BEGIN:VCALENDAR
PRODID:-//PSU Mathematics Department//Seminar iCalendar Generator//EN
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CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Logic Seminar
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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BEGIN:STANDARD
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:20140826T143000
DTEND;TZID=America/New_York:20140826T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22072
SUMMARY:Logic Seminar - Organizational Meeting
DESCRIPTION:Seminar: Logic Seminar\nTitle: Organizational Meeting\nAbstract
: Meet to discuss speakers for the semester.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140902T143000
DTEND;TZID=America/New_York:20140902T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22073
SUMMARY:Logic Seminar - An introduction to reverse mathematics
DESCRIPTION:Seminar: Logic Seminar\nTitle: An introduction to reverse mathe
matics\nSpeaker: Stephen G. Simpson\, Penn State\nAbstract: Reverse mathem
atics is a program of research in the foundations of mathematics. A basic
discovery\, emphasized by Hilbert and Bernays in the 1930s\, is that the
proofs of almost all theorems of core mathematics (analysis\, algebra\, ge
ometry\, combinatorics\, ...) are straightforwardly formalizable in subsys
tems of second-order arithmetic. Reverse mathematics is a series of case
studies\, initiated in the 1970s\, in which specific core mathematical the
orems are examined in order to determine the smallest subsystem of second-
order arithmetic in which the given theorem is provable. The program of r
everse mathematics is very rich\, with many sub-programs and many open pro
blems. Many concepts from mathematical logic come into play\, including T
uring computability\, the Turing jump operator\, basis theorems\, relative
hyperarithmeticity\, the hyperjump\, proof-theoretic ordinals\, and nonst
andard models of arithmetic. Over the past 40 years\, some interesting co
nclusions have emerged. For instance\, it turns out that many core mathem
atical theorems are logically equivalent to the axioms needed to prove the
m\, and this leads to a robust classification of such theorems up to logic
al equivalence. Indeed\, many such theorems fall into only five equivalen
ce classes\, the so-called "Big Five." An area of recent interest is the
reverse mathematics of measure theory\, which involves algorithmic randomn
ess.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140909T143000
DTEND;TZID=America/New_York:20140909T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22074
SUMMARY:Logic Seminar - Randomness\, Riesz Capacity\, Brownian Motion\, and
Complexity
DESCRIPTION:Seminar: Logic Seminar\nTitle: Randomness\, Riesz Capacity\, Br
ownian Motion\, and Complexity\nSpeaker: Jason Rute\, Penn State\nAbstract
: - Algorithmic randomness is a topic in computability theory which invest
igates which paths in a stochastic process behave randomly (with respect t
o all computable statistical tests).\n- Riesz capacity is an important con
cept in potential theory and stochastic processes. It is used to estimate
the probability that an n-dimensional Brownian motion hits a given set or
is zero on a given set of times.\n- The a priori complexity KM(x) is a me
asure of the computational complexity of a finite bit string x.\n\nI will
present the following result which connects these three subjects. The fol
lowing are equivalent for t in (0\,1].\n1) t is Martin-Löf random with re
spect to 1/2-Reisz capacity.\n2) t is a zero of some Martin-Löf random on
e-dimensional Brownian motion.\n3) sum_n 2^{n/2 - KM(t[0\,…\,n-1])} <
\\infty where t[0\,…\,n-1] is the first n bits of the binary expansion o
f t.\n\nThis is joint work with Joseph Miller.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140916T143000
DTEND;TZID=America/New_York:20140916T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22075
SUMMARY:Logic Seminar - Towards an Effective Theory of Levy Processes
DESCRIPTION:Seminar: Logic Seminar\nTitle: Towards an Effective Theory of L
evy Processes\nSpeaker: Adrian Maler\, Penn State\nAbstract: The Levy proc
esses constitute an interesting and important class of stochastic processe
s: basically\, the continuous time version of a random walk. We introduce
effective Skorokhod space\, which is a suitable setting in which to develo
p an effective theory of Levy processes. We present three definitions of a
"computable" Levy process\, and discuss their equivalences.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140923T143000
DTEND;TZID=America/New_York:20140923T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22076
SUMMARY:Logic Seminar - Proving RT_2^2 doesn't imply WKL_0
DESCRIPTION:Seminar: Logic Seminar\nTitle: Proving RT_2^2 doesn't imply WKL
