurston introduced these ideas in the context of complex dynamics by defin
ing the "core entropy" of a quadratic polynomials as the entropy of a cert
ain forward-invariant set of the Julia set (the Hubbard tree). As we sha
ll see\, the core entropy is a purely topological/combinatorial quantity w
hich nonetheless captures the richness of the fractal structure of the Man
delbrot set. In particular\, we will relate the variation of such a funct
ion to the geometry of the Mandelbrot set. We will also prove that the co
re entropy on the space of polynomials of a given degree varies continuous
ly\, answering a question of Thurston. Finally\, we will provide a new i
nterpretation of core entropy in terms of measured laminations\, and discu
ss its finer regularity properties such as its Holder exponent.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Hill (NYU Steinhardt)
DTSTART;VALUE=DATE-TIME:20210924T190000Z
DTEND;VALUE=DATE-TIME:20210924T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/23
DESCRIPTION:Title: Deep down\, everyone wants to be causal\nby Jennifer Hill
(NYU Steinhardt) as part of CRM-ISM Colloque des sciences mathématiques d
u Québec\n\nLecture held in Zoom.\n\nAbstract\nMost researchers in the so
cial\, behavioral\, and health sciences are taught to be extremely cautiou
s in making causal claims. However\, causal inference is a necessary goal
in research for addressing many of the most pressing questions around pol
icy and practice. In the past decade\, causal methodologists have increas
ingly been using and touting the benefits of more complicated machine lear
ning algorithms to estimate causal effects. These methods can take some o
f the guesswork out of analyses\, decrease the opportunity for “p-hackin
g\,” and may be better suited for more fine-tuned tasks such as identify
ing varying treatment effects and generalizing results from one population
to another. However\, should these more advanced methods change our fund
amental 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 be more
transparent in our inferences and honest about their limitations.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bo'az Klartag (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20211001T150000Z
DTEND;VALUE=DATE-TIME:20211001T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/24
DESCRIPTION:Title: (Nirenberg Lecture) Convexity and High-Dimensional Phenomena\nby Bo'az Klartag (Weizmann Institute of Science) as part of CRM-ISM Co
lloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\n
Abstract\nHigh-dimensional problems with a geometric flavor appear in a nu
mber of branches of mathematics and mathematical physics. A priori\, it s
eems that the immense diversity observed in high dimensions would make it
impossible to formulate general\, interesting theorems that apply to large
classes of high-dimensional geometric objects. In this talk we will disc
uss situations in which high dimensionality\, when viewed correctly\, indu
ces remarkable order and simplicity rather than complication. For example
\, Dvoretzky's theorem demonstrates that any high-dimensional convex body
possesses nearly-Euclidean sections of large dimension. Another example i
s the central limit theorem for convex bodies\, according to which any hig
h-dimensional convex body has approximately-Gaussian marginals. There are
strong motifs in high-dimensional geometry\, such as the concentration of
measure\, which appear to compensate for the large number of different co
nfigurations. Convexity allows us to harness these motifs in order to for
mulate elegant and non-trivial theorems.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuansi Chen (Duke University)
DTSTART;VALUE=DATE-TIME:20211008T150000Z
DTEND;VALUE=DATE-TIME:20211008T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/25
DESCRIPTION:Title: (Nirenberg Lecture) Recent progress on the Kannan-Lovasz-Simon
ovits (KLS) conjecture and Bourgain's slicing problem II\nby Yuansi Ch
en (Duke University) as part of CRM-ISM Colloque des sciences mathématiqu
es du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn recent work\, Chen
(2020) improved Eldan's stochastic localization proof technique\, which wa
s deployed in Lee and Vempala (2017)\, to prove an almost constant Cheeger
isoperimetric coefficient in the KLS conjecture with dimension dependency
d^o(1). Consequently\, his proof also provides a substantial advance tow
ard the resolution of Bourgain's slicing conjecture and the thin-shell con
jecture. After getting conformable with Eldan's stochastic localization t
echnique\, in this talk we navigate through how to refine the technique to
provide the current best bound. We will complete the self-contained proo
f of Chen (2020) and highlight the new ideas involved. Finally\, we will
discuss some extensions and provide an outlook for future research directi
ons.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Bonner (U of Western Ontario)
DTSTART;VALUE=DATE-TIME:20211126T203000Z
DTEND;VALUE=DATE-TIME:20211126T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/26
DESCRIPTION:Title: Adventures with Partial Identifications in Studies of Marked I
ndividuals\nby Simon Bonner (U of Western Ontario) as part of CRM-ISM
Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n
