BEGIN:VCALENDAR
PRODID:-//PSU Mathematics Department//Seminar iCalendar Generator//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Algebra and Number Theory 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
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:19701101T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140828T111500
DTEND;TZID=America/New_York:20140828T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21879
SUMMARY:Algebra and Number Theory Seminar - Lunch
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Lunch\nSpeak
er: ANT group\, PSU\nAbstract: Meet at 11:30 by Octacube
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140904T111500
DTEND;TZID=America/New_York:20140904T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21880
SUMMARY:Algebra and Number Theory Seminar - Galois groups of Mori polynomia
ls\, semistable curves and monodromy
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Galois group
s of Mori polynomials\, semistable curves and monodromy\nSpeaker: Yuri Zar
hin\, Penn State University\nAbstract: We study the monodromy of a certain
class of semistable hyperelliptic\ncurves that was introduced by Shigefum
o Mori forty years ago. Using ideas\nof Chris Hall\, we prove that the cor
responding monodromy groups are\n(almost) ``as large as possible".
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140911T111500
DTEND;TZID=America/New_York:20140911T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21881
SUMMARY:Algebra and Number Theory Seminar - The Strong CM Lifting Problem
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The Strong C
M Lifting Problem\nSpeaker: Taisong Jing\, Penn State University\nAbstract
: It is known that an abelian variety over a finite field may not admit a
lifting to an abelian variety with complex multiplication in characteristi
c 0. The question of strong CM lifting (sCML) asks whether we can kill the
obstructions to a CM lifting by requiring the whole ring of integers in t
he CM field act on the abelian variety. I will give counterexamples to que
stion (sCML)\, prove the answer to question (sCML) is affirmative under ce
rtain assumptions on the CM field\, and explain some follow-up problems th
at I have been working on.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140918T111500
DTEND;TZID=America/New_York:20140918T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21882
SUMMARY:Algebra and Number Theory Seminar - Hasse principle for generalized
Kummer varieties
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Hasse princi
ple for generalized Kummer varieties\nSpeaker: Alexei Skorobogatov\, Imper
ial College London\nAbstract: Rational points on Kummer varieties can be s
tudied via the variation of Selmer groups of quadratic twists of the under
lying abelian variety\, using an idea of Swinnerton-Dyer. In joint work wi
th Yonatan Harpaz we consider the case when the Galois action on 2-torsion
has a large image. Under a mild additional assumption we prove the Hasse
principle assuming the finiteness of relevant Shafarevich-Tate groups. Our
approach is inspired by the work of Mazur and Rubin.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20140925T111500
DTEND;TZID=America/New_York:20140925T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21883
SUMMARY:Algebra and Number Theory Seminar - Squares: Additive Questions and
Partitions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Squares: Add
itive Questions and Partitions\nSpeaker: Robert C. Vaughan\, Penn State Un
iversity
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141002T111500
DTEND;TZID=America/New_York:20141002T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21884
SUMMARY:Algebra and Number Theory Seminar - A reciprocity law for Drinfeld
modules
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: A reciprocit
y law for Drinfeld modules\nSpeaker: Mihran Papikian\, Penn State Universi
ty\nAbstract: First\, I will explain what is a "reciprocity law". Then I w
ill describe such law arising from Drinfeld modules. Finally\, I will appl
y this law to derive a criterion for the splitting modulo primes of a clas
s of non-solvable polynomials over $\\mathbb{F}_q(T)$ that was studied by
Abhyankar. (This is a joint work with Alina Cojocaru.)
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141009T111500
DTEND;TZID=America/New_York:20141009T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21885
SUMMARY:Algebra and Number Theory Seminar - A quick tour of discrepancy the
ory
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: A quick tour
of discrepancy theory\nSpeaker: William Chen\, MacQuarie University\nAbst
ract: The birth of geometric discrepancy theory is usually attributed\nto
the fundamental work of Klaus Roth in 1954. The present scope of the\nsubj
ect is due in no small part to the many important results of Wolfgang\nSch
midt in the 1960s and 1970s. It is fair to say that every subsequent\nwork
er in the subject have been motivated and encouraged\, directly or\nindire
ctly\, by these two pioneers and their work. Lower bound results in\ndiscr
epancy theory exhibit the limitations to just point distributions\,\nwhere
as upper bound results lead to point distributions that are close to\nbest
possible under such limitations. In this expository talk\, we shall\ndisc
uss some of the main results obtained over the last 60 years\, and\nintrod
uce to the audience a number of lower and upper bound techniques. We\nshal
l also briefly discuss some open questions.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141016T111500
DTEND;TZID=America/New_York:20141016T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21886
SUMMARY:Algebra and Number Theory Seminar - The divisor function on arithme
tic progressions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The divisor
function on arithmetic progressions\nSpeaker: Robert C. Vaughan\, Penn Sta
te University
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141023T111500
DTEND;TZID=America/New_York:20141023T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21887
SUMMARY:Algebra and Number Theory Seminar - Algebraic independence of deriv
atives of Carlitz periods
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Algebraic in
dependence of derivatives of Carlitz periods\nSpeaker: Dale Brownawell\, P
enn State University
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141030T111500
DTEND;TZID=America/New_York:20141030T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21888
SUMMARY:Algebra and Number Theory Seminar - Hilbert's Tenth Problem for sub
rings of the rational numbers
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Hilbert's Te
nth Problem for subrings of the rational numbers\nSpeaker: Kirsten Eisentr
aeger\, Penn State University\nAbstract: In 1970 Matiyasevich\, building o
n work by Davis\, Putnam and Robinson\, proved that Hilbert's Tenth Proble
m is undecidable. Since then\, analogues of this problem have been studied
by considering polynomial equations over commutative rings other than the
integers. The biggest open problem in the area is Hilbert's Tenth Problem
over the rational numbers. In this talk we will construct some subrings $
R$ of the rationals that have the property that Hilbert's Tenth Problem fo
r $R$ is Turing equivalent to Hilbert's Tenth Problem over the rationals.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141106T111500
DTEND;TZID=America/New_York:20141106T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21889
SUMMARY:Algebra and Number Theory Seminar - Portraits of rational functions
modulo primes
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Portraits of
rational functions modulo primes\nSpeaker: Tom Tucker\, University of Roc
hester\nAbstract: Let F be a rational function of degree > 1 over a numb
er\nfield or function field K and let z be a point that is not preperiodic
. Ingram and Silverman conjecture that for all but finitely many positiv
e integers (m\,n)\, there is a prime p such that z has exact preperiodic m
and exact period n (we call this pair (m\,n) the portrait of z modulo p).
