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:20150115T111500
DTEND;TZID=America/New_York:20150115T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24840
SUMMARY:Algebra and Number Theory Seminar - The Erdos-Heilbronn Problem for
Finite Groups
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The Erdos-He
ilbronn Problem for Finite Groups\nSpeaker: Jeffrey Paul Wheeler\, Univers
ity of Pittsburgh\nAbstract: Additive Number Theory can be best described
as the study of sums of sets of integers. A simple example is given two su
bsets A and B of a set of integers\, what facts can we determine about A+B
where A+B := { a+b | a \\in A andb \\in B }? Note that Lagrange's Four S
quare Theorem can be expressed as N_0 = S + S +\nS + S where N_0 is the se
t of nonnegative integers and S the set of all perfect squares. As well t
he binary version of Goldbach's Conjecture can stated E \\subseteq P + P w
here E be the set of even integers greater than 2 and P the primes\,\n\nA
classic problem in Additive Number Theory was a conjecture of Paul Erdos a
nd Hans Heilbronn which stood as an open problem for over 30 years until p
roved in 1994 by Dias da Silva and Hamidounne. The conjecture had its roo
ts in the Cauchy-Davenport Theorem\, namely if A and B are nonempty subset
s of Z/pZ with p prime\, then |A+B| >= min{p\,|A|+|B|-1\\}\, where A+B :=
{a+b | a \\in A and b \\in B}. Erdos and Heilbronn conjecture in the ear
ly 1960s that if the operation is changed to a restricted sum A \\dot{+} B
:= {a+b | a \\in A and b \\in B\, a \\ne b}\, then |A \\dot{+} B| >=\nmi
n{p\,|A|+|B|-3\\}. We extend these results from Z/pZ to finite groups.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150122T111500
DTEND;TZID=America/New_York:20150122T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24841
SUMMARY:Algebra and Number Theory Seminar - No seminar today
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: No seminar t
oday\nSpeaker: See Colloquium\, Job Candidate
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150129T111500
DTEND;TZID=America/New_York:20150129T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24842
SUMMARY:Algebra and Number Theory Seminar - Descent for specializations of
Galois branched covers
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Descent for
specializations of Galois branched covers\nSpeaker: Ryan Eberhart\, Penn S
tate University\nAbstract: Let G be a finite group and K a number field. H
ilbert's irreducibility theorem states that a regular G-Galois branched co
ver of P^1_K\, the projective line over K\, gives rise to G-Galois field e
xtensions of K by specializing the cover (i.e. plugging in specific coordi
nates into the equations for the cover). A common tactic for progress on t
he Inverse Galois Problem over Q is to construct a G-Galois branched cover
of P^1_Q. We investigate a related line of inquiry: given a G-Galois bran
ched of P^1_K\, do any of the specializations descend to a G-Galois field
extension of Q\, even though the cover itself may not? We prove that the a
nswer is yes when G is cyclic if one allows specializations at closed poin
ts. However\, we show that the answer is in general no if we restrict to s
pecializations at K-rational points. This is joint work with Hilaf Hasson.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150202T111500
DTEND;TZID=America/New_York:20150202T120500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=27339
SUMMARY:Algebra and Number Theory Seminar - Cancelled\, owing to inclement
weather
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Cancelled\,
owing to inclement weather\nSpeaker: Jeffery Lagarias\, University of Mich
igan\nAbstract: Let F_n denote the product of all nonzero\nFarey fractions
of order n and let G_n denote the product\nof all reduced and unreduced F
arey fractions\nof order n. It is known that the reciprocal of G_n is the
product of binomial coefficients on the n-th row of Pascal's triangle. We
present results on the growth rate of log F_n and of log G_n\, and on the
behavior of the p-adic norms of F_n and G_n.\n The p-adic behavior of
G_n is related to the Riemann zeta function on the line Re(s)=0. We presen
t experimental results suggesting that F_n is related to behavior of the
Riemann zeta function on another line. (This is joint work with Harsh Meh
ta (U. South Carolina).)