\nAbstract\nMonitoring marked individuals is a common strategy in studies
of wild animals (referred to as mark-recapture or capture-recapture experi
ments) and hard to track human populations (referred to as multi-list meth
ods or multiple-systems estimation). A standard assumption of these techn
iques is that individuals can be identified uniquely and without error\,
but this can be violated in many ways. In some cases\, it may not be poss
ible to identify individuals uniquely because of the study design or the c
hoice of marks. Other times\, errors may occur so that individuals are in
correctly identified. I will discuss work with my collaborators over the
past 10 years developing methods to account for problems that arise when a
re only individuals are only partially identified. I will present theoret
ical aspects of this research\, including an introduction to the latent mu
ltinomial model and algebraic statistics\, and also describe applications
to studies of species ranging from the golden mantella (an endangered frog
endemic to Madagascar measuring only 20 mm) to the whale shark (the large
st known species of sh measuring up to 19 m).\n
LOCATION:https://researchseminars.org/talk/generalmathematics/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiffany Timbers (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20211029T193000Z
DTEND;VALUE=DATE-TIME:20211029T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/27
DESCRIPTION:Title: Opinionated practices for teaching reproducibility: motivation
\, guided instruction and practice\nby Tiffany Timbers (University of
British Columbia) as part of CRM-ISM Colloque des sciences mathématiques
du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn the data science cours
es at the University of British Columbia\, we define data science as the s
tudy\, development and practice of reproducible and auditable processes to
obtain insight from data. While reproducibility is core to our definition
\, most data science learners enter the field with other aspects of data s
cience in mind\, for example predictive modelling\, which is often one of
the most interesting topic to novices. This fact\, along with the highly t
echnical nature of the industry standard reproducibility tools currently e
mployed in data science\, present out-ofthe gate challenges in teaching re
producibility in the data science classroom. Put simply\, students are not
as intrinsically motivated to learn this topic\, and it is not an easy on
e for them to learn. What can a data science educator do? Over several ite
rations of teaching courses focused on reproducible data science tools and
workflows\, we have found that providing extra motivation\, guided instru
ction and lots of practice are key to effectively teaching this challengin
g\, yet important subject. Here we present examples of how we deeply motiv
ate\, effectively guide and provide ample practice opportunities to data s
cience students to effectively engage them in learning about this topic.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louise Poirier (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20211105T193000Z
DTEND;VALUE=DATE-TIME:20211105T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/28
DESCRIPTION:Title: Les mathématiques ont une histoire et une géographie\nby
Louise Poirier (Université de Montréal) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n
La présentation se divise en deux temps. Dans un premier temps\, les pri
ncipaux résultats de notre étude sur le « portrait mathématique » des
étudiants du Québec effectué dans le cadre du projet En avant math! (p
rojet conjoint CRM-CIRANO soutenu par le Ministère des finances) seront p
résentés. Ce rapport se fonde d’une part sur les résultats des tests
internationaux TIMS et PISA pour les élèves québécois du primaire et
du secondaire et d’autre part\, sur la situation des mathématiques dans
les universités québécoises dégagée des données du Bureau de coopé
ration interuniversitaire (BCI) ( évolution des inscriptions étudiantes
et portrait des étudiants tant en genre qu’en statut). Les données du
BCI montrent que l'étudiant typique inscrit en maths dans les université
s québécoises est citoyen canadien\, blanc et masculin. Et le nombre tot
al d'inscrits baisse à chaque année (sauf\, peut-être au doctorat). Où
sont les filles? Où sont les étudiants issus de l'immigration récente?
Et pourtant aux tests PISA et TIMMS les élèves issus de l'immigration p
erforment mieux au Canada que les élèves canadiens (c'est l'inverse pour
la moyenne des pays de l'OCDE).\n\nPuis\, dans un deuxième temps\, à la
lumière des résultats du portrait des étudiants\, nous discuterons des
enjeux sociaux pour des mathématiques plus inclusives. Une recherche col
laborative avec les communautés inuit du Nunavik viendra illustrer nos pr
opos. \n\nNote : Denis Gued m’excusera l’emprunt de ce titre. Ces prop
os se retrouvent dans son entrevue « Rendons les mathématiques aimables
» accordée à L’express. https://www.lexpress.fr/informations/rendons
-les-mathematiques-aimables_640643.html\n
LOCATION:https://researchseminars.org/talk/generalmathematics/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabor Lugosi (UPF and BSE)
DTSTART;VALUE=DATE-TIME:20211112T203000Z
