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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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140123T153500
DTEND;TZID=America/New_York:20140123T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20852
SUMMARY:Department of Mathematics Colloquium - A topological approach for u
ncovering hidden structure in neural activity.
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: A topolog
ical approach for uncovering hidden structure in neural activity.\nSpeaker
: Vladimir Itskov\nAbstract: Experimental neuroscience is achieving rapid
progress in the ability to collect neural activity and connectivity data.
This holds promise to directly test many theoretical ideas\, and thus adva
nce our understanding of "how the brain works." How to interpret this data
\, and what exactly it can tell us about the structure of neural circuits
\, is still not well-understood. A major obstacle is that these data ofte
n measure quantities that are related to more "fundamental" variables by a
n unknown nonlinear transformation. We find that combinatorial topology ca
n be used to obtain meaningful answers to important questions about the st
ructure of neural activity. In this talk I will first introduce a new meth
od\, using tools from computational topology\, for detecting structure in
correlation matrices that is obscured by an unknown nonlinear transformati
on. I will then illustrate its use by testing the "coding space" hypothes
is on neural data.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140130T153500
DTEND;TZID=America/New_York:20140130T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20853
SUMMARY:Department of Mathematics Colloquium - A geometric approach to unde
rstanding neural codes in recurrent networks
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: A geometr
ic approach to understanding neural codes in recurrent networks\nSpeaker:
Carina Curto\, University of Nebraska-Lincoln\nAbstract: Synapses in many
cortical areas of the brain are dominated by local\, \nrecurrent connectio
ns. It has long been suggested\, therefore\, that \ncortical networks may
serve to restore a noisy or incomplete signal by \nevolving it towards a
stored pattern of activity. These “preferred” \nactivity patterns are
constrained by the excitatory connections\, and \ncomprise the neural cod
e of the recurrent network. In this talk I will \nbriefly review the permi
tted and forbidden sets model for cortical \nnetworks\, first introduced b
y Hahnloser et. al. (Nature\, 2000)\, in which \npreferred activity patter
ns are modeled as “permitted sets” - that is\, as \nsubsets of neurons
that co-fire at stable fixed points of the network \ndynamics. I will the
n present some recent results that provide a geometric \nhandle on the rel
ationship between permitted sets and network \nconnectivity. This allows u
s to precisely characterize the structure of \nneural codes that arise fro
m a simple learning rule. In particular\, we \nfind “natural codes” th
at can be learned from few examples\, and that \nclosely mimic receptive f
ield codes that have been observed in the brain. \nFinally\, we use our ge
ometric description of permitted sets to prove that \nthese networks can p
erform error correction and pattern completion for a \nwide range of conne
ctivities.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140206T153500
DTEND;TZID=America/New_York:20140206T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20850
SUMMARY:Department of Mathematics Colloquium - Syzygies of Veronese embeddi
ngs
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Syzygies
of Veronese embeddings\nSpeaker: Claudiu Raicu\, Princeton University\nAbs
tract: Syzygies are important classical invariants attached to \nalgebraic
varieties. They can be defined iteratively starting from the \ndefining e
quations of a variety and continuing with the relations \nbetween these eq
uations\, the relations between the relations etc. In the \nspecial case o
f the Veronese embeddings of the projective space\, the \nstructure of syz
ygies is particularly rich due to the presence of a \nlarge group of symme
tries. Their study can be approached through a \nvariety of techniques\, p
lacing them at the confluence of algebraic \ngeometry\, commutative algebr
a\, representation theory and combinatorics. \nI will discuss some recent
results on the structure of the syzygies of \nVeronese embeddings\, and ex
plain how their vanishing controls the \nasymptotic vanishing behavior (in
the sense of Ein and Lazarsfeld) of \nsyzygies of arbitrary algebraic var
ieties.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140213T153500
DTEND;TZID=America/New_York:20140213T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20849
SUMMARY:Department of Mathematics Colloquium - Evolution equations driven b
