BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Gaurav Patil (University of Toronto)
DTSTART:20241017T200000Z
DTEND:20241017T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/1
DESCRIPTION:Title: Par
ametrization of rings of finite rank - a geometric approach and their use
in counting number fields\nby Gaurav Patil (University of Toronto) as
part of Calgary Algebra and Number Theory Seminar\n\nLecture held in MS 33
7.\n\nAbstract\nWe describe parametrizations of rings that generalize the
notions of monogenic rings and binary rings. We use these parametrizations
to give better lower bounds on the number of number fields of degree n an
d bounded discriminant.\n\nRecorded video Passcode: $+*v9L8p\n
LOCATION:https://researchseminars.org/talk/ANTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renate Scheidler (University of Calgary)
DTSTART:20241024T200000Z
DTEND:20241024T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/2
DESCRIPTION:Title: Ori
enteering with One Endomorphism\nby Renate Scheidler (University of Ca
lgary) as part of Calgary Algebra and Number Theory Seminar\n\nLecture hel
d in MS 337.\n\nAbstract\nGiven two elliptic curves\, the path finding pro
blem asks to find an isogeny (i.e. a group homomorphism) between them\, su
bject to certain degree restrictions. Path finding has uses in number theo
ry as well as applications to cryptography. For supersingular curves\, thi
s problem is known to be easy when one small endomorphism or the entire en
domorphism ring are known. Unfortunately\, computing the endomorphism ring
\, or even just finding one small endomorphism\, is hard. How difficult i
s path finding in the presence of one (not necessarily small) endomorphism
? We use the volcano structure of the oriented supersingular isogeny graph
to answer this question. We give a classical algorithm for path finding t
hat is subexponential in the degree of the endomorphism and linear in a ce
rtain class number\, and a quantum algorithm for finding a smooth isogeny
(and hence also a path) that is subexponential in the discriminant of the
endomorphism. A crucial tool for navigating supersingular oriented isogeny
volcanoes is a certain class group action on oriented elliptic curves whi
ch generalizes the well-known class group action in the setting of ordinar
y elliptic curves.\n\nThe recorded video Passcode: Z&7TyEGW\n
LOCATION:https://researchseminars.org/talk/ANTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Avci (Boğaziçi University)
DTSTART:20241031T200000Z
DTEND:20241031T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/3
DESCRIPTION:Title: Tor
sion of Rational Elliptic Curves over the Cyclotomic Extensions of $\\math
bb{Q}$\nby Omer Avci (Boğaziçi University) as part of Calgary Algebr
a and Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nLet $E
$ be an elliptic curve defined over $\\Q$. Let $p>3$ be a prime such that
$p-1$ is not divisible by $3\,4\,5\,7\,11$. In this article we classify
the groups that can arise as $E(\\mathbb{Q}(\\zeta_p))_{\\text{tors}}$ up
to isomorphism. The method illustrates techniques for eliminating possible
structures that can appear as a subgroup of $E(\\mathbb{Q}^{ab})_{\\text{
tors}}.$\n
LOCATION:https://researchseminars.org/talk/ANTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART:20241121T210000Z
DTEND:20241121T220000Z
DTSTAMP:20260422T225822Z
UID:ANTS/4
DESCRIPTION:Title: Pac
kets and the fine structure of L-functions\nby Clifton Cunningham (Uni
versity of Calgary) as part of Calgary Algebra and Number Theory Seminar\n
\nLecture held in MS 337.\n\nAbstract\nAutomorphic representations\, which
provide a vast generalization of modular forms\, are are grouped together
into so-called L-packets according to the L-functions they produce. From
this point of view\, automorphic representations give a kind of fine-struc
ture to L-functions themselves. While L-packets of automorphic representat
ions are natural from this point of view\, they have some deficiencies whe
n one looks for how L-functions transfer between different groups that are
related by what we call “functoriality” in the Langlands program. To
address these deficiencies\, Arthur introduced A-packets of automorphic re
presentations\; each A-packet is an enlarged L-packet. However\, A-packets
have not been defined in the same generality as L-packets. In this talk I