DTEND;VALUE=DATE-TIME:20211112T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/29
DESCRIPTION:Title: Estimating the mean of a random vector\nby Gabor Lugosi (U
PF and BSE) as part of CRM-ISM Colloque des sciences mathématiques du Qu
ébec\n\nLecture held in Zoom.\n\nAbstract\nOne of the most basic problems
in statistics is the estimation of the mean of a random vector\, based on
independent observations. This problem has received renewed attention in
the last few years\, both from statistical and computational points of vi
ew. In this talk\, we review some recent results on the statistical perfo
rmance of mean estimators that allow heavy tails and adversarial contamina
tion in the data. In particular\, we are interested in estimators that ha
ve a near-optimal error in all directions in which the variance of the one
dimensional marginal of the random vector is not too small. The material
of this talk is based on a series of joint papers with Shahar Mendelson.\
n
LOCATION:https://researchseminars.org/talk/generalmathematics/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Tosatti (McGill University)
DTSTART;VALUE=DATE-TIME:20211203T203000Z
DTEND;VALUE=DATE-TIME:20211203T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/30
DESCRIPTION:Title: K3 surfaces: geometry and dynamics\nby Valentino Tosatti (
McGill University) as part of CRM-ISM Colloque des sciences mathématiques
du Québec\n\nLecture held in Zoom.\n\nAbstract\nK3 surfaces are a class
of compact complex manifolds that enjoys many special properties and play
an important role in several areas of mathematics. In this colloquium I wi
ll discuss a new interplay between complex geometry and analysis on K3 sur
faces equipped with their Calabi-Yau metrics\, and dynamics of holomorphic
diffeomorphisms of these surfaces\, that Simion Filip and I have been inv
estigating recently.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke University)
DTSTART;VALUE=DATE-TIME:20211210T190000Z
DTEND;VALUE=DATE-TIME:20211210T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/31
DESCRIPTION:Title: Stark's Conjectures and Hilbert's 12th Problem\nby Samit D
asgupta (Duke University) as part of CRM-ISM Colloque des sciences mathém
atiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn this talk we w
ill discuss two central problems in algebraic number theory and their inte
rconnections: explicit class field theory and the special values of L-func
tions. The goal of explicit class field theory is to describe the abelian
extensions of a ground number field via analytic means intrinsic to the g
round field\; this question lies at the core of Hilbert's 12th Problem. M
eanwhile\, there is an abundance of conjectures on the values of L-functio
ns at certain special points. Of these\, Stark's Conjecture has relevance
toward explicit class field theory. I will describe two recent joint res
ults with Mahesh Kakde on these topics. The first is a proof of the Brume
r-Stark conjecture away from p=2. This conjecture states the existence of
certain canonical elements in abelian extensions of totally real fields.
The second is a proof of an exact formula for Brumer-Stark units that has
been developed over the last 15 years. We show that these units together
with other easily written explicit elements generate the maximal abelian e
xtension 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://researchseminars.org/talk/generalmathematics/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-Tsung Huang (Institute of Statistical Science\, Academia Sinic
a)
DTSTART;VALUE=DATE-TIME:20211217T150000Z
DTEND;VALUE=DATE-TIME:20211217T160000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/32
DESCRIPTION:Title: Nonparametric causal mediation in a time-to-event setting\
nby Yen-Tsung Huang (Institute of Statistical Science\, Academia Sinica) a
s part of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLectu
re held in Zoom.\n\nAbstract\nA causal mediation model with multiple time-
to-event mediators is exemplified by the natural course of human disease m
arked by sequential milestones with a time-to-event nature. For example\,
from hepatitis B infection to death\, patients may experience intermediat
e events such as liver cirrhosis and liver cancer. The sequential events
of hepatitis\, cirrhosis\, cancer\, and death are susceptible to right cen
soring\; moreover\, the latter events may preclude the former events. Cas
ting the natural course of human diseases in the framework of causal media
tion modeling\, we establish a model with intermediate and terminal events
as the mediators and outcomes\, respectively. We define the intervention
al analog of path-specific effects (iPSEs) as the effect of an exposure on
a terminal event mediated (or not mediated) by any combination of interme
diate events without parametric models. The expression of a counting proc
ess-based counterfactual hazard is derived under the sequential ignorabili
ty assumption. We employ composite nonparametric likelihood estimation to
obtain maximum likelihood estimators for the counterfactual hazard and iP
SEs. Our proposed estimators achieve asymptotic unbiasedness\, uniform co
nsistency\, and weak convergence. Applying the proposed method\, we show