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150205T111500
DTEND;TZID=America/New_York:20150205T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24843
SUMMARY:Algebra and Number Theory Seminar - No seminar today
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: No seminar t
oday\nSpeaker: See Colloquium\, Job Candidate
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150212T111500
DTEND;TZID=America/New_York:20150212T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24844
SUMMARY:Algebra and Number Theory Seminar - Moduli Interpretations for Nonc
ongruence Modular Curves
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Moduli Inter
pretations for Noncongruence Modular Curves\nSpeaker: Will Chen\, Penn Sta
te University\nAbstract: Quotients of the upper half plane by congruence s
ubgroups of SL(2\,Z) are called modular curves because they are known to b
e moduli spaces parameterizing elliptic curves with an “abelian” level
structure. In my talk I will show that quotients by noncongruence subgrou
ps of SL(2\,Z) also deserve to be called modular curves by showing that th
ey are also moduli spaces parameterizing elliptic curves together with a
nonabelian” level structure.\n\nIf time allows I will also discuss a r
elationship with the unbounded denominators conjecture.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150219T111500
DTEND;TZID=America/New_York:20150219T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24845
SUMMARY:Algebra and Number Theory Seminar - Congruences for Fishburn Number
s
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Congruences
for Fishburn Numbers\nSpeaker: James Sellers\, Penn State University\nAbst
ract: The Fishburn numbers\, originally considered by Peter C. Fishburn\,
have been shown to enumerate a variety of combinatorial objects. These inc
lude unlabelled interval orders on n elements\, (2+2)--avoiding posets wit
h n elements\, upper triangular matrices with nonnegative integer entries
and without zero rows or columns such that the sum of all entries equals n
\, non--neighbor--nesting matches on [2n]\, a certain set of permutations
of [n] which serves as a natural superset of the set of 231--avoiding perm
utations of [n]\, and ascent sequences of length n. \n\nIn December 2013\,
Rob Rhoades (Stanford) gave a talk in the Penn State Algebra and Number T
heory Seminar in which he described\, among other things\, the relationshi
p between Fishburn numbers\, quantum modular forms\, and Ramanujan's mock
theta functions. Motivated by Rhoades' talk\, George Andrews and I were l
ed to study the Fishburn numbers from an arithmetic point of view - someth
ing which had not been done prior. In the process\, we proved that the Fi
shburn numbers satisfy infinitely many Ramanujan--like congruences modulo
certain primes p (the set of which we will easily describe in the talk). I
n this talk\, we will describe this result in more detail as well as discu
ss how our work has served as the motivation for a great deal of related w
ork in the last year by Garvan\, Straub\, and many others.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150226T111500
DTEND;TZID=America/New_York:20150226T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24846
SUMMARY:Algebra and Number Theory Seminar - Jordan Groups and Automorphism
Groups of Algebraic Surfaces
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Jordan Group
s and Automorphism Groups of Algebraic Surfaces\nSpeaker: Tatiana Bandman
\, Bar-Ilan University\nAbstract: A classical theorem of Jordan may be vie
wed as an assertion that all finite subgroups of the complex general linea
r group GL(n) are ``almost abelian". I will discuss a similar property of
the automorphism group of a complex algebraic variety. This is a joint w
ork with Yuri Zarhin.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150305T111500
DTEND;TZID=America/New_York:20150305T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24847
SUMMARY:Algebra and Number Theory Seminar - Zeros of Dirichlet series
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Zeros of Dir
ichlet series\nSpeaker: Robert Vaughan\, Penn State University\nAbstract:
We are concerned here with Dirichlet series\nf(s) = 1 +\\sum_{n=2}^{\\inft
y} \\frac{c(n)}{n^s}\nwhich satisfy a function equation similar to that of
the Riemann zeta function\, typically of the form\nf(s) = \\epsilon 2^s q
^{1/2-s} \\pi^{s-1} \\Gamma(1-s) \\big(\\sin\\textstyle\\frac{\\pi}{2}(s+
\\kappa)\\big) f(1-s)\,\nbut for which the Riemann hypothesis is false.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150312T111500
DTEND;TZID=America/New_York:20150312T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24848
SUMMARY:Algebra and Number Theory Seminar - No seminar today
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: No seminar t
oday\nSpeaker: Spring Break\, Somewhere sunny
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150319T111500
DTEND;TZID=America/New_York:20150319T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24849
SUMMARY:Algebra and Number Theory Seminar - Construction of abelian varieti
es with a given Weil number
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Construction
of abelian varieties with a given Weil number\nSpeaker: Frans Oort\, Univ
ersity of Utrecht\, visiting University of Pennsylvania\nAbstract: In this
talk we sketch methods of algebraic geometry to show once a Weil number i
s given how to construct an abelian variety with that number as Frobenius.
