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SUMMARY:Mylene Maida (Université de Lille\, France)
DTSTART:20210308T160000Z
DTEND:20210308T165000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/1
DESCRIPTION:Title: Mathematical aspects of two-dimensional Yang-Mills theory : an introd
uction\nby Mylene Maida (Université de Lille\, France) as part of BIR
S workshop: Stochastics and Geometry\n\n\nAbstract\nIn the fifties\, Chen
Ning Yang and Robert Mills made a major breakthrough in quantum field theo
ry by extending the concept of gauge theory to non-abelian groups. The mat
hematical and physical consequences of going from a commutative to a non-c
ommutative theory are major and since then\, the mathematics of Yang-Mills
theory has been a very active field of research. In this talk\, meant to
be an introductory as possible\, I will focus on the last two-decade devel
opments of Yang-Mills theory on two-dimensional manifolds with gauge group
U(N) or SU(N). I will rely on the fascinating properties of the heat kern
el (ie the Brownian motion and bridge) on these groups. I will in particul
ar explain the construction of the master field\, arising in the large-N l
imit for these models\, in relation with free probability theory.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/1/
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BEGIN:VEVENT
SUMMARY:Fabrice Baudoin (University of Connecticut)
DTSTART:20210308T171000Z
DTEND:20210308T180000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/2
DESCRIPTION:Title: On log-Sobolev inequalities and their applications\nby Fabrice Ba
udoin (University of Connecticut) as part of BIRS workshop: Stochastics an
d Geometry\n\n\nAbstract\nAbstract: In this talk\, after a brief historica
l perspective\, we will review some applications of the family log-Sobolev
inequalities to partial differential equations\, differential geometry an
d stochastic analysis in infinite-dimensional path spaces. A particular em
phasis will be put on the fundamental contributions by Bruce Driver.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Bela Cruzeiro (Instituto Superior Técnico\, Lisbon)
DTSTART:20210309T160000Z
DTEND:20210309T165000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/3
DESCRIPTION:Title: On stochastic Clebsch variational principles\nby Ana Bela Cruzeir
o (Instituto Superior Técnico\, Lisbon) as part of BIRS workshop: Stochas
tics and Geometry\n\n\nAbstract\nWe develop a stochastic Clebsch action pr
inciple and derive the corresponding stochastic differential equations. Th
e configuration space is a Riemannian manifold on which a Lie group acts t
ransitively. This is joint work with D.D. Holm and T.S. Ratiu.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hall (University of Notre Dame)
DTSTART:20210309T171000Z
DTEND:20210309T180000Z
DTSTAMP:20260422T185428Z
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: Stochastics and
Geometry\n\n\nAbstract\nI will explain how tools from the theory of partia
l differential equations can be used to compute the eigenvalue distributio
n of large random matrices. I will discuss several examples where this me
thod can be used and show lots of pictures illustrating the results. I wil
l then explain how the method works in the simplest interesting example\,
for random matrices of the form $X+iY$\, where $X$ is drawn from the Gauss
ian Unitary Ensemble and $Y$ is an arbitrary Hermitian random matrix indep
endent of $X$. The talk should be accessible to a wide audience.\n\nThe PD
E approach to the subject was introduced in a work of mine with Bruce Driv
er and Todd Kemp and the specific example I will discuss is joint work of
mine with Ching Wei Ho.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elton Hsu (Northwesthern University)
DTSTART:20210309T190000Z
DTEND:20210309T195000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/5
DESCRIPTION:Title: Stochastic analysis on Riemannian manifolds\nby Elton Hsu (Northw
esthern University) as part of BIRS workshop: Stochastics and Geometry\n\n
\nAbstract\nWe will discuss several problems related to stochastic analysi
s on manifolds\, especially analysis on the path space over a Riemannian m
anifold based on the Wiener measure (Riemannian Brownian motion)\, an area
of stochastic analysis that Bruce Driver made groundbreaking contribution
. These include the quasi-invariance of the Wiener measure under the Camer
on-Martin flow\, integration by parts formula and the logarithmic Sobolev
inequality as well as the more general Beckner’s inequality on the path
space. We survey the history of path space analysis and highlight some of
its most recent developments such as sharp constants for functional inequa
lities and time-dependent Riemannian metrics.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismael Bailleul (Universite Rennes 1)
DTSTART:20210310T160000Z
DTEND:20210310T165000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/6
DESCRIPTION:Title: Gardening in the field of stochastic differential geometry\nby Is
mael Bailleul (Universite Rennes 1) as part of BIRS workshop: Stochastics
and Geometry\n\n\nAbstract\nWe will take the time of this talk to look for
some of the roots of stochastic differential geometry inside and outside
of the field of probability theory\, to emphasize some of its noticeable a
chievements\, and to pay attention to which directions the leaves are grow
ing or may be growing.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Haslhofer (University of Toronto)
DTSTART:20210310T171000Z
DTEND:20210310T180000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/7
DESCRIPTION:Title: Analysis on path space\, Einstein metrics and Ricci flow\nby Robe
rt Haslhofer (University of Toronto) as part of BIRS workshop: Stochastics
and Geometry\n\n\nAbstract\nI will survey how analysis on path space can
be used in the study Ricci curvature. As a motivation\, I will start by di
scussing Driver’s foundational work on quasi-invariance and integration
by parts on path space. Next\, I will discuss joint work with Aaron Naber\
, which characterizes solutions of the Einstein equations and the Ricci fl
ow in terms of certain sharp estimates on path space. In particular\, this
motivates a notion of weak solutions. Finally\, I will mention joint work
with Beomjun Choi\, where we prove that noncollapsed limits are indeed we
ak solutions.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Saloff-Coste (Cornell University)
DTSTART:20210310T190000Z
DTEND:20210310T195000Z
DTSTAMP:20260422T185428Z
UID:BIRS_21w5184/8
DESCRIPTION:Title: Thirty-six views of the ubiquitous heat kernel:a personal selection\nby Laurent Saloff-Coste (Cornell University) as part of BIRS workshop:
Stochastics and Geometry\n\n\nAbstract\nWhy is the heat kernel useful? Ho
w does it help us understand other problems? This talk will be a leisure w
alk driven by these questions.\n
LOCATION:https://researchseminars.org/talk/BIRS_21w5184/8/
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