that hepatitis B induced mortality is mostly mediated through liver cancer
and/or cirrhosis whereas hepatitis C induced mortality may be through ext
rahepatic diseases.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Stupfler (ENSAI)
DTSTART;VALUE=DATE-TIME:20220128T203000Z
DTEND;VALUE=DATE-TIME:20220128T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/33
DESCRIPTION:Title: Risk assessment\, heavy tails\, and asymmetric least squares t
echniques\nby Gilles Stupfler (ENSAI) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nS
tatistical risk assessment\, in particular in finance and insurance\, requ
ires estimating simple indicators to summarize the risk incurred in a give
n situation. Of most interest is to infer extreme levels of risk so as to
be able to manage high-impact rare events such as extreme climate episode
s or stock market crashes. A standard procedure in this context\, whether
in the academic\, industrial or regulatory circles\, is to estimate a wel
l-chosen single quantile (or Value-at-Risk). One drawback of quantiles 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 coherent risk
measure\, which is a serious concern in actuarial and financial applicati
ons. In this talk\, after giving a leisurely tour of extreme quantile est
imation\, I will explain how\, starting from the formulation of a quantile
as the solution of an optimization problem\, one may come up with two alt
ernative families of risk measures\, called expectiles and extremiles\, in
order to address these two drawbacks. I will give a broad overview of th
eir properties\, as well as of their estimation at extreme levels in heavy
-tailed models\, and explain why they constitute sensible alternatives for
risk assessment using real data applications. This is based on joint wor
k with Abdelaati Daouia\, Irène Gijbels\, Stéphane Girard\, Simone Padoa
n and Antoine Usseglio-Carleve.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (Polytechnic University of Catalonia)
DTSTART;VALUE=DATE-TIME:20220114T160000Z
DTEND;VALUE=DATE-TIME:20220114T170000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/34
DESCRIPTION:Title: Looking at hydrodynamics through a contact mirror: From Euler
to Turing and beyond\nby Eva Miranda (Polytechnic University of Catalo
nia) as part of CRM-ISM Colloque des sciences mathématiques du Québec\n\
nLecture held in Zoom.\n\nAbstract\nWhat physical systems can be non-compu
tational? (Roger Penrose\, 1989). Is hydrodynamics capable of calculation
s? (Cris Moore\, 1991). Can a mechanical system (including the trajectory
of a fluid) simulate a universal Turing machine? (Terence Tao\, 2017).\n\n
The movement of an incompressible fluid without viscosity is governed by E
uler equations. Its viscid analogue is given by the Navier-Stokes equation
s whose regularity is one of the open problems in the list of problems for
the Millenium by\nthe Clay Foundation. The trajectories of a fluid are co
mplex. Can we measure its levels of complexity (computational\, logical an
d dynamical)?\n\nIn this talk\, we will address these questions. In partic
ular\, we will show how to construct a 3-dimensional Euler flow which is T
uring complete. Undecidability of fluid paths is then a consequence of the
classical undecidability of the halting\n\nproblem proved by Alan Turing
back in 1936. This is another manifestation of complexity in hydrodynamics
which is very different from the theory of chaos.\n\nOur solution of Eule
r equations corresponds to a stationary solution or Beltrami field. To add
ress this problem\, we will use a mirror [5] reflecting Beltrami fields as
Reeb vector fields of a contact\n\nstructure. Thus\, our solutions import
techniques from geometry to solve a problem in fluid dynamics. But how ge
neral are Euler flows? Can we represent any dynamics as an Euler flow? We
will address this universality problem using the Beltrami/Reeb mirror agai
n and Gromov's h-principle. We will also consider the non-stationary case.
These universality features illustrate the complexity of Euler flows. How
ever\, this construction is not "physical" in the sense that the associate
d metric is not the euclidean metric. We will announce an euclidean const
ruction and its implications to complexity and undecidability.\n\n These c
onstructions [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 a
nd flexibility of Reeb\nembeddings. https://arxiv.org/abs/1911.01963.\n[2]
R. Cardona\, E. Miranda\, D. Peralta-Salas\, F. Presas. Constructing Turi
ng complete Euler flows in\ndimension 3. Proc. Natl. Acad. Sci. 118 (2021)
e2026818118.\n[3] R. Cardona\, E. Miranda\, D. Peralta-Salas. Turing univ
ersality of the incompressible Euler equations\nand a conjecture of Moore.
Int. Math. Res. Notices\, \, 2021\;\, rnab233\,\nhttps://doi.org/10.1093/
imrn/rnab233\n[4] R. Cardona\, E. Miranda\, D. Peralta-Salas. Computabilit
y and Beltrami fields in Euclidean space.\nhttps://arxiv.org/abs/2111.0355
9 \n[5] J. Etnyre\, R. Ghrist. Contact topology and hydrodynamics I. Beltr
ami fields and the Seifert conjecture.\nNonlinearity 13 (2000) 441–458.\
n[6] C. Moore. Generalized shifts: unpredictability and undecidability 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 equation on com
pact manifolds. Discrete\nCont. Dyn. Sys. A 38 (2018) 1553–1565.\n[9] T.