This result was known before\, but proofs were through analytic parametr
izations. This is joint work with Ching-Li Chai.\n\nFor a given prime pow
er q a Weil q-number is an algebraic integer having root q as absolute val
ue. We will see that these numbers are easily classified\, and using eleme
ntary algebra we can construct many examples. Weil showed that the Froben
ius of an abelian variety over a field with q elements is a Weil q-number
(the first proven case of the Weil conjectures). We recall a (well-known)
easy proof of this deep theorem.\n Honda and Tate showed that every We
il number appears in this way. Hence\nwe have access to existence of abel
ian varieties just by choosing Weil numbers. We will present a proof that
indeed every Weil number appears this way (the trickiest part of the Hoda-
Tate theory).\n\n In my talk I will give explicit definitions of conce
pts used\, and I will\npresent proofs\, that are understandable for a gene
ral audience. These deep and beautiful results are now easily understood!
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150326T111500
DTEND;TZID=America/New_York:20150326T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24850
SUMMARY:Algebra and Number Theory Seminar - Arithmetic Combinatorics and Ch
aracter Sums
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Arithmetic C
ombinatorics and Character Sums\nSpeaker: Brandon Hanson\, University of T
oronto\nAbstract: In this talk I will present a few ideas as to how charac
ter sums may be useful in arithmetic combinatorics and vice versa. I will
talk about how character sums can be used to make progress on problems com
ing from arithmetic combinatorics. On the other hand\, arithmetic combina
torics can prove useful when going the other way. Indeed\, many character
sums are easy to estimate provided they have enough summands - this is som
etimes called the square-root barrier and is a natural obstruction. I will
show how the sum-product phenomenon can be leveraged to push past this ba
rrier.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150402T111500
DTEND;TZID=America/New_York:20150402T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24851
SUMMARY:Algebra and Number Theory Seminar - Homogeneous additive equations
over p-adic fields
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Homogeneous
additive equations over p-adic fields\nSpeaker: Mike Knapp\, Loyola Univer
sity\nAbstract: In this talk\, we will study solutions of the equation a_1
x_1^d + a_2x_2^d + ... + a_sx_s^d = 0 in p-adic integers. It has been kno
wn since the 1960s that if s>= d^2 + 1\, then this equation will have nont
rivial p-adic solutions for any prime p\, regardless of the coefficients.