We present some counterexamples to this conjecture and show that a gener
alized form of abc implies -- one that is true for function fields -- impl
ies that these are the only counterexamples. One may also ask a similar q
uestion for tuples of portraits for several point in a number field or fun
ction field. This work is still in progress. The talk represents joint w
ork with several other authors.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141113T111500
DTEND;TZID=America/New_York:20141113T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21890
SUMMARY:Algebra and Number Theory Seminar - The Entropy of Schur-Weyl measu
res
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The Entropy
of Schur-Weyl measures\nSpeaker: Sevak Mkrtchyan\, University of Rochester
\nAbstract: We will study local and global statistical properties of Young
diagrams with respect to a Plancherel-type family of measures called Schu
r-Weyl measures and use the results to answer a question from asymptotic r
epresentation theory. ore precisely\, we will solve a variational problem
to prove a limit-shape result for random Young diagrams with respect to t
he Schur-Weyl measures and apply the results to obtain logarithmic\, order
-sharp bounds for the dimensions of certain representations of finite symm
etric groups.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141120T111500
DTEND;TZID=America/New_York:20141120T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21891
SUMMARY:Algebra and Number Theory Seminar - Zagier polynomials and modified
N\\"{o}rlund polynomials
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Zagier polyn
omials and modified N\\"{o}rlund polynomials\nSpeaker: Atul Dixit\nAbstrac
t: In 1998\, Don Zagier studied the numbers B_{n}^{*} which he\ncalled the
'modified Bernoulli numbers'. They satisfy amusing variants of the\nprope
rties of the ordinary Bernoulli numbers. Recently\, Victor H. Moll\,\nChri
stophe Vignat and I studied an obvious generalization of the modified\nBer
noulli numbers\, which we call 'Zagier polynomials'. These polynomials\nar
e also rich in structure\, and we have shown that a theory parallel to tha
t of ordinary Bernoulli polynomials exists. Zagier showed that his asympto
tic formula for B_{2n}^{*} can be replaced by an exact formula. In an ongo
ing joint work with M. L. Glasser and K. Mahlburg\, we have shown that a s
imilar thing is true for the Zagier polynomials. This exact formula involv
es Chebyshev polynomials and infinite series of Bessel function $Y_{n}(z)$
. Through a motivation coming from diffraction theory\, C. M. Linton has a
lready proved this\, but in a disguised form\, and our proof is new and gi
ves new results along the way. We also derive Zagier's formula as a limiti
ng case of this general formula\, which is interesting in itself. In the s
econd part of my talk\, I will discuss another generalization of the modif
ied Bernoulli numbers that we recently studied along with A. Kabza\, namel
y 'modified N\\"{o}rlund polynomials'\nB_{n}^{(\\alpha)*}\, \\alpha\\in\\m
athbb{N}\, and obtain their generating\nfunction along with applications.â
€‹ The talk will include an interesting mix of special functions\, number
theory\, probability and umbral calculus.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141127T111500
DTEND;TZID=America/New_York:20141127T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21892
SUMMARY:Algebra and Number Theory Seminar - No meeting
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: No meeting\n
Speaker: Mr Turkey\, Thanksgiving
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141204T111500
DTEND;TZID=America/New_York:20141204T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21893
SUMMARY:Algebra and Number Theory Seminar - Uniform Dilations in High Dimen
sions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Uniform Dila
tions in High Dimensions\nSpeaker: Michael Kelly\, University of Michigan
\nAbstract: It is a theorem of Glasner that given an infinite subset X of
the torus R/Z and an epsilon greater than 0 there exists a positive intege
r n such that any interval of length epsilon in R/Z contains a point of th
e set nX (that is\, nX is epsilon-dense in R/Z). The set nX is called a di
lation of X by n. Alon and Peres have shown that the dilation factor n can
be chosen to be a prime or n=f(m) for some integral polynomial f with deg
ree(f)>0 and integer m. We will discuss various developments on these sort
s of topics and I'll present joint work with Le Thai Hoang where we consid
er this phenomenon in higher dimensions.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20141211T111500
DTEND;TZID=America/New_York:20141211T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=21894
SUMMARY:Algebra and Number Theory Seminar - Integral points and orbits in t
he projective plane
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Integral poi
nts and orbits in the projective plane\nSpeaker: Aaron Levin\, Michigan St
ate University\nAbstract: We will begin by discussing the problem of class
ifying the behavior of integral points on affine subsets of the projective
plane. As an application of this study\, we will examine the problem of
classifying endomorphisms of the projective plane with an orbit containing
a Zariski dense set of integral points (with respect to some plane curve)
. This is joint work with Yu Yasufuku.
END:VEVENT
END:VCALENDAR