BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mylene Maida (Université de Lille\, France)
DTSTART:20210308T160000Z
DTEND:20210308T165000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/1
DESCRIPTION:Title: Mathematical aspects of two-dimensional Yang-Mills theory : an
introduction\nby Mylene Maida (Université de Lille\, France) as part
of BIRS workshop: Stochastics and Geometry\n\n\nAbstract\nIn the fifties\
, Chen Ning Yang and Robert Mills made a major breakthrough in quantum fie
ld theory by extending the concept of gauge theory to non-abelian groups.
The mathematical and physical consequences of going from a commutative to
a non-commutative theory are major and since then\, the mathematics of Yan
g-Mills theory has been a very active field of research. In this talk\, me
ant to be an introductory as possible\, I will focus on the last two-decad
e developments of Yang-Mills theory on two-dimensional manifolds with gaug
e group U(N) or SU(N). I will rely on the fascinating properties of the he
at kernel (ie the Brownian motion and bridge) on these groups. I will in p
articular explain the construction of the master field\, arising in the la
rge-N limit for these models\, in relation with free probability theory.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrice Baudoin (University of Connecticut)
DTSTART:20210308T171000Z
DTEND:20210308T180000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/2
DESCRIPTION:Title: On log-Sobolev inequalities and their applications\nby Fab
rice Baudoin (University of Connecticut) as part of BIRS workshop: Stochas
tics and Geometry\n\n\nAbstract\nAbstract: In this talk\, after a brief hi
storical perspective\, we will review some applications of the family log-
Sobolev inequalities to partial differential equations\, differential geom
etry and stochastic analysis in infinite-dimensional path spaces. A partic
ular emphasis will be put on the fundamental contributions by Bruce Driver
.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Bela Cruzeiro (Instituto Superior Técnico\, Lisbon)
DTSTART:20210309T160000Z
DTEND:20210309T165000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/3
DESCRIPTION:Title: On stochastic Clebsch variational principles\nby Ana Bela
Cruzeiro (Instituto Superior Técnico\, Lisbon) as part of BIRS workshop:
Stochastics and Geometry\n\n\nAbstract\nWe develop a stochastic Clebsch ac
tion principle and derive the corresponding stochastic differential equati
ons. The configuration space is a Riemannian manifold on which a Lie group
acts transitively. This is joint work with D.D. Holm and T.S. Ratiu.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hall (University of Notre Dame)
DTSTART:20210309T171000Z
DTEND:20210309T180000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/4
DESCRIPTION:Title: Partial differential equations in random matrix theory\nby
Brian Hall (University of Notre Dame) as part of BIRS workshop: Stochasti
cs and Geometry\n\n\nAbstract\nI will explain how tools from the theory of
partial differential equations can be used to compute the eigenvalue dist
ribution of large random matrices. I will discuss several examples where
this method can be used and show lots of pictures illustrating the results
. I will then explain how the method works in the simplest interesting exa
mple\, for random matrices of the form $X+iY$\, where $X$ is drawn from th
e Gaussian Unitary Ensemble and $Y$ is an arbitrary Hermitian random matri
x independent of $X$. The talk should be accessible to a wide audience.\n\
nThe PDE approach to the subject was introduced in a work of mine with Bru
ce Driver and Todd Kemp and the specific example I will discuss is joint w
ork of mine with Ching Wei Ho.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elton Hsu (Northwesthern University)
DTSTART:20210309T190000Z
DTEND:20210309T195000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/5
DESCRIPTION:Title: Stochastic analysis on Riemannian manifolds\nby Elton Hsu
(Northwesthern University) as part of BIRS workshop: Stochastics and Geome
try\n\n\nAbstract\nWe will discuss several problems related to stochastic
analysis on manifolds\, especially analysis on the path space over a Riema
nnian manifold based on the Wiener measure (Riemannian Brownian motion)\,
an area of stochastic analysis that Bruce Driver made groundbreaking contr
ibution. These include the quasi-invariance of the Wiener measure under th
e Cameron-Martin flow\, integration by parts formula and the logarithmic S
obolev inequality as well as the more general Beckner’s inequality on th
e path space. We survey the history of path space analysis and highlight s
ome of its most recent developments such as sharp constants for functional
inequalities and time-dependent Riemannian metrics.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismael Bailleul (Universite Rennes 1)
DTSTART:20210310T160000Z
DTEND:20210310T165000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/6
DESCRIPTION:Title: Gardening in the field of stochastic differential geometry
\nby Ismael Bailleul (Universite Rennes 1) as part of BIRS workshop: Stoch
astics and Geometry\n\n\nAbstract\nWe will take the time of this talk to l
ook for some of the roots of stochastic differential geometry inside and o
utside of the field of probability theory\, to emphasize some of its notic
eable achievements\, and to pay attention to which directions the leaves a
re growing or may be growing.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Haslhofer (University of Toronto)
DTSTART:20210310T171000Z
DTEND:20210310T180000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/7
DESCRIPTION:Title: Analysis on path space\, Einstein metrics and Ricci flow\n
by Robert Haslhofer (University of Toronto) as part of BIRS workshop: Stoc
hastics and Geometry\n\n\nAbstract\nI will survey how analysis on path spa
ce can be used in the study Ricci curvature. As a motivation\, I will star
t by discussing Driver’s foundational work on quasi-invariance and integ
ration by parts on path space. Next\, I will discuss joint work with Aaron
Naber\, which characterizes solutions of the Einstein equations and the R
icci flow in terms of certain sharp estimates on path space. In particular
\, this motivates a notion of weak solutions. Finally\, I will mention joi
nt work with Beomjun Choi\, where we prove that noncollapsed limits are in
deed weak solutions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Saloff-Coste (Cornell University)
DTSTART:20210310T190000Z
DTEND:20210310T195000Z
DTSTAMP:20260404T060944Z
UID:BIRS_21w5184/8
DESCRIPTION:Title: Thirty-six views of the ubiquitous heat kernel:a personal sele
ction\nby Laurent Saloff-Coste (Cornell University) as part of BIRS wo
rkshop: Stochastics and Geometry\n\n\nAbstract\nWhy is the heat kernel use
ful? How does it help us understand other problems? This talk will be a le
isure walk driven by these questions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5184/8/
END:VEVENT
END:VCALENDAR