This bound is sharp when $d+1$ is prime\, but can be reduced when $d+1$ i
s composite. Given a degree d\, we define \\Gamma^*(d) to be the smallest
number of variables which guarantees that the above equation has nontrivi
al p-adic solutions for all p. In the first half of the talk\, we will ev
aluate the exact values of \\Gamma^*(d) for some small degrees. After tha
t\, we will focus specifically on the 2-adic version of the problem and gi
ve an exact formula for the smallest number of variables which guarantees
that the equation has nontrivial 2-adic solutions.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150409T111500
DTEND;TZID=America/New_York:20150409T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24852
SUMMARY:Algebra and Number Theory Seminar - Rational points near hypersurfa
ces: with applications to the Dimension Growth Conjecture and metric dioph
antine approximation
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Rational poi
nts near hypersurfaces: with applications to the Dimension Growth Conjectu
re and metric diophantine approximation\nSpeaker: Jing-Jing Huang\, Univer
sity of Toronto\nAbstract: The distribution of rational points on algebrai
c varieties is a central problem in number theory. An even more general pr
oblem is to investigate rational points near manifolds\, where the algebra
ic condition is replaced with the non-vanishing curvature condition. In th
is talk\, we will establish a sharp bound for the number of rational point
s of a given height and within a given distance to a hypersurface. This ha
s surprising applications to counting rational points lying on the manifol
d\; indeed setting the distance to zero\, we are able to prove an analogue
of Serre's Dimension Growth Conjecture (originally stated for projective
varieties) in this general setup. In the second half of the talk\, we will
focus on metric diophantine approximation on manifolds. A long standing c
onjecture in this area is the Generalized Baker-Schmidt Problem. As anothe
r consequence of the main counting result above\, we settle this problem f
or all hypersurfaces with non-vanishing Gaussian curvatures. Finally\, if
time permits\, we will briefly elaborate on the main ideas behind the proo
f.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150416T111500
DTEND;TZID=America/New_York:20150416T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24853
SUMMARY:Algebra and Number Theory Seminar - Power Partitions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Power Partit
ions\nSpeaker: Ayla Gafni\, Penn State University\nAbstract: In 1918\, Har
dy and Ramanujan published a seminal paper which included an asymptotic fo
rmula for the partition function. In their paper\, they also state withou
t proof an asymptotic equivalence for the number of partitions of a number
into $k$-th powers. In 1934\, E. Maitland Wright [Acta Mathematica\, 63
(1934) 143--191] gives a very precise asymptotic formula for this restrict
ed partition function\, but his argument is quite long and difficult. In
this talk\, I will present an asymptotic formula for the number of partiti
ons into $k$-th powers using a relatively simple method\, while maintainin
g a decent error term.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150423T111500
DTEND;TZID=America/New_York:20150423T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24854
SUMMARY:Algebra and Number Theory Seminar - Arithmetic properties of the Fr
obenius traces defined by a rational abelian variety
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Arithmetic p
roperties of the Frobenius traces defined by a rational abelian variety\nS
peaker: Alina Cojocaru\, University of Illinois at Chicago
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150424T111500
DTEND;TZID=America/New_York:20150424T120500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=27929
SUMMARY:Algebra and Number Theory Seminar - Faltings heights and modular fo
rms
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Faltings hei
ghts and modular forms\nSpeaker: Prof. Shouwu Zhang\, Princeton University
\nAbstract Link: http://\nAbstract: In his seminal work on Tate\, Shafarev
ich and Mordell conjectures\, Faltings introduced his modular height for
\nan abelian variety over a number field. Despite its importance in many a
pplications in arithmetic geometry\,\nit is difficult to evaluate this he
ight in dimension greater than 1. I will first describe some construction
of modular forms attached\nto abelian varieties with Faltings heights a
s constant terms\, and then give some applications.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150430T111500
DTEND;TZID=America/New_York:20150430T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24855
SUMMARY:Algebra and Number Theory Seminar - Products of Farey fractions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Products of
Farey fractions\nSpeaker: Jeff Lagarias\, University of Michigan\nAbstract
: Let F_n denote the product of all nonzero Farey fractions of order n and
let G_n denote the product of all reduced and unreduced Farey fractions o
f order n. It is known that the reciprocal of G_n is the product of binomi
al coefficients on the n-th row of Pascal's triangle. We present results o
n the growth rate of log F_n and of log G_n\, and on the behavior of the p
-adic norms of F_n and G_n. The p-adic behavior of G_n is related to the R
iemann zeta function on the line Re(s)=0. We present experimental results
suggesting that F_n is related to behavior of the Riemann zeta function on
another line. (This is joint work with Harsh Mehta (U. South Carolina).)
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150507T111500
DTEND;TZID=America/New_York:20150507T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=24856
SUMMARY:Algebra and Number Theory Seminar - TBA
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: TBA\nAbstrac
t Link: http://
END:VEVENT
END:VCALENDAR