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:20160114T111500
DTEND;TZID=America/New_York:20160114T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29223
SUMMARY:Algebra and Number Theory Seminar - Systems of $\\ell$-adic represe
ntations arising from abelian varieties
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Systems of $
\\ell$-adic representations arising from abelian varieties\nSpeaker: Yuri
Zarhin\, Penn State University\nAbstract: Famous (and still unproven in fu
ll generality) conjectures of\nSerre-Grothendieck\, Tate and Fontaine-Mazu
r describe $\\ell$-adic\nrepresentations that arise from the action of th
e absolute Galois group of\na number field $K$ on the (twisted) $\\ell$-ad
ic cohomology groups of varieties that are defined over $K$.\n\nAssuming a
ll these conjectures\, we discuss the following question: which $\\ell$-ad
ic representations correspond to the $\\ell$-adic Tate modules of an abeli
an variety? We give an answer for abelian varieties without complex multi
plication.\n\nThis is a report on a joint work with Stefan Patrikis (U of
Utah) and Felipe Voloch (U of Texas\, Austin).
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160121T111500
DTEND;TZID=America/New_York:20160121T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29224
SUMMARY:Algebra and Number Theory Seminar - Rational curves on elliptic sur
faces
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Rational cur
ves on elliptic surfaces\nSpeaker: Douglas Ulmer\, Georgia Institute of Te
chnology\nAbstract: Given a non-isotrivial elliptic curve E over K=F_q(t)
\, there is always a finite extension L of K which is itself a rational fu
nction field such that E(L) has large rank. The situation is completely d
ifferent over complex function fields: For "most" E over K=C(t)\, the rank
E(L) is zero for any rational function field L=C(u). The yoga that sugge
sts this theorem leads to other remarkable statements about rational curve
s on surfaces generalizing a conjecture of Lang.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160128T111500
DTEND;TZID=America/New_York:20160128T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29225
SUMMARY:Algebra and Number Theory Seminar - The asymptotic formula in Warin
g's problem: higher order expansions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The asymptot
ic formula in Waring's problem: higher order expansions\nSpeaker: Robert C
. Vaughan\, Penn State University\nAbstract: When k>1 and s is sufficientl
y large in terms of k\, in joint work with Trevor Wooley an explicit multi
-term asymptotic expansion for the number of representations of a large na
tural number as the sum of s positive integral k-th powers is derived.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160204T111500
DTEND;TZID=America/New_York:20160204T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29226
SUMMARY:Algebra and Number Theory Seminar - TBA
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: TBA\nSpeaker
: Yeong-Wook Kwon\, Sungkyunkwan University
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160211T111500
DTEND;TZID=America/New_York:20160211T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29227
SUMMARY:Algebra and Number Theory Seminar - Connections Between Path Partit
ions and Restricted m-ary Partitions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Connections
Between Path Partitions and Restricted m-ary Partitions\nSpeaker: James Se
llers\, Penn State University\nAbstract: In this talk\, we will describe u
nique path partitions (whose motivation comes from representation theory o
f the symmetric group). Once this introduction is complete\, we will disc
uss an explicit characterization of the unique path partitions of n (or up
-partitions for short) in terms of partitions we call strongly decreasing
(and which are closely related to the non-squashing partitions of Sloane a
nd JAS). We then discuss numerous connections between up-partitions and ce
rtain types of binary partitions. Thanks to such connections with binary p
artitions\, we conjecture and prove various arithmetic properties of u(n)
\, the number of unique path partitions of n. We will close the talk with
a discussion of generalizations to certain types of m-ary partitions as we
ll as very recent work on arithmetic properties satisfied by such m-ary pa
rtition functions. This talk will touch on joint works of Christine Besse
nrodt\, Jorn Olsson\, and JAS\; George Andrews\, Aviezri Fraenkel\, and JA
S\; and George Andrews\, Eduardo Brietzke\, Oystein Rodseth\, and JAS.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160218T111500
DTEND;TZID=America/New_York:20160218T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29228
SUMMARY:Algebra and Number Theory Seminar - Cones of higher codimension cyc
les
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Cones of hig
her codimension cycles\nSpeaker: Izzet Coskun\, University of Illinois at
Chicago\nAbstract: There is a well-developed theory of effective and nef d
ivisors on projective varieties. In contrast\, the theory of higher codime
nsion cycles is much more difficult and we lack good criteria for determin
ing when cycle classes are effective or nef. In this talk\, I will discuss
joint work with John Lesieutre on higher codimension pseudo-effective con
es of blowups of projective space. In particular\, we show that for a very
general point blowup of projective space which is a Mori Dream Space all
