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BEGIN:VEVENT
SUMMARY:Alexandre Baraviera (UFRGS)
DTSTART:20200812T170000Z
DTEND:20200812T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/1
DESCRIPTION:Title: Medidas estacionárias em grafos infinitos\nby Alexand
re Baraviera (UFRGS) as part of Webinários do PPGMat - UFRGS\n\n\nAbstrac
t\nGrafos são objetos interessantes que aparecem naturalmente na modelage
m de diversos problemas\, como por exemplo a difusão de uma doença ou a
eficiência da comunicação em uma certa rede de transmissão de dados\,
dentre muitos outros. A caracterização destes fenômenos em geral envolv
e conhecer o espectro associado ao grafo\, e por isso técnicas de obtenç
ão desse tipo de informação se fazem importantes. Nessa direção\,
o método da redução isospectral desenvolvido por Bunimovich e Webb se
mostra uma ferramenta eficiente\, que permite trocar um grafo por subgrafo
s menores onde em principio a obtenção de autovalores pode ser uma taref
a mais simples.\n\nNessa palestra pretendo contar de maneira relativamente
elementar uma parte da história acima (tentando ilustrar os conceitos en
volvidos) e falar sobre um trabalho escrito em colaboração com Joana Tor
res (Universidade do Minho) e Pedro Duarte (Universidade de Lisboa) no qua
l uma extensão dos métodos de Bunimovich-Webb para grafos infinitos é u
sada para obter estados estacionários de certos processos estocásticos n
uma classe de grafos. Minha intenção é focalizar a exposição em exemp
los de forma a deixá-la acessível a um público amplo.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Oliveira (UFF)
DTSTART:20200819T170000Z
DTEND:20200819T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/2
DESCRIPTION:Title: Sounding a Riemannian manifold with hard spheres\nby G
onçalo Oliveira (UFF) as part of Webinários do PPGMat - UFRGS\n\n\nAbstr
act\nGiven a Riemannian manifold M one may attempt at exploring its geomet
ry by sounding it with hard spheres. Regarding these spheres as the atomic
constituents of a gas filling M\, one can compute an equation of state re
lating its several macroscopic quantities such as pressure\, volume\, and
temperature. \n\nThis talk is an exercise in statistical mechanics where I
shall explain how the resulting equation depends on the underlying Rieman
nian geometry.\n\nLink will appear shortly before the seminar.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alveri Alves Sant'Ana (UFRGS)
DTSTART:20200826T170000Z
DTEND:20200826T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/3
DESCRIPTION:Title: Extensões de Ore e álgebras de Hopf\nby Alveri Alves
Sant'Ana (UFRGS) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\n
Extensões de Ore são anéis de polinômios nos quais os coeficientes nã
o comutam necessariamente com a variável. Muitas álgebras bem conhecidas
da literatura podem ser obtidas via extensões de Ore (ou por um quocient
e delas). Em particular\, M. Beattie\, S. Dascalescu e L. Grunenfelder con
struíram uma família infinita de álgebras de Hopf não isomorfas\, de u
ma certa dimensão fixa\, via extensões de Ore de anéis de grupo\, dando
uma resposta negativa à décima conjectura de Kaplansky. Posteriormente\
, Panov deu uma caracterização das assim chamadas extensões Hopf-Ore (e
xtensões de Ore de álgebras de Hopf que contém a álgebra base como uma
subálgebra de Hopf)\, bem como classificou estas extensões das álgebra
s de grupo. \n\nNesta palestra pretendemos abordar o enredo acima\, com ê
nfase nos resultados de Panov e finalizaremos com uma generalização do T
eorema de Panov para o contexto das álgebras de Hopf fracas\, obtida num
trabalho em conjunto com C. Lomp (U. Porto) e R. Santos (FURG). Tentaremos
evitar ao máximo as tecnicalidades para atingirmos uma audiência mais a
mpla.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juliana Fernandes (UFRJ)
DTSTART:20200902T170000Z
DTEND:20200902T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/4
DESCRIPTION:Title: Blow-up and grow-up for parabolic PDEs\nby Juliana Fer
nandes (UFRJ) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nWe d
iscuss recent results on finite and infinite time blow-up solutions of par
abolic PDEs. We are mainly interested in the limiting dynamics as it appro
aches the maximal time of existence.\n\nLink will appear shortly before th
e talk.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrícia Gonçalves (Instituto Superior Técnico)
DTSTART:20200909T130000Z
DTEND:20200909T140000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/5
DESCRIPTION:Title: Symmetric exclusion with reservoirs\nby Patrícia Gon
çalves (Instituto Superior Técnico) as part of Webinários do PPGMat - U
FRGS\n\n\nAbstract\nIn this seminar I will describe the derivation of some
partial differential equations that rule the space-time evolution of the
density of some stochastic processes. The goal is to describe the connecti
on between the macroscopic (continuous) equations and the microscopic (dis
crete) system of random particles. \n\nThe former can be either PDEs or st
ochastic PDEs depending on whether one is looking at the law of large numb
ers or the central limit theorem scaling\; while the latter is a collectio
n of particles that move randomly according to a transition probability. \
n\nI will focus on a model for which we can obtain a collection of (fracti
onal) reaction-diffusion equations given in terms of the regional fraction
al Laplacian with different types of boundary conditions. \n\nThis is a jo
int work with Cédric Bernardin\, Byon Jiménez-Oviedo and Stefano Scotta.
