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PRODID:-//PSU Mathematics Department//Seminar iCalendar Generator//EN
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METHOD:PUBLISH
X-WR-CALNAME:MASS 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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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150903T132500
DTEND;TZID=America/New_York:20150903T142500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=28189
SUMMARY:MASS Colloquium - A tour of Pritchard Lab
DESCRIPTION:Seminar: MASS Colloquium\nTitle: A tour of Pritchard Lab\nSpeak
er: Diane Henderson\, Penn State\nAbstract: The MASS students will be intr
oduced to the Pritchard Fluids Lab\, a physics that is a part of the Mathe
matics Department.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150910T132500
DTEND;TZID=America/New_York:20150910T142500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=28190
SUMMARY:MASS Colloquium - Congruences for Fishburn Numbers
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Congruences for Fishburn Numbe
rs\nSpeaker: James Sellers\, Penn State\nAbstract: The Fishburn numbers\,
originally considered by Peter C. Fishburn\, have been shown to enumerate
a variety of combinatorial objects. These include unlabelled interval orde
rs on n elements\, (2+2)--avoiding posets with n elements\, upper triangul
ar matrices with nonnegative integer entries and without zero rows or colu
mns such that the sum of all entries equals n\, non--neighbor--nesting mat
ches on [2n]\, a certain set of permutations of [n] which serves as a natu
ral superset of the set of 231--avoiding permutations of [n]\, and ascent
sequences of length n. In December 2013\, Rob Rhoades (Stanford) gave a ta
lk in the Penn State Algebra and Number Theory Seminar in which he describ
ed\, among other things\, the relationship between Fishburn numbers\, quan
tum modular forms\, and Ramanujan's mock theta functions. Motivated by Rho
ades' talk\, George Andrews and I were led to study the Fishburn numbers f
rom an arithmetic point of view - something which had not been done prior.
In the process\, we proved that the Fishburn numbers satisfy infinitely m
any Ramanujan--like congruences modulo certain primes p (the set of which
we will easily describe in the talk). In this talk\, we will describe this
result in more detail as well as discuss how our work has served as the m
otivation for a great deal of related work in the last year by Garvan\, St
raub\, and many others.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150917T132500
DTEND;TZID=America/New_York:20150917T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28191
SUMMARY:MASS Colloquium - Real enumeration problems
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Real enumeration problems\nSpe
aker: Oleg Viro\, Stony Brook University\nAbstract: We will consider probl
ems of mixed setup\, in which the initial object belongs to the elementary
differential geometry (say\, a smoothly immersed generic planar or spheri
cal curve) and we are counting with certain weights the simplest algebraic
curves in special position to the original curve. Say\, bitangent lines o
r tritangent circles. The resulting quantity happens to be a topological i
nvariant of the curve\, which can be calculated combinatorially.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150924T132500
DTEND;TZID=America/New_York:20150924T142500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=28192
SUMMARY:MASS Colloquium - Rectangling the square
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Rectangling the square\nSpeake
r: Aaron Abrams\, Washington and Lee University\nAbstract: There is a famo
us problem called ``squaring the square\,'' named in reference to\nthe cla
ssical problem of squaring the circle (though the problems are unrelated).
\nTo ``square the square'' means to divide a square into smaller squares\,
all of \nwhich have different sizes. Many solutions are known\, and the
problem has many \nvariants.\n\nIn this talk I will discuss this problem a
nd some of its rectangular relatives. One \nquestion we will answer is so
rt of dual to the above: rather than using (rectangular)\ntiles with fixe
d shapes (i.e. squares) and varying sizes\, how can you tile a square \nwi
th (rectangular) tiles that have prescribed sizes but variable shapes?
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151001T132500
DTEND;TZID=America/New_York:20151001T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28193
SUMMARY:MASS Colloquium - Recurrences for Eisenstein series
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Recurrences for Eisenstein ser
ies\nSpeaker: Larry Rolen\, Penn State\nAbstract: In this talk\, we will l
earn about recursive formulas for Eisenstein series\, some of which are cl
assical\, and some of which are surprisingly new. In particular\, we will
see that these important examples of modular forms can be recursively defi
ned in many ways\, which directly yields surprising identities between con
volution sums of sums of divisor functions as well as relations among the
classical Bernoulli numbers. Along the way\, we will learn about important
examples of doubly periodic\, meromorphic functions\, also known as ellip
tic functions\, and their connections to modular forms. This talk will be
self-contained\, and no prior knowledge of modular forms or the related ob
jects mentioned above will be assumed.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151015T132500
DTEND;TZID=America/New_York:20151015T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28195
SUMMARY:MASS Colloquium - Mono-monostatic bodies: the story of the Gömböc
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Mono-monostatic bodies: the st
ory of the Gömböc\nSpeaker: Gábor Domokos\, Budapest University of Tech
nology and Ecomonics\nAbstract: In 1995\, V.I. Arnold conjectured that con
vex\, homogeneous solids with just two static balance points (so-called mo
no-monostatic bodies) may exist. Ten years later\, based on a constructive
proof\, the first such object (dubbed "Gömböc") was built. \n\nThe newl
y discovered objects show various interesting features. We will point out
that mono-monostatic bodies are neither flat\, nor thin\, they are not sim
ilar to typical objects with more equilibria and they are hard to approxim
ate by polyhedra. Despite these "negative" traits\, there seems to be stro
ng indication that these forms appear in the living Nature due to their sp
ecial mechanical properties: some turtle species evolved special shell geo
metries close to the Gömböc to facilitate self-righting.\n\nThe first nu
mbered Gömböc (Gömböc 001) was given to V.I. Arnold on the occasion of
his 70th birthday in Moscow. Here Arnold proposed that the Gömböc may p
lay a role in explaining the geometric evolution of pebbles. I will discus
s some mathematical and geophysical aspects of this conjecture in the Depa
rtment Colloquium.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151022T132500
DTEND;TZID=America/New_York:20151022T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28203
SUMMARY:MASS Colloquium - Flavor of Morse Theory
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Flavor of Morse Theory\nSpeake
r: Augustin Banyaga\, Penn State\nAbstract: In 1934\, Marston Morse initia
ted a study (now known as Morse Theory) relating critical points of some s
pecial function f on a smooth manifold M to some topological invariants of
M\, which are independent\nof the particular choice of the function f.
