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PRODID:-//PSU Mathematics Department//Seminar iCalendar Generator//EN
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X-WR-CALNAME:Department of Mathematics Colloquium
X-WR-TIMEZONE:America/New_York
BEGIN:VTIMEZONE
TZID:America/New_York
X-LIC-LOCATION:America/New_York
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:19700308T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
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TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:19701101T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160114T153500
DTEND;TZID=America/New_York:20160114T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30195
SUMMARY:Department of Mathematics Colloquium - Random walk parameters and t
he geometry of groups
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Random wa
lk parameters and the geometry of groups\nSpeaker: Tianyi Zheng\, Stanford
University\nAbstract: The first characterization of groups by an asymptot
ic description of random walks on their Cayley graphs dates back to Kesten
’s criterion of amenability. I will first review some connections betwee
n the random walk parameters and the geometry of the underlying groups. I
will then discuss a flexible construction that gives solution to the inver
se problem (given a function\, find a corresponding group) for large class
es of speed\, entropy and return probability and Hilbert compression funct
ions of groups of exponential volume growth. Based on joint work with Jere
mie Brieussel.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160121T153500
DTEND;TZID=America/New_York:20160121T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30196
SUMMARY:Department of Mathematics Colloquium - Topics in Stochastic Analysi
s
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Topics in
Stochastic Analysis\nSpeaker: Fabrice Baudoin\, Perdue University\nAbstra
ct: Abstract: Starting from basic principles we will present some recent d
evelopments in the theory of rough paths and in the theory of sub-Riemanni
an diffusions. The first part of the talk will be devoted to the theory of
rough paths. This theory was developed in the 1990’s by T. Lyons and al
lows to give a sense to solutions of differential equations driven by irre
gular paths. The theory itself has nothing to do with probability theory b
ut has had a tremendous impact on several recent developments in stochasti
c analysis and served as an inspiration to Hairer’s regularity structure
theory\, for which he was awarded the Fields medal in 2014. In the second
part of the talk\, we will address several problems in the geometric anal
ysis of some sub-Riemannian manifolds\, which can surprisingly solved usin
g diffusion semigroups techniques.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160128T153500
DTEND;TZID=America/New_York:20160128T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30197
SUMMARY:Department of Mathematics Colloquium - Superintegrability and exact
ly solvable problems in classical and quantum mechanics
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Superinte
grability and exactly solvable problems in classical and quantum mechanics
\nSpeaker: Willard Miller\, Jr.\, University of Minnesota\nAbstract: Quant
um superintegrable systems are systems with maximum symmetry\, which\nperm
its their explicit solvability. Integrable systems in n dimensional spac
e are defined by n mutually commuting symmetry operators. Superintegrable
systems admit 2n-1 symmetry operators which cannot all mutually commute.
The symmetries generate closed algebraic structures\, usually not Lie alge
bras\, The irreducible representations of these algebras yield important
information about the eigenvalues and eigenspaces of the quantum systems.
Distinct superintegrable systems and their symmetry algebras are related
by geometric contractions which have important physical and geometric impl
ications\, such as the Askey scheme for obtaining all hypergeometric ortho
gonal polynomials as limits of Racah/Wilson polynomials. We introduce the
subject and and survey the theory behind the discovery and classification
of these remarkable systems.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160204T153500
DTEND;TZID=America/New_York:20160204T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30198
SUMMARY:Department of Mathematics Colloquium - Free Boundary Problems Arisi
ng in Biology
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Free Boun
dary Problems Arising in Biology\nSpeaker: Professor Avner Friedman\, Ohio
State University\nAbstract: In a free boundary problem one seeks to solve
a system of PDEs in a domain G whose boundary\, or a part of it\, is unkn
own\, and to also determine the free boundary. Classical free boundary pro
blems include contact problems in elasticity\, melting of ice\, propagatio
n of jets\, and cavitational flows. In recent years new free boundary prob
lems arose in the context of biological or biomedical processes. Examples
include the healing of a wound\, the growth of a tumor\, the formation of
a plaque in the artery\, the development of granulomas in tuberculosis\, a