_0\nSpeaker: Jake Pardo\, Penn State\nAbstract: The different versions of
Ramsey's Theorem have long been significant in the study of reverse mathem
atics\, and RT_2^2 has proven to be a particularly significant version. I
t was a long standing open question whether RT_2^2 implied WKL_0 or not -
it was known that the latter doesn't imply the former - however this was r
ecently solved by Liu. I will explain a little bit of the background of t
his problem and then dive right into the intuitive yet highly technical pr
oof of Liu's great result.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140930T143000
DTEND;TZID=America/New_York:20140930T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22077
SUMMARY:Logic Seminar - An Overview of Model Theory
DESCRIPTION:Seminar: Logic Seminar\nTitle: An Overview of Model Theory\nSpe
aker: Jan Reimann\, Penn State\nAbstract: This talk will give a brief intr
oduction to the central topics of model theory. Model theory studies mathe
matical structures and theories (such as groups\, fields\, graphs\, orders
) from the point of view of mathematical logic. Central notions are\, amon
g others\, definability (which subsets of a structures can be defined by a
formula)\, categoricity (how many structures satisfying a given set of ax
ioms are there up to isomorphism)\, and stability (how many types are real
ized).\n\nThe talk is intended to give necessary background for a series o
f talks on continuous model theory coming up this semester.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141007T143000
DTEND;TZID=America/New_York:20141007T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22078
SUMMARY:Logic Seminar - The Muchnik topos
DESCRIPTION:Seminar: Logic Seminar\nTitle: The Muchnik topos\nSpeaker: Sank
ha Basu\, Penn State\nAbstract: A. A. Muchnik in his 1963 paper titled "St
rong and weak reduciblity of algorithmic problems" described how mass prob
lems under weak reduciblity form a model for intuitionistic propositional
calculus. This interpretation formalized the well known 'Calculus of probl
ems' introduced by Kolmogorov in 1932. \nA recent paper\, submitted for pu
blication\, authored by the speaker and Stephen Simpson\, discusses an ext
ension of this semantics to higher-order intuitionistic logic and mathemat
ics. This model has been named as the Muchnik topos. The paper also introd
uces a new class of intuitionistic real numbers\, called the Muchnik reals
\, which are different from the Cauchy and the Dedekind reals. Within the
Muchnik topos\, we obtain a choice principle (\\forall x\\exists y A(x\,y)
)\\implies(\\exists w\\forall x A(x\,wx)) and a bounding principle (\\fora
ll x\\exists y A(x\,y))\\implies(\\exists z\\forall x\\exists y (y\\le_{
\\mathrm{T}}(x\,z)\\land A(x\,y))\, where x\,y\,z range over Muchnik reals
\, w ranges over functions from Muchnik reals to Muchnik reals\, and A(x\,
y) is a formula not containing w or z.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141014T143000
DTEND;TZID=America/New_York:20141014T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22079
SUMMARY:Logic Seminar - Hausdorff dimension
DESCRIPTION:Seminar: Logic Seminar\nTitle: Hausdorff dimension\nSpeaker: Ma
nfred Denker\, Penn State\nAbstract: It is a difficult problem to calcula
te the Hausdorff dimension of a set. In general\, this number is hard to
compute with some given precision. For some sets\, like the Cantor set\, a
formula for the dimension is known. In other cases\, like the attractor o
f the Henon map computer calculations showed varying results. Box counting
methods are a bit more reliable\, but they may not calculate Hausdorff di
mension\, but the Minkowski dimension. Grassberger and Procaccia introduce
d a new type of dimension\, called correlation dimension. Although it does
not calculate the Hausdorff dimension in general\, it is a notion which i
s estimable in the sense of regression analysis. I will review this method
and the mathematical theory needed for such an approach.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141021T143000
DTEND;TZID=America/New_York:20141021T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22080
SUMMARY:Logic Seminar - Uniform distribution and algorithmic randomness
DESCRIPTION:Seminar: Logic Seminar\nTitle: Uniform distribution and algorit
hmic randomness\nSpeaker: Jeremy Avigad\, Carnegie Mellon University\nAbst
ract: A seminal theorem due to Weyl states that if (a_n) is any sequence o
f distinct integers\, then\, for almost every real number x\, the sequence
(a_n x) is uniformly distributed modulo one. In particular\, for almost e
very x in the unit interval\, the sequence (a_n x) is uniformly distribute
d modulo one for every *computable* sequence (a_n) of distinct integers. C
all such an x *UD random*. Every Schnorr random real is UD random\, but th