will review this story and sketch work by my research group on a generali
zation of A-packets. The talk includes comments on applications of A-packe
ts to number theory\, some of which are highly speculative.\n
LOCATION:https://researchseminars.org/talk/ANTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dang-Khoa Nguyen (University of Calgary)
DTSTART:20241128T210000Z
DTEND:20241128T220000Z
DTSTAMP:20260422T225822Z
UID:ANTS/5
DESCRIPTION:Title: On
some open problems about polynomials\nby Dang-Khoa Nguyen (University
of Calgary) as part of Calgary Algebra and Number Theory Seminar\n\nLectur
e held in MS 337.\n\nAbstract\nOver the years\, there have been several op
en problems involving polynomials that I\n would love to tell
others about. This opportunity to speak at\n my ``home groun
d'' seems the perfect time to do so. More specifically\, I will discuss th
e following:\n\n (1) A conjecture of Ruzsa for integers and a r
elated problem in a joint work with Bell for polynomials over finite field
s. \n\n\n (2) A conjectural lower bound for t
he degree of irreducible factors of\n certain
polynomials from a joint work with DeMarco\, Ghioca\, Krieger\, Tucker\, a
nd Ye. \n \n\n(3) The irreducibil
ity of certain Gleason polynomials.\n
LOCATION:https://researchseminars.org/talk/ANTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Péringuey (University of British Columbia)
DTSTART:20241205T210000Z
DTEND:20241205T220000Z
DTSTAMP:20260422T225822Z
UID:ANTS/6
DESCRIPTION:Title: Ref
inements of Artin's primitive root conjecture\nby Paul Péringuey (Uni
versity of British Columbia) as part of Calgary Algebra and Number Theory
Seminar\n\nLecture held in MS 337.\n\nAbstract\nLet $\\rm{ord}_p(a)$ be th
e order of $a$ in $\\left(\\mathbb{Z}/p\\mathbb{Z}\n\\right)^*$. In 1927\,
Artin conjectured that the set of primes $p$ for which an\ninteger $a\\ne
q -1\,\\square$ is a primitive root (i.e. $\\rm{ord}_p(a)=p-1$) has\na pos
itive asymptotic density among all primes. In 1967 Hooley proved this\ncon
jecture assuming the Generalized Riemann Hypothesis (GRH).\n\nIn this talk
we will study the behaviour of $\\rm{ord}_p(a)$ as $p$ varies over\nprime
s\, in particular we will show\, under GRH\, that the set of primes $p$ fo
r\nwhich $\\rm{ord}_p(a)$ is ``$k$ prime factors away'' from $p-1$ has a p
ositive\nasymptotic density among all primes except for particular values
of $a$ and\n$k$. We will interpret being ``$k$ prime factors away'' in thr
ee different\nways\, namely $k=\\omega(\\frac{p-1}{\\rm{ord}_p(a)})$\, $k=
\\Omega(\\frac{p-1}\n{\\rm{ord}_p(a)})$ and $k=\\omega(p-1)-\\omega(\\rm{o
rd}_p(a))$\, and present\nconditional results analogous to Hooley's in all
three cases and for all\ninteger $k$. From this\, we will derive conditio
nally the expectation for these\nquantities.\n\nFurthermore we will provid
e partial unconditional answers to some of these\nquestions.\n\nThis is jo
int work with Leo Goldmakher and Greg Martin.\n
LOCATION:https://researchseminars.org/talk/ANTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (University of Lethbridge)
DTSTART:20250130T200000Z
DTEND:20250130T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/7
DESCRIPTION:Title: Cla
ssification of some Galois fields with a fixed Polya index\nby Abbas M
aarefparvar (University of Lethbridge) as part of Calgary Algebra and Numb
er Theory Seminar\n\nLecture held in MS 337.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ANTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubhodip Mondal (UBC)
DTSTART:20250206T200000Z
DTEND:20250206T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/8
DESCRIPTION:Title: Zet
a functon of F-gauges and special values\nby Shubhodip Mondal (UBC) as
part of Calgary Algebra and Number Theory Seminar\n\nLecture held in MS 3
37.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ANTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Olechnowicz (Concordia University)
DTSTART:20250213T200000Z
DTEND:20250213T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/9
DESCRIPTION:Title: Bad
reduction of rational maps.\nby Matt Olechnowicz (Concordia Universit
y) as part of Calgary Algebra and Number Theory Seminar\n\nLecture held in
MS 337.\n\nAbstract\nWe show that the reduction of a projective endomorph
ism modulo a discrete valuation naturally takes the form of a set-theoreti
c correspondence. This raises the possibility of classifying "reduction ty