\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wagner de Oliveira Cortes (UFRGS)
DTSTART:20200916T170000Z
DTEND:20200916T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/6
DESCRIPTION:Title: Loops\, quasigrupos e temas relacionados\nby Wagner de
Oliveira Cortes (UFRGS) as part of Webinários do PPGMat - UFRGS\n\n\nAbs
tract\nNesta palestra\, iremos falar de uma maneira introdutória sobre lo
ops e quasigrupos que seriam uma versão não-associativa de grupo\, onde
exibiremos exemplos. Esta teoria é muito rica e amplamente explorada. Ire
mos explanar também sobre grupoides e semigrupos inversos. Como quasigrup
os são “versões” não associativas de grupos\, o que seriam versões
não associativas de grupoides e semigrupos inversos? Nesta direção\, i
remos introduzir uma versão não-associativa de grupoide e uma versão n
ão associativa de semigrupos inversos e exibir exemplos. Parte da teoria
a ser apresentada nesta palestra foi obtida juntamente com a Professora Ma
ria de Lourdes Giuliani.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo Muniz Alves (UFPR)
DTSTART:20200930T170000Z
DTEND:20200930T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/7
DESCRIPTION:Title: Teoria clássica de invariantes e códigos auto-duais\
nby Marcelo Muniz Alves (UFPR) as part of Webinários do PPGMat - UFRGS\n\
n\nAbstract\nDada uma ação de um grupo $G$ em um conjunto $X$\, um invar
iante para ação é um elemento que permanece inalterado pela aplicação
de qualquer elemento de $G$. Invariantes fazem parte\, entre outros\, da
Geometria Analítica\, onde temos a classificação das cônicas por meio
do discriminante\, que é um invariante sob os movimentos do plano\; na Á
lgebra Linear\, em que o polinômio minimal\, o polinômio característico
\, o determinante e o traço são invariantes da ação por conjugação d
o grupo linear geral $GL(n\,K)$ no espaço das matrizes\; na Teoria de Gal
ois\, cujo principal resultado é a correspondência entre subcorpos de $K
$ e subgrupos do grupo de Galois por meio de subcorpos invariantes\; e mes
mo do estudo de EDP's clássicas\, onde funções no círculo são identif
icadas com funções periódicas da reta\, que são o mesmo que invariante
s para ação de um grupo de translações da reta. Nós apresentaremos de
talhes sobre o caso em que G é um subgrupo finito do grupo linear geral $
GL(n\,K)$ agindo em um anel de polinômios $K[x_1\,x_2\, ...\, x_n]$\, sen
do que esta ação é induzida da ação canônica de $GL(n\,K)$ em $K^n$.
Neste caso\, o conjunto de invariantes sob G forma um subanel do anel de
polinômios e o problema de descrever este subanel foi um forte tema de pe
squisa entre o final do século XIX e as primeiras décadas do século XX.