Tao. Searching for singularities in the Navier-Stokes equations. Nature R
ev. Phys. 1 (2019) 418–419.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Hynd (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20220211T203000Z
DTEND;VALUE=DATE-TIME:20220211T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/35
DESCRIPTION:Title: Sticky particle dynamics\nby Ryan Hynd (University of Penn
sylvania) as part of CRM-ISM Colloque des sciences mathématiques du Québ
ec\n\nLecture held in Zoom.\n\nAbstract\nI will discuss the time evolution
of a collection of particles that interact primarily through perfectly in
elastic collisions. I will explain why this problem is tractable if the pa
rticles are constrained to lie on a line versus if they are allowed to mo
ve freely in space. In particular\, I'll also describe an equation at th
e heart of this difficulty which some researchers believe has been solve
d and others do not. This topic has motivations in astronomy and connec
tions with optimal mass transportation which I will touch upon if time per
mits.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell University)
DTSTART;VALUE=DATE-TIME:20220121T190000Z
DTEND;VALUE=DATE-TIME:20220121T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/37
DESCRIPTION:Title: The commuting variety and generic pipe dreams\nby Allen Kn
utson (Cornell University) as part of CRM-ISM Colloque des sciences mathé
matiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nNobody knows whe
ther the scheme "pairs of commuting nxn matrices" is reduced. I'll show ho
w this scheme relates to matrix Schubert varieties\, and give a formula fo
r its equivariant cohomology class (and that of many other varieties) usin
g "generic pipe dreams" that I'll introduce. These interpolate between ord
inary and bumpless pipe dreams. With those\, I'll rederive both formulae (
ordinary and bumpless) for double Schubert polynomials. This work is joint
with Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Zerbes (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20220204T170000Z
DTEND;VALUE=DATE-TIME:20220204T180000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/38
DESCRIPTION:Title: Euler systems and the Birch—Swinnerton-Dyer conjecture\n
by Sarah Zerbes (ETH Zurich) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nL-functions ar
e one of the central objects of study in number theory. There are many bea
utiful theorems and many more open conjectures linking their values to ari
thmetic problems. The most famous example is the conjecture of Birch and S
winnerton-Dyer\, which is one of the Clay Millenium Prize Problems. I will
discuss this conjecture and some related open problems\, and I will descr
ibe some recent progress on these conjectures\, using tools called `Euler
systems’.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Forrest Crawford (Yale University)
DTSTART;VALUE=DATE-TIME:20220429T193000Z
DTEND;VALUE=DATE-TIME:20220429T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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 gained pr
ominence in the early days of the pandemic. These models provided research
ers and policymakers with qualitative insight into the dynamics of transmi
ssion and quantitative predictions of disease incidence. More sophistica
ted models incorporated new information about the natural history of COVID
-19 disease and the interaction of infected individuals with the healthcar
e system\, to predict diagnosed cases\, hospitalization\, ventilator usage
\, and death. Models also provided intuition for discussions about outbrea
ks\, vaccination\, and the effects of non-pharmaceutical interventions lik
e social distancing guidelines and stay-at-home orders. But as the pandemi
c progressed\, complex real-world interventions took effect\, people every
where changed their behavior\, and the usefulness of simple mathematical m
odels of COVID-19 transmission diminished. This challenge forced researc
hers to think more broadly about empirical data sources that could help pr
edictive models regain their utility for guiding public policy. In this pr
esentation\, I will describe my view of the successes and failures of popu
lation-level transmission models in the context of the COVID-19 pandemic.
I will outline the evolution of a project to predict COVID-19 incidence
in the state of Connecticut\, from development of a transmission model to
engagement with public health policymakers and initiation of a new data c
ollection effort. I argue that a new data source – passive measurement o
f close interpersonal contact via mobile device location data – is a pro
mising way to overcome many of the shortcomings of traditional transmissio
n models. I conclude with a summary of the impact this work has had on t
he COVID-19 response in Connecticut and beyond.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stanislav Volgushev (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220218T203000Z
DTEND;VALUE=DATE-TIME:20220218T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/40
DESCRIPTION:Title: Structure learning for Extremal graphical models\nby Stani
slav Volgushev (University of Toronto) as part of CRM-ISM Colloque des sci
ences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nExtr
emal graphical models are sparse statistical models for multivariate extre
me events. The underlying graph encodes conditional independencies and en
ables a visual interpretation of the complex extremal dependence structure
. For the important case of tree models\, we provide a data-driven method
ology for learning the graphical structure. We show that sample versions
of the extremal correlation and a new summary statistic\, which we call th
e extremal variogram\, can be used as weights for a minimum spanning tree
to consistently recover the true underlying tree. Remarkably\, this impli
es that extremal tree models can be learned in a completely non-parametric
fashion by using simple summary statistics and without the need to assume
discrete distributions\, existence of densities\, or parametric models fo
r marginal or bivariate distributions. Extensions to more general graphs
are also discussed.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Gorksy (UC Davis)
DTSTART;VALUE=DATE-TIME:20220311T203000Z