pes" of such dynamical systems\, reminiscent of the additive/multiplicativ
e dichotomy for elliptic curves. These correspondences facilitate the exac
t evaluation of certain integrals of dynamical Green's functions\, which a
rise as local factors in the context of counting rational points ordered b
y the Call-Silverman canonical height. No prior knowledge of arithmetic dy
namics will be assumed.\n
LOCATION:https://researchseminars.org/talk/ANTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20250227T200000Z
DTEND:20250227T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/10
DESCRIPTION:Title: No
Talk\nby No Talk as part of Calgary Algebra and Number Theory Seminar
\n\nLecture held in MS 337.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ANTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20250220T200000Z
DTEND:20250220T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/11
DESCRIPTION:Title: No
Talk\nby No Talk as part of Calgary Algebra and Number Theory Seminar
\n\nLecture held in MS 337.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ANTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Quesada-Herrera (University of Lethbridge)
DTSTART:20250306T200000Z
DTEND:20250306T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/12
DESCRIPTION:Title: Fo
urier optimization and the least quadratic non-residue\nby Emily Quesa
da-Herrera (University of Lethbridge) as part of Calgary Algebra and Numbe
r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will explore h
ow a Fourier optimization framework may be used to study two classical pro
blems in number theory involving Dirichlet characters: The problem of esti
mating the least character non-residue\; and the problem of estimating the
least prime in an arithmetic progression. In particular\, we show how thi
s Fourier framework leads to subtle\, but conceptually interesting\, impro
vements on the best current asymptotic bounds under the Generalized Rieman
n Hypothesis\, given by Lamzouri\, Li\, and Soundararajan. Based on joint
work with Emanuel Carneiro\, Micah Milinovich\, and Antonio Ramos.\n
LOCATION:https://researchseminars.org/talk/ANTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Leudière (University of Calgary)
DTSTART:20250313T190000Z
DTEND:20250313T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/13
DESCRIPTION:Title: El
liptic curves\, Drinfeld modules\, and computations\nby Antoine Leudi
ère (University of Calgary) as part of Calgary Algebra and Number Theory
Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will talk about Drinfel
d modules\, and how they compare to elliptic curves for algorithms and com
putations.\n\nDrinfeld modules can be seen as function field analogues of
elliptic curves. They were introduced in the 1970's by Vladimir Drinfeld\,
to create an explicit class field theory of function fields. They were in
strumental to prove the Langlands program for GL2 of a function field\, or
the function field analogue of the Riemann hypothesis.\n\nElliptic curves
\, to the surprise of many theoretical number theorists\, became a fundame
ntal computational tool\, especially in the context of cryptography (ellip
tic curve Diffie-Hellman\, isogeny-based post-quantum cryptography) and co
mputer algebra (ECM method).\n\nDespite a rather abstract definition\, Dri
nfeld modules offer a lot of computational advantages over elliptic curves
: one can benefit from function field arithmetics\, and from objects calle
d Ore polynomials and Anderson motives.\n\nWe will use two examples to hig
hlight the practicality of Drinfeld modules computations\, and mention som
e applications.\n
LOCATION:https://researchseminars.org/talk/ANTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hoi Yip (Georgia Institute of Technology)
DTSTART:20250327T190000Z
DTEND:20250327T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/14
DESCRIPTION:Title: Di
ophantine tuples and their generalizations\nby Chi Hoi Yip (Georgia In
stitute of Technology) as part of Calgary Algebra and Number Theory Semina
r\n\nLecture held in MS 337.\n\nAbstract\nA set {a1\,a2\,…\,am} of dist
inct positive integers is a Diophantine m-tuple if the product of any two
distinct elements in the set is one less than a square. In this talk\, I w
ill discuss some recent results related to Diophantine tuples and their ge
neralizations. Joint work with Ernie Croot\, Seoyoung Kim\, and Semin Yoo.