Nós veremos resultados fundamentais de Noether e Molien desta época sob
re o anel de invariantes. A teoria de invariantes "resssurgiu" novamente n
os anos 1970 em Geometria Algébrica\, mas também na teoria de códigos c
orretores de erros. Estes códigos surgiram na década de 1950 com o objet
ivo de implementar uma correção automática de erros de leitura em compu
tadores\, e tornaram-se a espinha dorsal de boa parte dos processos de com
unicação e armazenamento de informação digital que temos hoje. Os prob
lemas práticos da teoria de códigos levam naturalmente a problemas de á
lgebra\, geometria finita e combinatória\; um desses "spin-offs" é o est
udo dos códigos auto-duais e é aqui que aparecem aplicações da teoria
clássica de invariantes. Ao final falamos de um trabalho sobre códigos a
uto-duais feito por Welington Santos em sua tese defendida recentemente no
PPGM-UFPR.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeovanny de Jesus Muentes Acevedo (Universidad Tecnológica de Bol
ívar)
DTSTART:20201007T170000Z
DTEND:20201007T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/8
DESCRIPTION:Title: Aplicações contínuas com dimensão métrica média posi
tiva\nby Jeovanny de Jesus Muentes Acevedo (Universidad Tecnológica d
e Bolívar) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nM. Gro
mov introduziu a dimensão média para uma aplicação contínua no final
dos anos 1990\, o qual é um invariante sob conjugação topológica. Por
outro lado\, a noção de dimensao métrica média para um sistema dinâmi
co foi introduzida por Lindenstrauss e Weiss em 2000\, a qual refina a ent
ropia topológica para sistemas dinâmicos com entropia topológica infini
ta. Nesta palestra\, mostraremos alguns resultados relacionados à existê
ncia de aplicações contínuas com dimensao métrica média positiva.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams (Williams College)
DTSTART:20201014T170000Z
DTEND:20201014T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/9
DESCRIPTION:Title: Volumes of Hyperbolic 3-Manifolds\nby Colin Adams (Wil
liams College) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nGiv
en a link in a 3-manifold that can be appropriately decomposed into tangle
s\, we define certain types of hyperbolicity for the tangles and an associ
ated volume. Using results of Agol-Storm-Thurston\, we show that links obt
ained from the tangles are themselves hyperbolic. Further\, we obtain surp
risingly accurate lower bounds on the volumes of the links from the sum of
the volumes of the constituent tangles in various 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Levon Nurbekyan (UCLA)
DTSTART:20201028T170000Z
DTEND:20201028T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/10
DESCRIPTION:Title: Spectral methods for nonlocal mean-field games\nby Le
von Nurbekyan (UCLA) as part of Webinários do PPGMat - UFRGS\n\n\nAbstrac
t\nMean-field games (MFG) theory is a framework to model and study huge po
pulations of agents that play non-cooperative differential games. I will d
iscuss some of the recent developments in applying spectral methods for a
numerical and possibly theoretical resolution of MFG systems with nonlocal
interactions among agents. I will also draw connections with kernel metho
ds in machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paulo Varandas (UFBA & FCT-CMUP)
DTSTART:20201104T170000Z
DTEND:20201104T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/11
DESCRIPTION:Title: Phase transitions and appearance of ghost measures\nb
y Paulo Varandas (UFBA & FCT-CMUP) as part of Webinários do PPGMat - UFRG
S\n\n\nAbstract\nThe thermodynamic formalism for transitive uniformly hype
rbolic dynamics is nowadays well understood and\, among other aspects\, it
is worth mentioning that regular potentials (meaning Holder continuous) a
re so that the pressure function is differentiable and admit unique equili
brium states. The situation changes drastically in simple examples beyond
uniform hyperbolicity\, as the case of the Manneville-Pomeau maps\, where
different kinds of phase transitions appear due to the phenomenon of inter
mittency of an indifferent fixed point. In this talk I will focus on this
family and discuss a new aspect of the phase transitions\, namely the appe
arance of finitely additive absolutely continuous invariant measures. This
is part of a joint work with A. Castro (UFBA) and L. Cioletti (UnB).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Yapu
DTSTART:20201111T170000Z
DTEND:20201111T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/12
DESCRIPTION:Title: First integrals and hamiltonization of nonholonomic syste
ms: the example of a homogeneous ball on a convex surface of revolution\nby Luis Yapu as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nUs
ing the geometric approach to nonholonomic mechanical systems\, we will ex
plain the utility of having special first integrals coming from symmetries
(or horizontal gauge momenta) in order to obtain a hamiltonian formulati
on of the reduced dynamics (hamiltonization). The main result gives suffic
ient conditions on the horizontal gauge momenta in order to obtain a twist
ed-Poisson (or sometimes Poisson) structure in the reduced space using the
method of gauge transformations by a 2-form\, which has explicit expressi
ons. The leaves of the reduced (twisted-)Poisson structure are given by th
e joint level sets of casimirs coming from the first integrals. We will fo
cus on the example of a homogenous ball rolling on a convex surface of rev
olution to illustrate the theory. This is a joint work with Paula Balseiro
.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sérgio Romaña (UFRJ)
DTSTART:20201118T170000Z
DTEND:20201118T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/13
DESCRIPTION:Title: Como a dinâmica hiperbólica do fluxo geodésico pode co
ntrolar a geometria\nby Sérgio Romaña (UFRJ) as part of Webinários
do PPGMat - UFRGS\n\n\nAbstract\nNeste seminário vamos tratar de relaçõ