DTEND;VALUE=DATE-TIME:20220311T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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 mathéma
tiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nKhovanov and Rozan
sky defined in 2005 a triply graded link homology theory which generalizes
HOMFLY-PT polynomial. In this talk\, I will outline some known results an
d structures in Khovanov-Rozansky homology\, describe its connection to q\
,t-Catalan combinatorics and present several geometric models for some cla
sses of links.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Macbeth (Fordham university)
DTSTART;VALUE=DATE-TIME:20220325T193000Z
DTEND;VALUE=DATE-TIME:20220325T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/42
DESCRIPTION:Title: Making mathematics computer-checkable\nby Heather Macbeth
(Fordham university) as part of CRM-ISM Colloque des sciences mathématiqu
es du Québec\n\nLecture held in Zoom.\n\nAbstract\nIn the last thirty yea
rs\, computer proof verification became a mature technology\, with success
es including the checking of the Four-Colour Theorem\, the Odd Order Theor
em\, and Hales' proof of the Kepler Conjecture. Recent advances such as t
he "Liquid Tensor Experiment" verifying a recent theorem of Scholze have p
rovided further momentum\, as likewise have promising experiments integrat
ing this technology with machine learning.\n\nI will briefly describe some
of these developments. I will then try to describe\, more generally\, wh
at it *feels* like to carry out research-level computer verifications of m
athematics proofs: the level of expression one has access to\, the ways on
e finds oneself interrogating and reorganizing a paper proof\, the kinds o
f arguments which are more tedious (or less tedious!) than on paper.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll (University of Cologne)
DTSTART;VALUE=DATE-TIME:20220401T180000Z
DTEND;VALUE=DATE-TIME:20220401T190000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/43
DESCRIPTION:Title: Gentle algebras\, surfaces and a glimpse of homological mirror
symmetry\nby Sibylle Schroll (University of Cologne) as part of CRM-I
SM Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom
.\n\nAbstract\nDerived categories are in general not easy to parse. Howeve
r\, in certain cases\, combinatorial models give a good picture of these c
ategories. One such case are the bounded derived categories of gentle alge
bras which can be represented in terms of curves and crossings of curves o
n surfaces. In this talk\, we will give the construction of these surface
models and briefly explain how they are connected to the homological mirro
r symmetry programme. We will show how a combination of surface combinator
ics and representation theory can give new insights into the associated ca
tegories.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Cardaliaguet (Université Paris-Dauphine)
DTSTART;VALUE=DATE-TIME:20220415T190000Z
DTEND;VALUE=DATE-TIME:20220415T200000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/44
DESCRIPTION:Title: Some aspects of Mean Field Games\nby Pierre Cardaliaguet (
Université Paris-Dauphine) as part of CRM-ISM Colloque des sciences math
ématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nMean Field Gam
e is the study of the dynamical behavior of a large number of agents in in
teraction. 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 an
alysis of these models\, first introduced in the economic literature under
the terminology of “heterogenous agent models\, has known a spectacular
development with the pioneering woks of Lasry and Lions and of Caines\, H
uang and Malhamé. The aim of the talk will be to illustrate the theory th
rough a few models and present some of the main results and open questions
.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220422T193000Z
DTEND;VALUE=DATE-TIME:20220422T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/45
DESCRIPTION:Title: Cactus groups and monodromy\nby Joel Kamnitzer (University
of Toronto) as part of CRM-ISM Colloque des sciences mathématiques du Qu
ébec\n\nLecture held in Zoom.\n\nAbstract\nThe cactus group is a cousin o
f 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 o
n many collections of combinatorial objects. I will explain how we use t
he cactus group to understand monodromy of eigenvectors for Gaudin algebra
s.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Derrida ((École Normale Supérieure\, Paris\, France))
DTSTART;VALUE=DATE-TIME:20220318T193000Z
DTEND;VALUE=DATE-TIME:20220318T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/46
DESCRIPTION:Title: The importance of large deviations in non-equilibrium systems<
/a>\nby Bernard Derrida ((École Normale Supérieure\, Paris\, France)) as
part of CRM-ISM Colloque des sciences mathématiques du Québec\n\nLectur
e held in Zoom.\n\nAbstract\n2022 Aisenstadt Chair recipient\n\nStatistica
l Physics allowed to unify\, at the end of the 19th century\, Newton's mec
hanics and thermodynamics. It gave a way to predict the amplitude of fluct
uations around the physical laws which were known at that time. Einstein\,
in his very first works\, showed that the measurement of these fluctuatio
ns allowed to estimate the size of atoms. His reasoning\, which was at the
origin of the linear response theory\, applied to the black body gave one
of the first evidences of the duality wave-particle in Quantum Mechanics.
Statistical Physics gives also a framework to predict large deviations fo
r systems at equilibrium. In the last two decades\, major efforts were dev
oted to extend our understanding of the statistical laws of fluctuations a
nd large deviations to non-equilibrium systems. This talk will try to pres
ent some of the recent progresses.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (Ecole Normale Supérieure)
DTSTART;VALUE=DATE-TIME:20220520T193000Z
DTEND;VALUE=DATE-TIME:20220520T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/47
DESCRIPTION:Title: Mathematical analysis of dilute gases : derivation of the Bolt
zmann equation\, fluctuations and large deviations\nby Isabelle Gallag
her (Ecole Normale Supérieure) as part of CRM-ISM Colloque des sciences m
athématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n2022 Aisens
tadt Chair recipient\n\nThe evolution of a gas can be described by differe