y nonlocal infinitesimal generators and their probabilistic interpretation
s
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Evolution
equations driven by nonlocal infinitesimal generators and their probabili
stic interpretations\nSpeaker: Wojbor Woyczynski\, Case Western Reserve Un
iversity\nAbstract: One of the motivations of our program was to develop u
nderstanding of the interplay between the nonlinear and nonlocal component
s in evolution equation driven by the infinitesimal generators of stochast
ic processes with jumps\, such as Levy processes and flights. In particul
ar\, we also studied probabilistic approximations (propagation of chaos) f
or several extensions of the classical quasilinear and strongly linear PDE
s\, including the conservation laws\, porous medium and Hamilton-Jacobi e
quations\, and reaction-diffusion type equations for Darwinian evolutiona
ry population models where the hydrodynamic limits may still preserve some
"background" random noise.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140220T153500
DTEND;TZID=America/New_York:20140220T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20848
SUMMARY:Department of Mathematics Colloquium - Sharp Gagliardo--Nirenberg--
Sobolev inequalities and conformal geometry
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Sharp Gag
liardo--Nirenberg--Sobolev inequalities and conformal geometry\nSpeaker: J
effrey Case\, Princeton University\nAbstract: There is a deep connection b
etween curvature prescription problems in conformal geometry and sharp Sob
olev inequalities. One famous example is the connection between prescribin
g conformal metrics with constant scalar curvature and the sharp $L^2$ Sob
olev inequalty. Another example is the connection between prescribing Per
elman's weighted scalar curvature and the sharp logarithmic Sobolev inequa
lity. In this talk\, I will describe an interpolating family of curvature
prescription problems on smooth metric measure spaces which connect the sc
alar curvature to Perelman's weighted scalar curvature and are related to
the family of sharp Gagliardo-Nirenberg-Sobolev inequalities discovered by
Del Pino and Dolbeault. In particular\, this provides a new perspective o
n Perelman's $W$-functional and suggests an approach to finding higher ord
er analogues.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140227T153500
DTEND;TZID=America/New_York:20140227T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20847
SUMMARY:Department of Mathematics Colloquium - The Atlas of Lie Groups and
representations
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: The Atlas
of Lie Groups and representations\nSpeaker: Jeffrey Adams\, University of
Maryland\nAbstract: One of the fundamental problems in the theory of Lie
groups is to classify the Unitary Dual of a group G: the irreducible repre
sentations of G\, acting on a (typically infinite dimensional) Hilbert spa
ce\, preserving the inner product. This is a very difficult problem\, unso
lved except in some special cases\, and the answer is known to be very com
plicated.\n\nThe primary goal of the Atlas project is to compute the Unita
ry Dual by computer\, even though it is not obvious there is a finite algo
rithm in principle\, not to mention in practice. An important auxiliary go
al is to provide software for doing computations in Lie theory and represe
ntation theory.\n\nI'll discuss the current state of the project\, in broa
d terms\, and talk about what we've learned by rethinking our entire subje
ct in computational terms.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140306T153500
DTEND;TZID=America/New_York:20140306T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20846
SUMMARY:Department of Mathematics Colloquium - Quasiergodic hypothesis and
Arnold Diffusion in dimension 3
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Quasiergo
dic hypothesis and Arnold Diffusion in dimension 3\nSpeaker: Vadim Kaloshi
n\, University of Maryland\nAbstract: The famous ergodic hypothesis claims
that a typical Hamiltonian dynamics on a typical energy surface is ergodi
c. However\, KAM theory disproves this. It establishes a persistent set of
positive measure of invariant KAM tori. The (weaker) quasi-ergodic hypoth
esis\, proposed by Ehrenfest and Birkhoff\, says that a typical Hamiltonia
n dynamics on a typical energy surface has a dense orbit. This question is
wide open. In early 60th Arnold constructed an example of instabilities f
or a nearly integrable Hamiltonian of dimension n>2 and conjectured that t
his is a generic phenomenon\, nowadays\, called Arnold diffusion. In the l
ast two decades a variety of powerful techniques to attack this problem we
re developed. In particular\, Mather discovered a large class of invariant
sets and a delicate variational technique to shadow them. In a series of
preprints: one joint with P. Bernard\, K. Zhang and another joint with K.