\nIn this talk\, I describe these special functions ( called Morse functio
ns) and give some simple examples. Then I proceed with a simple result th
at the Euler characteristic of a manifold M can be given in terms of criti
cal points of a Morse function. Finally\, I will discuss ( and illustrate
by a simlpe example) the theorem that a Morse function on M determines a C
W complex structure on M. If time permits\, I will\nmention some groundbre
aking theorems obtained using Morse Theory\, like Smale's proof of Poincar
e conjecture in dimension bigger or equal to 5\,and the h-cobordism theore
m. I will also mention the construction of Morse Homology\, and Floer Homo
logy\, which play a central role in many areas of Mathematics and Mathema
tical Physics. \nI recommend reading the beautiful book by Milnor " Morse
Theory" and chapter 3 in the book "Morse Homology" by A.Banyaga and D.Hurt
ubise.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151029T132500
DTEND;TZID=America/New_York:20151029T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28196
SUMMARY:MASS Colloquium - Sphere packing in 2.5 dimensions
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Sphere packing in 2.5 dimensio
ns\nSpeaker: Ken Stephenson\, University of Tennessee\nAbstract: The dense
st packing of unit-diameter spheres (i.e. discs) in 2D\nis hexagonal --- n
amely\, the "penny-packing" wherein every disc is tangent\nto 6 others. Th
e 3D version of the penny-packing is the "grocer-packing"\,\nthe configura
tion you see with oranges stacked on a grocery counter. Around\n1600 Keple
r conjectured that this grocer-packing is the densest possible in 3D\,\nan
d after a mere 400 years\, Tom Hales\, his collaborators\, and clever comp
uter\nwork have proven Kepler correct.\n\nIn this talk we consider packing
s of unit-diameter spheres in 3D\, but now\nwith the side condition that t
hey all be tangent to a fixed cylinder. Taking\na cue from history\, we fo
cus on hexagonal patterns and speculate on density.\nHowever\, surprising
issues enter the picture and suggest that this new problem\nhovers somewhe
re between the 2D and 3D cases --- hence the 2.5D of our title.\nI will us
e plenty of pictures and hope to get you to exercise your\nintuition a lit
tle as we see if there's a reasonable conjecture to make.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151105T132500
DTEND;TZID=America/New_York:20151105T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28197
SUMMARY:MASS Colloquium - Mechanisms of Chaos
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Mechanisms of Chaos\nSpeaker:
Leonid Bunimovich\, Georgia Institute of Technology\nAbstract: Chaotic mot
ion is caused by internal instability of dynamics (system's evolution). th
e last means that starting with arbitrarily closed to each other states th
e system will evolve very differently. We explain why systems with chaotic
dynamics are typical among real systems as well as of their mathematical
models. The main mechanisms generating chaotic motion will be described.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151112T132500
DTEND;TZID=America/New_York:20151112T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28198
SUMMARY:MASS Colloquium - Latin squares
DESCRIPTION:Seminar: MASS Colloquium\nTitle: Latin squares\nSpeaker: Gary M
ullen\, Penn State\nAbstract: Good problems in mathematics are often easy
to describe but their solutions may be difficult to obtain\, or perhaps ar
e even unknown today. Many such problems arise in number theory. Latin sq
uares form another set of such problems. Latin squares are interesting com
binatorial objects with numerous properties. Many of these properties are
easy to describe\, and yet\, many of the them are very difficult to prove.
We will discuss the number of latin squares\, which despite the use of mo
dern computers\, is still not known except for some very small cases. We w
ill also discuss sets of mutually orthogonal latin squares for which we ha
ve many interesting open problems.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151119T132500
DTEND;TZID=America/New_York:20151119T142500
LOCATION:MB113
URL:http://www.math.psu.edu/seminars/meeting.php?id=28199
SUMMARY:MASS Colloquium - The mathematics of internet search
DESCRIPTION:Seminar: MASS Colloquium\nTitle: The mathematics of internet se
arch\nSpeaker: Gil Bor\, Centro de Investigación en Matemáticas\, Mexico
\nAbstract: An Internet search engine such as Google typically retrieves m
illions of search results in a fraction of a second\, of which only the to
p few results are ever used by the searcher\; the order in which the resul
ts are presented must therefore be chosen rather carefully. How is it done
? A key ingredient is a web page’s “rank”\, reflecting somehow the w
eb page importance. The rank is determined by the “PageRank algorithm”
\, which counts each link to a page as a “recommendation”\, weighing e
ach recommendation by the rank of the recommending page… We will see in
this talk how to avoid the obvious circularity of this procedure\, as well
as some other less-obvious traps. The algorithm is a remarkable applicati
on of the mathematical theory of Markov Chains\, developed over a century
ago. The same algorithm is useful in many other situations\, such as the
ranking of football teams and DNA’s genes.
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