higher codimension effective cones are finitely generated. This is false f
or blowups of projective space along higher dimensional subvarieties. If t
ime permits\, I will discuss joint work with Dawei Chen on higher codimens
ion cycles on moduli spaces of curves.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160225T111500
DTEND;TZID=America/New_York:20160225T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29229
SUMMARY:Algebra and Number Theory Seminar - Zeta-polynomials for modular fo
rm periods
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Zeta-polynom
ials for modular form periods\nSpeaker: Larry G. Rolen III\, Penn State Un
iversity\nAbstract: Answering problems of Manin\, we use the critical $L$-
values of even weight newforms $f$ to define zeta-polynomials $Z_f(s)$ whi
ch satisfy the functional equation $Z_f(s)=\\pm Z_f(1-s)$\, and which obey
the Riemann Hypothesis: if $Z_f(\\rho)=0$\, then $\\Re(\\rho)=1/2$. The z
eros of the $Z_f(s)$ on the critical line in $t$-aspect are distributed in
a manner which is somewhat analogous to those of classical zeta-functions
. \n These polynomials are assembled using (signed) Stirling numbers an
d "weighted moments" of critical values $L$-values. In analogy with Ehrha
rt polynomials which keep track of integer points in polytopes\, the $Z_f(
s)$ keep track of arithmetic information. Assuming the Bloch--Kato Tamagaw
a Number Conjecture\, they encode the arithmetic of a combinatorial arith
metic-geometric object which we call the "Bloch-Kato complex" for $f$. Loo
sely speaking\, these are graded sums of weighted moments of orders of \\v
{S}afarevi\\v{c}--Tate groups associated to the Tate twists of the modular
motives.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160303T111500
DTEND;TZID=America/New_York:20160303T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29230
SUMMARY:Algebra and Number Theory Seminar - A heuristic for boundedness of
elliptic curves
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: A heuristic
for boundedness of elliptic curves\nSpeaker: Jennifer Park\, University of
Michigan\nAbstract: I will discuss a heuristic that predicts that the ran
ks of all but finitely many elliptic curves defined over Q are bounded abo
ve by 21. This is joint work with Bjorn Poonen\, John Voight\, and Melanie
Matchett Wood.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160310T111500
DTEND;TZID=America/New_York:20160310T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29231
SUMMARY:Algebra and Number Theory Seminar - Spring Break
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Spring Break
\nSpeaker: No seminar\, PSU
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160317T111500
DTEND;TZID=America/New_York:20160317T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29232
SUMMARY:Algebra and Number Theory Seminar - Labeled trees\, divisorial valu
ations at infinity\, and the two-dimensional Jacobian Conjecture
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Labeled tree
s\, divisorial valuations at infinity\, and the two-dimensional Jacobian C
onjecture\nSpeaker: Alex Borisov\, Binghamton University\nAbstract: Starti
ng from a projective plane and performing several blowups of points at inf
inity\, one can get various smooth compactifications of the affine plane.
Each irreducible component of the complement of the affine plane gives a v
aluation on the field of rational functions in two variables. These valuat
ions are called divisorial valuations\, and they play an important role in
many geometric approaches to the two-dimensional Jacobian Conjecture. We
will introduce two discrete invariants of these valuations\, and discuss t
heir significance and limitations for the Jacobian Conjecture. Despite the
algebro-geometric motivation\, our methods are essentially combinatorial
\, based on the (dual) intersection graph of curves at infinity.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160324T111500
DTEND;TZID=America/New_York:20160324T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29233
SUMMARY:Algebra and Number Theory Seminar - Quantum unique ergodicity for h
alf-integral weight forms
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Quantum uniq
ue ergodicity for half-integral weight forms\nSpeaker: Maksym Radziwill\,
Rutgers Universsity\nAbstract: I will discuss joint work with Steve Lester
\, in which we establish conditionally on the Generalized Riemann Hypothes
is\, Quantum Unique Ergodicity for half-integral weight Hecke cusp forms b
elonging to Kohnen's subspace. The result can be viewed as the half-integ
ral analogue of the recent unconditional theorems addressing the integer w
eight cases (due to Lindenstrauss and Holowinsky-Soundararajan). I will d
iscuss the motivation for the question and the peculiarities of the half-i
ntegral setting. Moreover I will draw attention to an analogy between sie
ves and L-functions which is central to the proof.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160331T111500
DTEND;TZID=America/New_York:20160331T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29234
SUMMARY:Algebra and Number Theory Seminar - Moonshine
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Moonshine\nS
peaker: Michael Griffin\, Princeton University\nAbstract: In the 1970’s
\, as mathematicians worked to classify the finite simple groups\, Ogg\, M