es entre geometria e dinâmica. Muitos de nós já ouvimos falar que varie
dades de curvatura negativa implica hiperbolicidade para a dinâmica do se
u fluxo geodésico\, isto é\, a geometria controla\, de certa forma\, a d
inâmica. No entanto\, o que podemos dizer da recíproca? Quando a dinâmi
ca controla a geometria? Neste contexto\, vamos apresentar uma resposta ra
zoável a esta pergunta mostrado que\, em geral\, se o fluxo geodésico
é hiperbólico temos um controle sobre a curvatura da variedade e\, de ce
rta forma\, sobre a geometria. Apresentaremos também de algumas consequê
ncias deste resultado.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART:20201125T170000Z
DTEND:20201125T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/14
DESCRIPTION:Title: Quantitative stability for minimizing Yamabe metrics\
nby Robin Neumayer (Northwestern University) as part of Webinários do PPG
Mat - UFRGS\n\n\nAbstract\nThe Yamabe problem asks whether\, given a close
d Riemannian manifold\, one can find a conformal metric of constant scalar
curvature (CSC). An affirmative answer was given by Schoen in 1984\, foll
owing contributions from Yamabe\, Trudinger\, and Aubin\, by establishing
the existence of a function that minimizes the so-called Yamabe energy fun
ctional\; the minimizing function corresponds to the conformal factor of t
he CSC metric. \n\nWe address the quantitative stability of minimizing Yam
abe metrics. On any closed Riemannian manifold we show—in a quantitative
sense—that if a function nearly minimizes the Yamabe energy\, then the
corresponding conformal metric is close to a CSC metric. Generically\, thi
s closeness is controlled quadratically by the Yamabe energy deficit. Howe
ver\, we construct an example demonstrating that this quadratic estimate i
s false in the general. This is joint work with Max Engelstein and Luca Sp
olaor and will be accessible to a general graduate student audience.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dirceu Bagio (UFSM)
DTSTART:20201202T170000Z
DTEND:20201202T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/15
DESCRIPTION:Title: Representações de álgebras associativas\nby Dirceu
Bagio (UFSM) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nA id
eia de representar um objeto matemático complexo por algo mais simples é
muito antiga e tem sido muito utilizada em matemática. Por exemplo\, pod
emos representar um número complexo $z=a+bi$ pelo par ordenado $(a\,b)\\i
n \\mathbb{R}^2$ ou um operador linear $T$ definido sobre um espaço vetor
ial de dimensão finita $n$ por uma matriz $[T]$ de ordem $n\\times n$. \n
\nNesta palestra\, abordaremos sobre representações de álgebras associa
tivas. Veremos alguns dos principais problemas envolvidos\, bem como ferra
mentas que são usadas para resolvê-los. Por fim\, as representações si
mples e de dimensão finita de algumas álgebras associativas (dadas por g
eradores e relações) serão discutidas.\n\nTodos os conceitos necessári
os para entender o que será abordado serão introduzidos. Os únicos pré
-requisitos exigidos são o conhecimento dos resultados clássicos de álg
ebra linear e das definições das estruturas algébricas mais comuns (gru
pos\, anéis e módulos).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Vargas Pallete (Yale University)
DTSTART:20201209T170000Z
DTEND:20201209T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/16
DESCRIPTION:Title: Perfis isoperimétricos para variedades quasi-Fuchsianas<
/a>\nby Franco Vargas Pallete (Yale University) as part of Webinários do
PPGMat - UFRGS\n\n\nAbstract\nUm perfil isoperimétrico para uma variedade
Riemanniana é uma função que associa a cada número V > 0 o menor per
ímetro necessário para conter uma região de volume V. Nesta palestra ve
remos como para variedades quasi-Fuchsianas em dimensão 3 este problema s
e relaciona com o Volume Renormalizado. Usaremos algumas ferramentas da Re
latividade Geral (Hawking mass) para obter resultados de comparação com
variedades Fuchsianas. Trabalho em conjunto com Celso Viana (UFMG).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Giulietti (Università di Pisa)
DTSTART:20210303T170000Z
DTEND:20210303T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/17
DESCRIPTION:Title: Parabolic Dynamics via Renormalization theory\nby Pao
lo Giulietti (Università di Pisa) as part of Webinários do PPGMat - UFRG
S\n\n\nAbstract\nWe will present an overview of parabolic dynamics via ren
ormalization theory using transfer operators. I will present some results
(and some work in progress) which highlight the relations between the dist
ributions appearing in the study of ergodic averages of parabolic flows an
d the ones appearing in the study of the statistical properties of hyperbo
lic dynamical systems.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Tinaglia (King's College\, London)
DTSTART:20210324T130000Z
DTEND:20210324T140000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/18
DESCRIPTION:Title: Minimal surfaces and Plateau problem\nby Giuseppe Tin
aglia (King's College\, London) as part of Webinários do PPGMat - UFRGS\n
\n\nAbstract\nIn calculus of variations\, Plateau problem is the problem o
f finding the surface that minimises area among all surfaces spanning a gi
ven curve. This was posed Lagrange in 1760 and solved independently by Dou
glas and Radó in 1930. In 1936 Douglas was awarded the Fields Medal for h
is efforts. After an introduction to the field of minimal surfaces\, I wil
l talk about the Plateau problem and its proof.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Indrei (Purdue University)
DTSTART:20210331T170000Z
DTEND:20210331T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/19
DESCRIPTION:Title: The equilibrium shape of a planar crystal in a convex coe
rcive background is convex\nby Emanuel Indrei (Purdue University) as p
art of Webinários do PPGMat - UFRGS\n\n\nAbstract\nI'll discuss my recent
solution to a long-standing open problem posed by Almgren: https://arxiv.