ere are Kurtz random reals that are not UD random. On the other hand\, Wey
l's theorem still holds relative to a particular effectively closed null s
et\, so there are UD random reals that are not Kurtz random.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141028T143000
DTEND;TZID=America/New_York:20141028T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22081
SUMMARY:Logic Seminar - Continuous Model Theory
DESCRIPTION:Seminar: Logic Seminar\nTitle: Continuous Model Theory\nSpeaker
: Jan Reimann\, Penn State\nAbstract: While the basic framework of classic
al model theory is very suitable for algebraic structures\, it is less so
for metric structures\, where the basic relation is not so much equality\,
but the distance between two objects.\n\nOne can extend classical model t
heory to better capture metric notions. One approach that has gained parti
cular prominence is known as "continuous model theory". An essential featu
re of this approach is to replace the classical binary truth value by the
continuous interval [0\,1].\n\nIn this talk I will outline the basic featu
res of continuous model theory\, in particular how syntax and semantics wo
rk in this approach and how basic model theoretic notions such as elementa
ry substructures are being recast. This will be followed by a number of ta
lks over the next weeks that look at more advanced model theory from a con
tinuous point of view.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141104T143000
DTEND;TZID=America/New_York:20141104T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22082
SUMMARY:Logic Seminar - The compactness theorem for continuous model theory
DESCRIPTION:Seminar: Logic Seminar\nTitle: The compactness theorem for cont
inuous model theory\nSpeaker: Jake Pardo\, Penn State\nAbstract: The talk
will present a proof of the compactness theorem for continuous logic\, usi
ng ultraproducts of metric spaces.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141111T143000
DTEND;TZID=America/New_York:20141111T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22083
SUMMARY:Logic Seminar - The compactness theorem for continuous model theory
(II)
DESCRIPTION:Seminar: Logic Seminar\nTitle: The compactness theorem for cont
inuous model theory (II)\nSpeaker: Jake Pardo\, Penn State\nAbstract: This
talk continues the discussion of the compactness theorem for continuous m
odel theory.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141118T143000
DTEND;TZID=America/New_York:20141118T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22084
SUMMARY:Logic Seminar - Connectives and Constructions in Model Theory for M
etric Structures
DESCRIPTION:Seminar: Logic Seminar\nTitle: Connectives and Constructions in
Model Theory for Metric Structures\nSpeaker: Jason Rute\, PSU\nAbstract:
This is a continuation in the series on Model Theory for Metric Structures
. This week we will talk about how to express certain types of properties
in the language of metric structures\, namely existential properties and
implications between properties. In addressing this topic we will discuss
logical connectives\, Lowenheim-Skolem\, saturated models\, strong-homoge
neous models\, and equivalent ways to express implication.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141202T143000
DTEND;TZID=America/New_York:20141202T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22086
SUMMARY:Logic Seminar - Gelfand duality and Ramsey theory
DESCRIPTION:Seminar: Logic Seminar\nTitle: Gelfand duality and Ramsey theor
y\nSpeaker: Willem Fouché\, University of South Africa\nAbstract: In this
talk\, I want to discuss recent developments arising from the paper [1] (
1987). In this paper\, Andreas Blass introduced the idea of\, what he call
ed\, a Ramsey action of a group on a discrete space in the context of unde
rstanding the tension\, in set theory\, between the Axiom of Choice and th
e Prime Ideal Theorem for Boolean algebras.\n\nIn this talk\, I will discu
ss this very tension\, with the benefit of hindsight\, as to what has happ
ened to his viewpoint as viewed from the world of the dynamical aspects of
structural Ramsey theory. Some recent links with Gelfand duality of commu
tative C∗- algebras will be discussed.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141209T143000
DTEND;TZID=America/New_York:20141209T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22087
SUMMARY:Logic Seminar - TBA
DESCRIPTION:Seminar: Logic Seminar\nTitle: TBA\nAbstract Link: http://
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141216T143000
DTEND;TZID=America/New_York:20141216T154500
LOCATION:MB315
URL:http://www.math.psu.edu/seminars/meeting.php?id=22088
SUMMARY:Logic Seminar - TBA
DESCRIPTION:Seminar: Logic Seminar\nTitle: TBA\nAbstract Link: http://
END:VEVENT
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