nt models depending on the observation scale. A natural question\, raised
by Hilbert in his sixth problem\, is whether these models provide consiste
nt predictions. In particular\, for rarefied gases\, it is expected that c
ontinuum laws of kinetic theory can be obtained directly from molecular dy
namics governed by the fundamental principles of mechanics. In the case of
hard sphere gases\, Lanford showed in 1975 that the Boltzmann equation
emerges as the law of large numbers in the low density limit\, at least fo
r very short times. The goal of this talk is to explain the heuristics of
his proof and present recent progress in the understanding of this limitin
g process.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Raussendorf (UBC)
DTSTART;VALUE=DATE-TIME:20220408T193000Z
DTEND;VALUE=DATE-TIME:20220408T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/48
DESCRIPTION:Title: Hidden Variable Model for Universal Quantum Computation with M
agic States on Qubits\nby Robert Raussendorf (UBC) as part of CRM-ISM
Colloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n
\nAbstract\n2021 CAP-CRM Prize Recipient\n\nWe show that every quantum c
omputation can be described by a probabilistic update of a probability dis
tribution on a finite phase space. Negativity in a quasiprobability functi
on is not required in states or operations\, which is a very unusual featu
re. Nonetheless\, our result is consistent with Gleason’s Theorem and th
e Pusey-Barrett- Rudolph theorem. \n\nThe reason I have chosen this subje
ct for my talk is two-fold: (i) It gives the audience a glimpse of the que
st to understand the quantum mechanical cause for speed-up in quantum comp
utation\, 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 struct
ures underlying the above probabilistic model are the so-called Lambda-pol
ytopes\, which are highly symmetric objects. At present we only know ver
y few general facts about them. Help with analysing them would be apprecia
ted!\n\nJoint work with Michael Zurel and Cihan Okay\,\n\nJournal referenc
e: Phys. Rev. Lett. 125\, 260404 (2020)\n
LOCATION:https://researchseminars.org/talk/generalmathematics/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Solecki (Cornell University)
DTSTART;VALUE=DATE-TIME:20220506T193000Z
DTEND;VALUE=DATE-TIME:20220506T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/49
DESCRIPTION:Title: Generic measure preserving transformations and Descriptive Set
Theory\nby Slawomir Solecki (Cornell University) as part of CRM-ISM C
olloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/generalmathematics/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:test
DTSTART;VALUE=DATE-TIME:20220715T193000Z
DTEND;VALUE=DATE-TIME:20220715T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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://researchseminars.org/talk/generalmathematics/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (Université Laval)
DTSTART;VALUE=DATE-TIME:20220902T193000Z
DTEND;VALUE=DATE-TIME:20220902T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/51
DESCRIPTION:Title: Algèbres amassées et théorie des noeuds\nby Véronique
Bazier-Matte (Université Laval) as part of CRM-ISM Colloque des sciences
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 polynômes de
Laurent dont les générateurs s’obtiennent par un processus récursif
appelé mutation. On commence avec une graine\, paire formée d’un ensem
ble de n variables\, appelé amas\, et d’un graphe orienté à n points.
La mutation d’une graine remplace une variable à la fois et modifie le
graphe\, donnant ainsi une nouvelle graine. L’algèbre amassée est eng
endrée par toutes les variables obtenues par mutations successives\, qu
’on appelle variables amassées. \n \nLes algèbres amassées ont ét
é définies il y a 20 ans\, et depuis\, des liens entre elles et divers c
hamps de recherche ont été découverts. Récemment\, avec mon collaborat
eur\, nous avons établi un lien entre la théorie des noeuds et les algè
bres amassées. Cet exposé introduira d'abord les algèbres amassées pui
s présentera la connection entre ces dernières et le polynôme d'Alexand
er d'un noeud.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART;VALUE=DATE-TIME:20220916T193000Z
DTEND;VALUE=DATE-TIME:20220916T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/52
DESCRIPTION:Title: Modularity of Galois representations\, from Ramanujan to Serre
's conjecture and beyond\nby Chandrashekhar Khare (UCLA) as part of CR
M-ISM Colloque des sciences mathématiques du Québec\n\nLecture held in Z
oom.\n\nAbstract\nRamanujan made a series of influential conjectures in hi
s 1916 paper ``On some arithmetical functions’' on what is now called th
e Ramanujan $\\tau$ function. A congruence Ramanujan observed for $\\tau(n
)$ modulo 691 in the paper led to Serre and Swinnerton-Dyer developing a g
eometric theory of mod $p$ modular forms. It was in the context of the the
ory of mod $p$ modular forms that Serre made his modularity conjecture\, w
hich 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 formulation
of a first version of Serre's conjecture in 1973\, to its resolution in 20
09 by Jean-Pierre Wintenberger and myself. I will also try to indicate why
this subject is very much alive and\, in spite of all the progress\, stil
l in its infancy.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (Mcgill)
DTSTART;VALUE=DATE-TIME:20220923T193000Z
DTEND;VALUE=DATE-TIME:20220923T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/53
DESCRIPTION:Title: A story about pointwise ergodic theorems\nby Anush Tseruny
an (Mcgill) as part of CRM-ISM Colloque des sciences mathématiques du Qu
ébec\n\nLecture held in Zoom.\n\nAbstract\nPointwise ergodic theorems pro
vide a bridge between the global behaviour of the dynamical system and the
local combinatorial statistics of the system at a point. Such theorem hav
e been proven in different contexts\, but typically for actions of semigro
ups on a probability space. Dating back to Birkhoff (1931)\, the first kno
wn pointwise ergodic theorem states that for a measure-preserving ergodic
transformation T on a probability space\, the mean of a function (its glob
al average) can be approximated by taking local averages of the function a
t 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 t