org/abs/2008.02238.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramon Nunes (Federal University of Ceará)
DTSTART:20210526T170000Z
DTEND:20210526T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/20
DESCRIPTION:Title: Formas automorfas\, funções $L$ e o problema de subconv
exidade\nby Ramon Nunes (Federal University of Ceará) as part of Webi
nários do PPGMat - UFRGS\n\n\nAbstract\nNesta palestra faremos uma introd
ução ao conceito de formas automorfas e suas funções $L$. Estes últim
os objetos são funções meromorofas do plano complexo que satisfazem pro
priedades similares àquelas da celebrada função zeta de Riemann. Em par
ticular\, temos aqui uma conjectura análoga à hipótese de Riemann. O pr
oblema de subconvexidade consiste em provar estimativas não-triviais para
a função $L$ que visam suprir nossa ignorância com respeito à hipóte
se de Riemann. Por fim\, mostraremos uma aplicação do problema da subcon
vexidade e descreveremos uma estratégia comumente utilizada para estudá-
lo.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaqueline Mesquita (University of Brasilia)
DTSTART:20210602T170000Z
DTEND:20210602T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/21
DESCRIPTION:Title: Correspondência entre EDOs generalizadas e outros tipos
de equações: resultados e aplicações\nby Jaqueline Mesquita (Unive
rsity of Brasilia) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\
nNesta palestra\, iremos apresentar as EDOs generalizadas e mostraremos co
mo podemos relacionar estas equações com outros tipos de equações. Vam
os apresentar alguns resultados que podemos obter por meio destas correspo
ndências bem como algumas aplicações.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Bissacot (University of São Paulo)
DTSTART:20210609T170000Z
DTEND:20210609T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/22
DESCRIPTION:Title: A natural compactification for a countable Markov shift a
nd its thermodynamic formalism\nby Rodrigo Bissacot (University of Sã
o Paulo) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nIn 1999 R
uy Exel and Marcelo Laca solved an important problem in operator algebras
and constructed the Cuntz-Krieger algebra with infinitely many symbols. Gi
ven a transitive and infinite matrix $A$\, as a corollary of their argumen
ts appears for the first time what we call a generalized countable Markov
shift $X_A = \\Sigma_A \\cup Y_A$\, where $Y_A$ is a special set of finite
admissible words. For the most studied countable Markov shifts $\\Sigma_A
$\, as the full shift and renewal shift\, $X_A$ is a compactification of $
\\Sigma_A$. Differently from other proposals\, this compactification depen
ds only on the matrix $A$ and not on any extra structure.\n\nWe developed
the thermodynamic formalism on the space $X_A$\, studying conformal and ei
genmeasures on $X_A$ and its connections with standard measures on $\\Sigm
a_A$. New phenomena appear\, a length-type phase transition\, when the eig
enmeasure lives on $\\Sigma_A$ at high temperature and lives on $Y_A$ at l
ow temperature. Using a pressure-point definition proposed by M. Denker an
d M. Yuri in the context of iterated function systems\, we able to prove t
hat the Gurevich pressure is the natural definition for the pressure funct
ion also in the generalized setting. The Gurevich entropy plays a role of
a critical temperature to the existence of new conformal measures (KMS sta
tes) living on $Y_A$. We exhibit examples with infinitely (even uncountabl
e) many new extremal conformal measures\, which are undetectable in the us
ual formalism. Based on "Thermodynamic Formalism for Generalized Markov Sh
ifts on Infinitely Many States" available at arXiv:1808.00765\n\nJoint wor
k with Ruy Exel (UFSC\, Brazil)\, Rodrigo Frausino (University of Wollongo
ng\, Australia) and Thiago Raszeja (AGH University of Science and Technolo
gy\, Poland).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Sepe (Fluminense Federal University)
DTSTART:20210616T170000Z
DTEND:20210616T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/23
DESCRIPTION:Title: Monotone vs Fano: an equivariant perspective\nby Dani
ele Sepe (Fluminense Federal University) as part of Webinários do PPGMat
- UFRGS\n\n\nAbstract\nIntuitively speaking\, symplectic geometry studies
spaces on which the most fundamental quantity that can be measured is (ori
ented) area. While all complex submanifolds of projective space are symple
ctic\, the converse is false\, as first observed by Thurston. Nevertheless
a natural metaquestion in symplectic geometry is to understand the "diffe
rence" between symplectic manifolds and smooth complex projective varietie
s. In this talk we concentrate on the relation between monotone symplectic
manifolds and smooth Fano varieties: intuitively speaking\, both families
can be thought of as satisfying certain positivity conditions. Again\, th