nd biofilms. In this talk I will introduce some of the biological free bou
ndary problems\, focus on rigorous mathematical results\, and describe som
e open problems.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160211T153500
DTEND;TZID=America/New_York:20160211T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30199
SUMMARY:Department of Mathematics Colloquium - First-passage percolation
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: First-pas
sage percolation\nSpeaker: Arjun Krishnan\, University of Utah\nAbstract:
First-passage percolation is a random growth model on the cubic lattice Z^
d. It models\, for example\, the spread of fluid in a random porous medium
. This talk is about the asymptotic behavior of the first-passage time T(x
)\, which represents the time it takes for a fluid particle released at th
e origin to reach a point x on the lattice. \n\nThe first-order asymptotic
--- the law of large numbers --- for T(x) as x goes to infinity in a part
icular direction u\, is given by a deterministic function of u called the
time-constant. The first part of the talk will focus on a new variational
formula for the time-constant\, which results from a connection between fi
rst-passage percolation and stochastic homogenization for discrete Hamilto
n-Jacobi-Bellman equations. \n\nThe second-order asymptotic of the first-p
assage time describes its fluctuations\; i.e.\, the analog of the central
limit theorem for T(x). In two dimensions\, the fluctuations are (conjectu
red to be) in the Kardar-Parisi-Zhang (KPZ) or random matrix universality
class. We will present some new results (with J. Quastel) in the direction
of the KPZ universality conjecture. \n\nThe analysis of this problem will
involve tools and ideas from probability\, PDEs\, and ergodic theory.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160218T153500
DTEND;TZID=America/New_York:20160218T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30200
SUMMARY:Department of Mathematics Colloquium - Positivity in contact geomet
ry
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Positivit
y in contact geometry\nSpeaker: Peter Albers\, University of Muenster\, Ge
rmany\nAbstract: The notion of positivity in contact geometry was introduc
ed in 2000 by Eliashberg and Polterovich. For example\, geodesic flows (an
d more generally Reeb flows) are positive. This and other examples will be
explained during the talk. Positivity has connections to many phenomena s
uch as contact (non-)squeezing and biinvariant partial orders. Positivity
leads to a generalization of the classical Bott-Samelson theorem and has c
onnection to the famous Weinstein conjecture. Examples will be presented t
hroughout the talk.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160225T153500
DTEND;TZID=America/New_York:20160225T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30201
SUMMARY:Department of Mathematics Colloquium - Data-driven stochastic model
reduction in nonlinear dynamical systems
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Data-driv
en stochastic model reduction in nonlinear dynamical systems\nSpeaker: Fei
Lu\, University of California\, Berkeley\nAbstract: Prediction of high-di
mensional chaotic dynamic systems is often difficult when only partial obs
ervations are available\, because such systems are often expensive to solv
e in full and the initial data will be incomplete. The development of redu
ced models for the observed variables is thus needed. The challenges come
from the nonlinear interactions between the observed variables and the uno
bserved variables\, and the difficulties in quantifying uncertainties from
discrete data. \n\nWe address these challenges by developing discrete-tim
e stochastic reduced systems for the observable variables\, by using data
and statistical methods to account for the impact of the unobserved variab
les. A key ingredient in the construction of the stochastic reduced system
s is a discrete-time stochastic parametrization based on inference of nonl
inear time series. We demonstrate our approach on the two-layer Lorenz 96
system and the Kuramoto-Sivashinsky equation. \n\nA theoretical understan
ding of such a data-driven modeling problem requires ideas from dynamical
systems\, PDEs\, probability and statistics. Open questions will be discus
sed.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160303T153500
DTEND;TZID=America/New_York:20160303T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30202
SUMMARY:Department of Mathematics Colloquium - Numerical methods for parame
ter investigations in nonlinear systems
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Numerical
methods for parameter investigations in nonlinear systems\nSpeaker: Wenru
i Hao\, Ohio State University\nAbstract: Parameters are important for math
ematical models in physics and biology. In this talk\, I will present some
recent numerical methods on parameter study of nonlinear partial differen
tial equations (PDEs). These numerical methods include homotopy continuati
on\, bootstrapping and reduced basis methods. They make use of polynomial
systems (with thousands of variables) arising by discretization\, and can
be used to compute multiple solutions as well as bifurcation points. This