urn it backwards\, showing that the averages along trees of possible pasts
also approximate the global average. This backward theorem for a single
transformation surprisingly has applications to actions of free groups\, w
hich we will also discuss. This is joint work with Jenna Zomback.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pengfei Li (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20220930T193000Z
DTEND;VALUE=DATE-TIME:20220930T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/54
DESCRIPTION:Title: (Prix SSC) Full likelihood inference for abundance from captur
e-recapture data: semiparametric efficiency and EM-algorithm\nby Pengf
ei Li (University of Waterloo) as part of CRM-ISM Colloque des sciences ma
thématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\nCapture-reca
pture experiments are widely used to collect data needed to estimate the a
bundance of a closed population. To account for heterogeneity in the capt
ure probabilities\, Huggins (1989) and Alho (1990) proposed a semiparametr
ic model in which the capture probabilities are modelled parametrically an
d the distribution of individual characteristics is left unspecified. A c
onditional likelihood method was then proposed to obtain point estimates a
nd Wald-type confidence intervals for the abundance. Empirical studies sh
ow that the small-sample distribution of the maximum conditional likelihoo
d estimator is strongly skewed to the right\, which may produce Wald-type
confidence intervals with lower limits that are less than the number of ca
ptured individuals or even negative. \n\nIn this talk\, we present a fu
ll likelihood approach based on Huggins and Alho's model. We show that th
e null distribution of the empirical likelihood ratio for the abundance is
asymptotically chi-square with one degree of freedom\, and the maximum em
pirical likelihood estimator achieves semiparametric efficiency. We furth
er propose an expectation–maximization algorithm to numerically calculat
e the proposed point estimate and empirical likelihood ratio function. Si
mulation studies show that the empirical-likelihood-based method is superi
or to the conditional-likelihood-based method: its confidence interval has
much better coverage\, and the maximum empirical likelihood estimator has
a smaller mean square error.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balint Virag (University of Toronto)
DTSTART;VALUE=DATE-TIME:20221007T193000Z
DTEND;VALUE=DATE-TIME:20221007T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/55
DESCRIPTION:Title: (Prix-CRM-Fields-Pims) Random plane geometry -- a gentle intro
duction\nby Balint Virag (University of Toronto) as part of CRM-ISM Co
lloque des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\n
Abstract\nConsider Z^2\, and assign a random length of 1 or 2 to each edge
based on independent fair coin tosses. The resulting random geometry\, fi
rst passage percloation\, is conjectured to have a scaling limit.\n\nMost
random plane geometric models (including hidden geometries) should have th
e same scaling limit.\n\nI will explain the basics of the limiting geometr
y\, the "directed landscape"\, the central object in the class of models n
amed after\nKardar\, Parisi and Zhang.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yevgeny Liokumovich (University of Toronto)
DTSTART;VALUE=DATE-TIME:20221014T193000Z
DTEND;VALUE=DATE-TIME:20221014T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/56
DESCRIPTION:Title: (2022 André Aisenstadt Prize) New isoperimetric inequalities
and their applications to systolic geometry and minimal surfaces\nby Y
evgeny Liokumovich (University of Toronto) as part of CRM-ISM Colloque des
sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstract\n
I will describe two new isoperimetric inequalities for k-dimensional subma
nifolds 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 consequence o
f another\, we obtain an asymptotic formula for volumes of minimal submani
folds that was conjectured by Mikhail Gromov. The talk is based on joint w
orks with Boris Lishak\, Alexander Nabutovsky and Regina Rotman\; Fernando
Marques and Andre Neves\; Larry Guth.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derek Bingham (Simon Fraser University)
DTSTART;VALUE=DATE-TIME:20221028T193000Z
DTEND;VALUE=DATE-TIME:20221028T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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://researchseminars.org/talk/generalmathematics/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bernstein (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20221104T193000Z
DTEND;VALUE=DATE-TIME:20221104T203000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
UID:generalmathematics/58
DESCRIPTION:Title: Complexity of Submanifolds and Colding-Minicozzi Entropy\n
by Jacob Bernstein (Johns Hopkins University) as part of CRM-ISM Colloque
des sciences mathématiques du Québec\n\nLecture held in Zoom.\n\nAbstrac
t\nGiven a submanifold of Euclidean space\, Colding and Minicozzi defined
its entropy to be the supremum of the Gaussian weighted surface areas of a
ll of its translations and dilations. While initially introduced to study
singularities of mean curvature flow\, it has proven to be an interesting
geometric measure of complexity. In this talk I will survey some of the re
cent progress made on studying the Colding-Minicozzi entropy of hypersurfa
ces. In particular\, I will discuss a series of work by Lu Wang and myself
showing closed hypersurfaces with small entropy are simple in various sen
ses.\n
LOCATION:https://researchseminars.org/talk/generalmathematics/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Steorts (Duke University)
DTSTART;VALUE=DATE-TIME:20221125T203000Z
DTEND;VALUE=DATE-TIME:20221125T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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://researchseminars.org/talk/generalmathematics/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Besser (Ben Gurion University)
DTSTART;VALUE=DATE-TIME:20221202T203000Z
DTEND;VALUE=DATE-TIME:20221202T213000Z
DTSTAMP;VALUE=DATE-TIME:20220927T050147Z
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.\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/generalmathematics/60/
END:VEVENT
END:VCALENDAR