ere are compact monotone symplectic manifolds that are not Fano (as shown
by Reznikov\, Fine and Panov). After introducing all the above notions for
mally\, the aim of this talk is to show that monotone symplectic manifolds
are necessarily equivalent to smooth Fano varieties in the presence of "a
lmost maximal" toral symmetries. This is ongoing joint work with Isabelle
Charton and Silvia Sabatini.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Moreira (UFC)
DTSTART:20210901T170000Z
DTEND:20210901T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/24
DESCRIPTION:Title: Supersolutions to Fully Nonlinear PDEs and Convexity\
nby Diego Moreira (UFC) as part of Webinários do PPGMat - UFRGS\n\n\nAbst
ract\nIn this talk\, we present some sharp regularity results related to s
upersolutions to fully nonlinear equations that enjoy some kind of convexi
ty property. If time allows\, ideas of the proof and some open problems w
ill be addressed. This is joint work with Alessio Figalli (ETH-Zurich) and
J. Ederson Braga (UFC).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Lessa (UdelaR)
DTSTART:20210908T170000Z
DTEND:20210908T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/25
DESCRIPTION:Title: Geodesic random walks and fold maps\nby Pablo Lessa (
UdelaR) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nWe will di
scuss recent work with Lucas Oliveira on geodesic random walks. Our resul
ts yield a geometric proof of old results of Tsujishita on the regularity
of eigenfunctions of the spherical mean operator on a compact manifold wit
h non-positive curvature.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rayssa Caju (UFPB & University of Chicago)
DTSTART:20210915T170000Z
DTEND:20210915T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/26
DESCRIPTION:Title: On the singular Q-curvature problem (lecture in Portugues
e)\nby Rayssa Caju (UFPB & University of Chicago) as part of Webinári
os do PPGMat - UFRGS\n\n\nAbstract\nThe study of partial differential equa
tions on manifolds has been extensively explored in the last few decades.
In particular\, some problems arising in conformal geometry such as the cl
assical Yamabe problem\, can be reduced to the study of PDE’s with criti
cal exponent on manifolds. More recently\, another class of conformal equa
tions that has drawn considerable attention is the so-called Q-curvature e
quation\, which is a fourth-order elliptic PDE with critical exponent. \n\
nIn this talk\, I would like to discuss how to apply fixed point methods t
o understand the Q-curvature equation in a singular setting and discuss so
me interesting problems related to this topic. \n\nJoint work with J.H. An
drade\, J. M do Ó\, J. Ratzkin and A. Silva Santos.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tertuliano Franco (UFBA)
DTSTART:20210929T170000Z
DTEND:20210929T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/27
DESCRIPTION:Title: Large Deviations in the Supremum Norm for a Reaction-Diff
usion System\nby Tertuliano Franco (UFBA) as part of Webinários do PP
GMat - UFRGS\n\n\nAbstract\nWe present large deviations estimates for a sy
stem of independent random walks superposed with a birth-and-death dynamic
s evolving on the discrete torus whose density profiles converge in the su
premum norm. The scaling limit considered is the so-called high density li
mit where space\, time\, and initial quantity of particles are rescaled\,
and the associated rate functional obtained is a semi-linearised version o
f the rate function of Vares/Landim/Jona-Lasinio'93 (in a different topolo
gy setting). An ingredient in the proof of large deviations is to provide
the limit for a suitable class of perturbations of the original process: t
his is precisely one of the main contributions of this work\, a strategy t
o extend the original high density approach to weakly asymmetric systems.
Talk based in a joint work with Luana Amaral and Bernardo de Lima.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Thieullen (Université de Bordeaux)
DTSTART:20211013T170000Z
DTEND:20211013T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/28
DESCRIPTION:Title: Calibrated subaction for Anosov maps and flows\nby Ph
ilippe Thieullen (Université de Bordeaux) as part of Webinários do PPGMa
t - UFRGS\n\n\nAbstract\nThe Livsic theorem for Anosov maps or flows says
that a Lipschitz observable that has zero average on every periodic orbit
is necessarily cohomologuous to a Lipschitz coboundary. The sub-Livsic the
orem says that a Lipschitz observable that has non negative zero average o
n every periodic orbit is necessarily bounded from below by a coboundary.
In a paper with Artur Lopes we proved that in the invertible case (Anosov
diffeomorphism or flow) the coboundary may be chosen Holder. In a recent p
aper with Xifeng Su we prove that the coboundary may be chosen Lipschitz.