talk will also cover the applications of these numerical methods to severa
l biological models including atherosclerosis where the critical parameter
s are the LDL and HDL serum concentration\, and blood clotting model where
high dimensional parameters are explored.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160331T153500
DTEND;TZID=America/New_York:20160331T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30206
SUMMARY:Department of Mathematics Colloquium - Regularity and blow up in id
eal fluid
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Regularit
y and blow up in ideal fluid\nSpeaker: Alexander Kiselev\, Rice University
\nAbstract: The incompressible Euler equation of fluid mechanics has been
derived in 1755.\nIt is one of the central equations of applied analysis\,
yet due to its \nnonlinearity and non-locality many\nfundamental propert
ies of the solutions remain poorly understood. In \nparticular\, the glob
al regularity vs\nfinite time blow up question for incompressible three di
mensional \nEuler equation remains open.\n\nIn two dimensions\, it has be
en known since 1930s that solutions to \nEuler equation with smooth initi
al data are globally regular. The best \navailable upper bound on the siz
e of derivatives of the solution has \nbeen double exponential in time.\n
I will describe a construction showing that such fast generation of \nsma
ll scales can actually happen\, so that the double exponential bound \nis
qualitatively sharp.\n\nThis work has been motivated by numerical experim
ents due to Hou and \nLuo who propose a new scenario for singularity\nfor
mation in solutions of 3D Euler equation. The scenario is \naxi-symmetric
. The geometry of the scenario is related to the geometry \nof 2D Euler d
ouble exponential growth example and involves hyperbolic \npoints of the
flow located at the boundary\nof the domain. If time permits\, I will disc
uss some recent attempts to \ngain insight into the three-dimensional flu
id behavior in this scenario.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160407T153500
DTEND;TZID=America/New_York:20160407T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30207
SUMMARY:Department of Mathematics Colloquium - Close manfolds
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Close man
folds\nSpeaker: Professor Shmuel Weinberger\, University of Chicago\nAbstr
act: Gromov-Hausdorff space is a metric space of compact metric spaces. I
will discuss the relationship between nearby manifolds assuming a conditi
on that avoids local topology among the manifolds. The talk will expose i
deas of Ferry\, some joint with Dranishnikov and some with me\, as well.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160414T153500
DTEND;TZID=America/New_York:20160414T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30449
SUMMARY:Department of Mathematics Colloquium - Concentration of entropy dis
sipation for scalar conservation laws
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Concentra
tion of entropy dissipation for scalar conservation laws\nSpeaker: Stefano
Bianchini\, SISSA\nAbstract: Let $u(t\,x)$ be an entropy $L^\\infty$-solu
tion of the scalar conservation laws \n$u_t + f(u)_x = 0.$ \nBy entropy so
lution we means that for every convex function $\\eta$ it holds\n$\\eta_t
+ q_x \\leq 0\,$\nwhere the entropy flux $q$ is given by $q' = f' \\eta'$.
In particular it is a measure.\n\nUnder no assumptions on the flux functi
on $f$ the solution is in general only $L^\\infty$\, and thus questions re
garding the regularity of the dissipation measure were open.\n\nWe will re
view the basic theory of entropy solutions and show that the entropy dissi
pation is actually concentrated on a $1$-rectifiable set: there is a count
able set of Lipschitz curves $\\gamma_i(t)$ such that for all entropies $
\\eta$\, entropy flux $q$ it holds \n$\\eta_t + q_x = \\sum_i c_{\\eta\,i}
(t) \\mathcal H1 \\llcorner_{\\gamma_i}.$ \n\nCorollaries of this results
are regularity estimates for the original solution $u$: the existence of a
Lagrangian representation\, the structure of Young solutions\, the BV reg
ularity of $f'(u)$\, the strong continuity in time.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160421T153500
DTEND;TZID=America/New_York:20160421T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30209
SUMMARY:Department of Mathematics Colloquium - Faculty Meeting
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Faculty M
eeting\nSpeaker: Faculty Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160428T153500
DTEND;TZID=America/New_York:20160428T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=30210
SUMMARY:Department of Mathematics Colloquium - Uniform Distribution in Numb
er Theory
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Uniform D
istribution in Number Theory\nSpeaker: Professor John Friedlander\, Univer
sity of Toronto\nAbstract: Questions of uniform distribution of sequences
are ubiquitous in Number Theory. We survey just some of the many problems
and techniques which arise in this connection\, choices\, of course\, prej
udiced by the interests of the speaker.
END:VEVENT
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