cKay and others observed several striking apparent coincidences connecting
the then-conjectural Monster group (the largest of the sporadic simple gr
oups) to the theory of modular functions. These ‘coincidences’ became
known as “Monstrous Moonshine” and were made into a precise conjecture
by Conway and Norton. They conjectured the existence of a naturally occur
ring graded infinite dimensional Monster module whose graded traces at ele
ments of the monster group give the Fourier coefficients of distinguished
modular functions. Borcherds proved the conjecture in 1992\, embedding Moo
nshine in a deeper theory of vertex operator algebras. For this work Borch
erds was awarded a Fields Medal. Fifteen years after Borcherds’ proof\,
Witten conjectured important connections between Monstrous Moonshine and p
ure quantum gravity in three dimensions. Under Witten’s theory\, the irr
educible components of the Monster module represent black hole states. Wit
ten asked how these states are distributed. In joint work with Ken Ono and
John Duncan\, we answer Witten’s question giving exact formulas for the
se distributions.\n \nMoonshine type-phenomena have been observed for othe
r groups besides the Monster. Notably\, the Umbral Moonshine conjectures o
f Cheng\, Duncan\, and Harvey connects the automorphism groups of the 24 N
iemeier lattices to the Fourier coefficients of certain mock modular forms
. Many mathematical physicists anticipate physical interpretations for Umb
ral Moonshine similar to Witten’s application of Monstrous Moonshine. Th
e first case of Umbral Moonshine\, connected to the Leech Lattice\, is cov
ered by Monstrous Moonshine\, while the second is covered by Gannon’s pr
oof in 2013 of Moonshine for the Mathieu group M24. We verify the remainin
g 22 cases.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160407T111500
DTEND;TZID=America/New_York:20160407T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29235
SUMMARY:Algebra and Number Theory Seminar - Divisor sums in short intervals
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Divisor sums
in short intervals\nSpeaker: Bradley Rogers\, University of Michigan\nAbs
tract: In this talk we will discuss recent joint work with Jon Keating\, E
dva Roditty-Gershon\, and Zeev Rudnick regarding the distribution sums of
the k-fold divisor function over short intervals. This distribution is clo
sely related to moments of the Riemann zeta function. We will talk about n
ew conjectures for the variance of these sums\, which have several surpris
ing features\, and also discuss an analogous result in a function field se
tting which motivates the conjectures and which may be proved by using\, i
n part\, random matrix theory.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160414T111500
DTEND;TZID=America/New_York:20160414T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29236
SUMMARY:Algebra and Number Theory Seminar - The most popular values of the
largest prime divisor function
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: The most pop
ular values of the largest prime divisor function\nSpeaker: Nathan McNew\,
Towson University\nAbstract: Consider the largest prime factor of each of
the integers in the interval [2\,x] and let q(x) denote the prime number
which shows up most frequently in this list\, the mode of the largest prim
e factors of the integers in [2\,x]. In addition to using estimates of smo
oth numbers to investigate the behavior of this function as x tends to inf
inity\, we look at the range of q(x) and see that it misses most of the pr
imes. We conjecture that the set of these "popular primes" is related to o
ther interesting subsets of the prime numbers.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160421T111500
DTEND;TZID=America/New_York:20160421T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29237
SUMMARY:Algebra and Number Theory Seminar - Quantum and mock modular forms
arising from eta-theta functions
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Quantum and
mock modular forms arising from eta-theta functions\nSpeaker: Amanda Folso
m\, Amherst College\nAbstract: In this talk\, we will discuss joint work w
ith Garthwaite\, Kang\, Swisher\, and Treneer\, in which we construct quan
tum modular and mock modular forms. These forms arise from ordinary modul
ar forms which are simultaneously eta quotients and theta functions. Eta
quotients have been previously studied by Conway-Norton\, Dummit-Kisilevsk
y-McKay\, Lemke Oliver\, Martin\, and Mason\, among others. As corollarie
s to our work\, we explicitly evaluate Eichler integrals of eta-theta func
tions as finite q-hypergeometric sums\, and establish related curious alge
braic identities.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20160428T111500
DTEND;TZID=America/New_York:20160428T120500
LOCATION:MB106
URL:http://www.math.psu.edu/seminars/meeting.php?id=29238
SUMMARY:Algebra and Number Theory Seminar - Exceptional Dirichlet Character
s and some of their Footprints
DESCRIPTION:Seminar: Algebra and Number Theory Seminar\nTitle: Exceptional
Dirichlet Characters and some of their Footprints\nSpeaker: John Friedland
er\, University of Toronto\nAbstract: We begin with a survey of old result
s about exceptional characters and then discuss how this\, admittedly impl
ausible\, supposition manifests itself in connection with the counting of
primes\, whether by sieve methods or by\ncombinatorial identities.
END:VEVENT
END:VCALENDAR