We introduce a new Lax-Oleinik operator in the invertible case that could
be used in numerical experiments.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Marinho (UFRGS)
DTSTART:20211020T170000Z
DTEND:20211020T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/29
DESCRIPTION:Title: Sharp convergence to equilibrium of interacting particle
systems\nby Rodrigo Marinho (UFRGS) as part of Webinários do PPGMat -
UFRGS\n\n\nAbstract\nIn this seminar we will discuss the mixing times of
Markov chains. We will exhibit classical examples of card shuffles and use
them to introduce some interesting particle systems. Furthermore\, we wil
l show some recent results and some open problems which may be of interest
not only for probability theory researchers but also for the ones who wor
k with analysis\, pdes or spectral graph theory.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Pedro Ramos (ETH Zürich)
DTSTART:20211027T170000Z
DTEND:20211027T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/30
DESCRIPTION:Title: Revisiting the subcritical case of Hardy’s uncertainty
principle\nby João Pedro Ramos (ETH Zürich) as part of Webinários d
o PPGMat - UFRGS\n\n\nAbstract\nHardy's uncertainty principle is a pivotal
result in Fourier Analysis\, which states that if a function and its Four
ier transform both decay at least as fast as the standard Gaussian\, then
the function is either a Gaussian or identically zero. It seems\, however\
, that the subcritical case of this result has barely been explored so far
: while in the critical and supercritical cases one has explicit character
isations\, in the subcritical one only very recent results by Vemuri and E
scauriaza\, Kenig\, Ponce and Vega shed new light onto the structure of fu
nctions in the subcritical Hardy classes. \n\nIn this talk\, we will discu
ss these recent contributions in connection to an interesting norm extrapo
lation problem: if both $f$ and $\\widehat{f}$ are in $L^2(e^{2\\pi a |x|^
2})\,$ for $a \\in (0\,1)$\, can one say that $e^{a \\pi |x|^2}f\, e^{a \\
pi |x|^2} \\widehat{f} \\in L^{\\infty}$? We will show that this almost ho
lds in general\, in the sense that $e^{b \\pi |x|^2}f\, e^{b \\pi |x|^2} \
\widehat{f} \\in L^{\\infty}$\, for any $b < a.$ Further\, we will see tha
t this holds indeed in a class of generalised Laplace transforms of temper
ed distributions. Finally\, time-allowing\, we shall see how this problem
connects to a conjecture of Vemuri on decay of solutions to the time-depen
dent harmonic oscillator problem and the sharp estimates of Escauriaza-Ken
ig-Ponce-Vega. \n\n\nJoint work with Lucas Oliveira.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milton Jara (IMPA)
DTSTART:20211103T170000Z
DTEND:20211103T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/31
DESCRIPTION:Title: Mixing time of a stratified random walk on the hypercube<
/a>\nby Milton Jara (IMPA) as part of Webinários do PPGMat - UFRGS\n\n\nA
bstract\nWe study the speed of convergence to its stationary state of a st
ratified random walk on the hypercube. The dynamics is the following. At e
ach step\, two bits of a binary string of length $n$ are chosen\, and one
adds the second bit to the first bit. Ben-Hamou and Peres showed that the
mixing time of this chain is equal to $\\frac{3}{2} n \\log n + \\mathcal{
O}(n)$. We will provide a more refined description of the convergence to t
he stationary state of this chain\, which in particular allows us to compu
te the mixing time of the chain\, up to an error of order $o(n)$ for every
initial state of the chain\, and also to find the initial state for which
the convergence is fastest. Joint work with Freddy Hernández (Bogotá).\
n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Franceschini (MSRI\, UC Berkeley)
DTSTART:20211110T170000Z
DTEND:20211110T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/32
DESCRIPTION:Title: Algebraic approach to stochastic duality for Markov proce
sses with some examples and applications\nby Chiara Franceschini (MSRI
\, UC Berkeley) as part of Webinários do PPGMat - UFRGS\n\n\nAbstract\nIn
this talk I will introduce the concept of duality for Markov processes an
d explain how duality relations can be constructed starting from the descr
iption of the infinitesimal generator of the process with generators of a
suitable Lie algebra: I will provide some classical examples as well as mo
re recent results which involves orthogonal polynomials. I conclude with s
ome possible applications in the context of interacting particle systems.\
n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrique Borrin (UNICAMP)
DTSTART:20211117T170000Z
DTEND:20211117T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/33
DESCRIPTION:Title: Lagrangian structure of relativistic Vlasov systems\n
by Henrique Borrin (UNICAMP) as part of Webinários do PPGMat - UFRGS\n\n\
nAbstract\nIn this work\, we studied the Lagrangian structure of relativis
tic Vlasov systems in quasistatic limits of Maxwell's equations\, consider
ing the contribution of self-consistent electric and magnetic fields. As a
result\, we established the equivalence between renormalized and Lagrangi
an solutions\, i.e.\, solutions transported by an appropriately defined fl
ow and its global-in-time definition if finite energy conditions are impos
ed. We also defined the notion of a generalized solution and proved its ex
istence. Furthermore\, assuming higher integrability on the initial data\,
the existence of Lagrangian solutions with each energy bounded was shown.