\n
LOCATION:https://researchseminars.org/talk/ANTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemehzahra Janbazi (University of Toronto)
DTSTART:20250410T190000Z
DTEND:20250410T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/15
DESCRIPTION:Title: Ex
tensions of Birch-Merriman and Related Finiteness Theorems\nby Fatemeh
zahra Janbazi (University of Toronto) as part of Calgary Algebra and Numbe
r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nA classical theor
em of Birch and Merriman states that\, for fixed $n$\, the set of integral
binary $n$-ic forms with fixed nonzero discriminant breaks into finitely
many $\\mathrm{GL}_2(\\mathbb{Z})$-orbits. In this talk\, I’ll present s
everal extensions of this finiteness result. \n\nIn joint work with Arul S
hankar\, we study a representation-theoretic generalization to ternary $n$
-ic forms and prove analogous finiteness theorems for $\\mathrm{GL}_3(\\ma
thbb{Z})$-orbits with fixed nonzero discriminant. We also prove a similar
result for a 27-dimensional representation associated with a family of K3
surfaces. \n\nIn joint work with Sajadi\, we take a geometric perspective
and prove a finiteness theorem for Galois-invariant point configurations o
n arbitrary smooth curves with controlled reduction. This result unifies c
lassical finiteness theorems of Birch–Merriman\, Siegel\, and Faltings.\
n
LOCATION:https://researchseminars.org/talk/ANTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Ram Murty (Queen's University)
DTSTART:20250424T190000Z
DTEND:20250424T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/17
DESCRIPTION:Title: UN
IMODAL SEQUENCES: From Isaac Newton to the Riemann Hypothesis\nby M.
Ram Murty (Queen's University) as part of Calgary Algebra and Number Theor
y Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will give an expositi
on on the recent progress in the study of unimodal sequences\, beginning w
ith the work of Isaac Newton and then to the contemporary papers of June H
uh. We will also relate this topic to the Riemann hypothesis. In the proc
ess\, we will connect many areas of mathematics ranging from number theory
\, commutative algebra\, algebraic geometry and combinatorics.\n
LOCATION:https://researchseminars.org/talk/ANTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Duque Rosero (Boston University)
DTSTART:20251023T190000Z
DTEND:20251023T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/18
DESCRIPTION:Title: Tr
iangular modular curves\nby Juanita Duque Rosero (Boston University) a
s part of Calgary Algebra and Number Theory Seminar\n\nLecture held in MS
337.\n\nAbstract\nTriangular modular curves are a generalization of modula
r curves and arise as quotients of the complex upper half-plane by congrue
nce subgroups of hyperbolic triangle groups. These curves naturally parame
terize hypergeometric abelian varieties\, making them interesting arithmet
ic objects. In this talk\, we will focus on the Borel-kind triangular modu
lar curves. We will show that when restricting to prime level\, there are
finitely many such curves of any given genus\, and there is an algorithm t
o enumerate them. Time permitting\, we will explore generalizations to com
posite level. This is joint work with John Voight.\n
LOCATION:https://researchseminars.org/talk/ANTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tangli Ge (Princeton University)
DTSTART:20251113T210000Z
DTEND:20251113T220000Z
DTSTAMP:20260422T225822Z
UID:ANTS/19
DESCRIPTION:Title: Sp