Zhang we prove strong form of Arnold's conjecture in dimension n=3. Jointl
y with M. Guardia we also prove a weak form of quasiergodic hypothesis.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140320T153500
DTEND;TZID=America/New_York:20140320T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20844
SUMMARY:Department of Mathematics Colloquium - How black holes grow: An int
erplay between geometry and physics
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: How black
holes grow: An interplay between geometry and physics\nSpeaker: Abhay Ash
tekar\, Department of Physics\, Penn State University
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140403T153500
DTEND;TZID=America/New_York:20140403T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20842
SUMMARY:Department of Mathematics Colloquium - Localized representation of
low lying eigenspaces with applications in electronic structure analysis
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Localized
representation of low lying eigenspaces with applications in electronic s
tructure analysis\nSpeaker: Jianfeng Lu\, Duke University\nAbstract: Local
ized representation of eigenspaces play an important role in electronic st
ructure theory. They give nice physical understanding of the electronic st
ructure and are fundamental building blocks of fast algorithms. In this t
alk\, we will present some mathematical results and efficient algorithms f
or the localized representations. In particular\, we will discuss a convex
variational principle that gives us these representations.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140410T153500
DTEND;TZID=America/New_York:20140410T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20841
SUMMARY:Department of Mathematics Colloquium - The evolution of networks
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: The evolu
tion of networks\nSpeaker: David Kinderlehrer\, Carnegie Mellon University
\nAbstract: Cellular networks are ubiquitous in nature. Most technological
ly useful materials arise as polycrystalline microstructures\, composed of
a myriad of small crystallites\, the grains\, separated by interfaces\,
the grain boundaries. The energetics and connectivity of the network of bo
undaries are implicated in many properties across all scales of use. The
evolution of such networks\, coarsening\, is governed primarily by the at
tempt of the system to decrease interfacial energy subject to spatial cons
traints. The recently discovered grain boundary character distribution (G
BCD) characterizes texture and its existence illustrates that the boundary
network is ordered. We discuss a theory for the evolution of this statist
ic which bridges mesoscopic scales. It gives rise to many interesting ques
tions and challenges: we still have much to learn about these very ancient
questions.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140417T153500
DTEND;TZID=America/New_York:20140417T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20840
SUMMARY:Department of Mathematics Colloquium - Department Meeting
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Departmen
t Meeting\nSpeaker: Department Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140424T153500
DTEND;TZID=America/New_York:20140424T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20839
SUMMARY:Department of Mathematics Colloquium - String theory on elliptic cu
rves: topology\, algebraic geometry\, and physics
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: String th
eory on elliptic curves: topology\, algebraic geometry\, and physics\nSpea
ker: Jonathan Rosenberg\, University of Maryland\nAbstract: Supersymmetric
string theory in 10 dimensions is the leading candidate for a unified the
ory of all the fundamental forces of nature. For maximal supersymmetry\,
it is usually assumed that space-time is the product of flat Minkowski spa
cetime with a compact Calabi-Yau manifold (a complex manifold with trivial
canonical bundle). The simplest Calabi-Yau manifold is an elliptic curve
\, and in joint work with Chuck Doran and Stefan Mendez-Diez of the Univer
sity of Alberta\, we have recently made a thorough study of all "orientifo
ld" string theories on elliptic curves (crossed with flat spacetime). I w
ill explain how our findings illustrate deep connections between algebraic
topology\, algebraic geometry\, and physics.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140501T153500
DTEND;TZID=America/New_York:20140501T162500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=20836
SUMMARY:Department of Mathematics Colloquium - Asymptotic theory of finite
groups
DESCRIPTION:Seminar: Department of Mathematics Colloquium\nTitle: Asymptoti
c theory of finite groups\nSpeaker: Efim Zelmanov\, University of Californ
ia\, San Diego\nAbstract: We will discuss recent developments in the theor
y of profinite groups and their relations to Combinatorics and Number Theo
ry.
END:VEVENT
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