\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otávio Menezes (Purdue University)
DTSTART:20211124T170000Z
DTEND:20211124T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/34
DESCRIPTION:Title: Quenched CLT for a balanced random walk driven by the exc
lusion process\nby Otávio Menezes (Purdue University) as part of Webi
nários do PPGMat - UFRGS\n\n\nAbstract\nWe prove a quenched functional ce
ntral limit theorem for a one-dimensional random walk driven by a simple s
ymmetric exclusion process. This model can be viewed as a special case of
the random walk in a balanced random environment\, for which the weak quen
ched limit is constructed as a function of the invariant measure of the en
vironment viewed from the walk. We bypass the need to show the existence o
f this invariant measure. Instead\, we find the limit of the quadratic var
iation of the walk and give an explicit formula for it. Joint with Jonatho
n Peterson (Purdue University) and Yongjia Xie (Purdue University).\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sébastien Alvarez (UDELAR)
DTSTART:20211201T170000Z
DTEND:20211201T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/35
DESCRIPTION:Title: Earthquakes and graftings of hyperbolic surface laminatio
ns\nby Sébastien Alvarez (UDELAR) as part of Webinários do PPGMat -
UFRGS\n\n\nAbstract\nWe study compact hyperbolic surface laminations. Thes
e are a generalization of closed hyperbolic surfaces which appear to be mo
re suited to the study of Teichmüller theory than arbitrary non-compact s
urfaces. We show that the Teichmüller space of any non-trivial hyperbolic
surface lamination is infinite dimensional. In order to prove this result
\, we study the theory of deformations of hyperbolic surfaces\, and we der
ive what we believe to be a new formula for the derivative of the length o
f a simple closed geodesic with respect to the action of grafting. This fo
rmula complements those derived by McMullen\, in terms of the Weil-Peterss
on metric\, and by Wolpert for the case of earthquakes. This is joint work
with Graham Smith.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Eulália Vares (UFRJ)
DTSTART:20211208T170000Z
DTEND:20211208T180000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/36
DESCRIPTION:Title: Critical scaling for an anisotropic percolation system on
$\\mathbb{Z}^2$\nby Maria Eulália Vares (UFRJ) as part of Webinário
s do PPGMat - UFRGS\n\n\nAbstract\nMy basic goal in this talk is to discus
s one further example of the interplay between SPDEs and percolation metho
ds. We consider a highly anisotropic finite-range bond percolation on $\\m
athbb{Z}^2$: on horizontal lines we have edges connecting two vertices wit
hin distance $N$ and vertical edges are only between nearest neighbor vert
ices. On this graph we consider the following independent percolation mod
el: horizontal edges are open with probability $1/(2N)$\, while vertical e
dges are open with probability $\\epsilon$ to be suitably tuned as $N$ gro
ws to infinity. The main result tells that if $\\epsilon = \\kappa N^{-\\f
rac25}$\, then we see a phase transition in $\\kappa$: there exist positiv
e and finite constants $C_1\, C_2$ so that there is no percolation if $ \\
kappa < C_1$ while percolation occurs for $\\kappa >C_2$. The question is
motivated by a result on the analogously layered ferromagnetic Ising model
at mean field critical temperature\, treated in [2]. The proof relies on
the analysis of the scaling limit of the growth process restricted to each
horizontal layer. This is inspired by works of Mueller and Tribe on the l
ong range contact process (PTRF\, 1995). A renormalization scheme is used
for the percolative regime. The talk is based on a joint work with Thomas
Mountford and Hao Xue [1].\n\n\n\n [1] T. S. Mountford\, M. E. Vares\, H.
Xue. Critical scaling for an anisotropic percolation system on $\\mathbb{Z
}^2$ (Electronic Jr. in Probability\, 2020)\n\n [2]. L.R. Fontes\, D. H. M
archetti\, I. Merola\, E. Presutti\, M.E. Vares. Layered systems at the\nm
ean field critical temperature. J. Stat. Phys. 161\, (2015)\, 91--122.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Leplaideur (Université de la Nouvelle-Calédonie)
DTSTART:20211215T190000Z
DTEND:20211215T200000Z
DTSTAMP:20260404T110959Z
UID:Web-PPGMat-UFRGS/37
DESCRIPTION:Title: Nonlinear Thermodynamical Formalism\nby Renaud Leplai
deur (Université de la Nouvelle-Calédonie) as part of Webinários do PPG
Mat - UFRGS\n\n\nAbstract\nThe Thermodynamical Formalism aims to study equ
ilibrium states\, that are measures maximizing the entropy plus the integr
al of some observable (called a potential).\n\nWe will present a new forma
lism\, called nonlinear\, as it aims to study maximizing measures for the
entropy + some functional on the set of invariant measures.\n\nThis is a j
oint work with J. Buzzi and B. Kloeckner\, and extends previous results wi
th F. Watbled.\n\nThe main point is that classical mean field spin spaces
(as Potts or Curie-Weiss models) in Statistical Mechanics can be seen with
in this formalism.\n
LOCATION:https://stable.researchseminars.org/talk/Web-PPGMat-UFRGS/37/
END:VEVENT
END:VCALENDAR