arsity of intersections with group subschemes within an abelian scheme
\nby Tangli Ge (Princeton University) as part of Calgary Algebra and Numbe
r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nI will talk about
a unification of two bounded height results around abelian varieties. The
first is Silverman’s specialization theorem\, which states for an abeli
an scheme A/C with no fixed part over a curve C\, that the set of points o
n C where the generic Mordell—Weil group fails to specialize injectively
has bounded height. The second is by Habegger in an abelian variety: a su
itable subvariety intersected with all torsion cosets up to complementary
dimension gives a set of bounded height. I will take the point of view fro
m unlikely intersections and discuss the key idea of the arithmetic part o
f the proof by homomorphism approximations using Ax—Schanuel results.\n
LOCATION:https://researchseminars.org/talk/ANTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jit Wu Yap (MIT)
DTSTART:20251120T200000Z
DTEND:20251120T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/20
DESCRIPTION:Title: Ul
trafilters in Arithmetic Dynamics\nby Jit Wu Yap (MIT) as part of Calg
ary Algebra and Number Theory Seminar\n\nLecture held in MS 337.\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/ANTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Villagra Torcomian (Simon Fraser University)
DTSTART:20260212T200000Z
DTEND:20260212T210000Z
DTSTAMP:20260422T225822Z
UID:ANTS/21
DESCRIPTION:Title: Th
e role of hyperelliptic curves in the modular method\nby Lucas Villagr
a Torcomian (Simon Fraser University) as part of Calgary Algebra and Numbe
r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nIn this talk we w
ill briefly review the modular method\, the strategy used by Wiles to prov
e Fermat’s Last Theorem. We will then explain how hyperelliptic curves h
ave emerged as an important tool in recent years to approach generalized F
ermat equations\, and summarize the current state of the art results.\n
LOCATION:https://researchseminars.org/talk/ANTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debanjana Kundu (University of Regina)
DTSTART:20260413T190000Z
DTEND:20260413T200000Z
DTSTAMP:20260422T225822Z
UID:ANTS/22
DESCRIPTION:Title: On
the $p$-ranks of class groups of certain Galois extensions\nby Debanj
ana Kundu (University of Regina) as part of Calgary Algebra and Number The
ory Seminar\n\nLecture held in MS 337.\n\nAbstract\nLet $p$ be an odd prim
e\, let $N$ be a prime with $N \\equiv 1 \\pmod{p}$\, and let $\\zeta_p$ b
e a primitive $p$-th root of unity. We study the $p$-rank of the class gro
up of $\\mathbb{Q}(\\zeta_p\, N^{1/p})$ using Galois cohomological methods
and obtain an exact formula for the $p$-rank in terms of the dimensions o
f certain Selmer groups. Using our formula\, we provide a numerical criter
ion to establish upper and lower bounds for the $p$-rank\, analogous to th
e numerical criteria provided by F.~Calegari--M.~Emerton and K.~Schaefer--
E.~Stubley for the $p$-ranks of the class group of $\\mathbb{Q}(N^{1/p})$.
In the case $p=3$\, we use Redei matrices to provide a numerical criterio
n to exactly calculate the $3$-rank\, and also study the distribution of t
he $3$-ranks as $N$ varies through primes which are $4\,7 \\pmod{9}$. This
is joint work with Ufuoma Asenhesa\, Rusiru Gambheera\, Enrique Nunez Lon
-Wo\, and Arshay Sheth.\n
LOCATION:https://researchseminars.org/talk/ANTS/22/
END:VEVENT
END:VCALENDAR