BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Gaurav Patil (University of Toronto)
DTSTART:20241017T200000Z
DTEND:20241017T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/1
DESCRIPTION:Title: Parametrization of rings of finite rank - a geometric approach and the
ir use in counting number fields\nby Gaurav Patil (University of Toron
to) as part of Calgary Algebra and Number Theory Seminar\n\nLecture held i
n MS 337.\n\nAbstract\nWe describe parametrizations of rings that generali
ze the notions of monogenic rings and binary rings. We use these parametri
zations to give better lower bounds on the number of number fields of degr
ee n and bounded discriminant.\n\nRecorded video Passcode: $+*v9L8p\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renate Scheidler (University of Calgary)
DTSTART:20241024T200000Z
DTEND:20241024T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/2
DESCRIPTION:Title: Orienteering with One Endomorphism\nby Renate Scheidler (Universit
y of Calgary) as part of Calgary Algebra and Number Theory Seminar\n\nLect
ure held in MS 337.\n\nAbstract\nGiven two elliptic curves\, the path find
ing problem asks to find an isogeny (i.e. a group homomorphism) between th
em\, subject to certain degree restrictions. Path finding has uses in numb
er theory as well as applications to cryptography. For supersingular curve
s\, this problem is known to be easy when one small endomorphism or the en
tire endomorphism ring are known. Unfortunately\, computing the endomorphi
sm ring\, or even just finding one small endomorphism\, is hard. How diff
icult is path finding in the presence of one (not necessarily small) endom
orphism? We use the volcano structure of the oriented supersingular isogen
y graph to answer this question. We give a classical algorithm for path fi
nding that is subexponential in the degree of the endomorphism and linear
in a certain class number\, and a quantum algorithm for finding a smooth i
sogeny (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 cur
ves which generalizes the well-known class group action in the setting of
ordinary elliptic curves.\n\nThe recorded video Passcode: Z&7TyEGW\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omer Avci (Boğaziçi University)
DTSTART:20241031T200000Z
DTEND:20241031T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/3
DESCRIPTION:Title: Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of
$\\mathbb{Q}$\nby Omer Avci (Boğaziçi University) as part of Calgary
Algebra 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 suc
h that $p-1$ is not divisible by $3\,4\,5\,7\,11$. In this article we cl
assify the groups that can arise as $E(\\mathbb{Q}(\\zeta_p))_{\\text{tors
}}$ up to isomorphism. The method illustrates techniques for eliminating p
ossible structures that can appear as a subgroup of $E(\\mathbb{Q}^{ab})_{
\\text{tors}}.$\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clifton Cunningham (University of Calgary)
DTSTART:20241121T210000Z
DTEND:20241121T220000Z
DTSTAMP:20260404T111134Z
UID:ANTS/4
DESCRIPTION:Title: Packets and the fine structure of L-functions\nby Clifton Cunningh
am (University of Calgary) as part of Calgary Algebra and Number Theory Se
minar\n\nLecture held in MS 337.\n\nAbstract\nAutomorphic representations\
, which provide a vast generalization of modular forms\, are are grouped t
ogether into so-called L-packets according to the L-functions they produce
. From this point of view\, automorphic representations give a kind of fin
e-structure to L-functions themselves. While L-packets of automorphic repr
esentations are natural from this point of view\, they have some deficienc
ies when one looks for how L-functions transfer between different groups t
hat are related by what we call “functoriality” in the Langlands progr
am. To address these deficiencies\, Arthur introduced A-packets of automor
phic representations\; 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 g
eneralization of A-packets. The talk includes comments on applications of
A-packets to number theory\, some of which are highly speculative.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dang-Khoa Nguyen (University of Calgary)
DTSTART:20241128T210000Z
DTEND:20241128T220000Z
DTSTAMP:20260404T111134Z
UID:ANTS/5
DESCRIPTION:Title: On some open problems about polynomials\nby Dang-Khoa Nguyen (Univ
ersity of Calgary) as part of Calgary Algebra and Number Theory Seminar\n\
nLecture held in MS 337.\n\nAbstract\nOver the years\, there have been sev
eral open problems involving polynomials that I\n would love
to tell others about. This opportunity to speak at\n my ``hom
e ground'' seems the perfect time to do so. More specifically\, I will dis
cuss the following:\n\n (1) A conjecture of Ruzsa for integers
and a related problem in a joint work with Bell for polynomials over finit
e fields. \n\n\n (2) A conjectural lower boun
d for the degree of irreducible factors of\n c
ertain polynomials from a joint work with DeMarco\, Ghioca\, Krieger\, Tuc
ker\, and Ye. \n \n\n(3) The irre
ducibility of certain Gleason polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Péringuey (University of British Columbia)
DTSTART:20241205T210000Z
DTEND:20241205T220000Z
DTSTAMP:20260404T111134Z
UID:ANTS/6
DESCRIPTION:Title: Refinements of Artin's primitive root conjecture\nby Paul Péringu
ey (University 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 the 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
$a\\neq -1\,\\square$ is a primitive root (i.e. $\\rm{ord}_p(a)=p-1$) has
\na positive asymptotic density among all primes. In 1967 Hooley proved th
is\nconjecture assuming the Generalized Riemann Hypothesis (GRH).\n\nIn th
is talk we will study the behaviour of $\\rm{ord}_p(a)$ as $p$ varies over
\nprimes\, in particular we will show\, under GRH\, that the set of primes
$p$ for\nwhich $\\rm{ord}_p(a)$ is ``$k$ prime factors away'' from $p-1$
has a positive\nasymptotic density among all primes except for particular
values of $a$ and\n$k$. We will interpret being ``$k$ prime factors away''
in three different\nways\, namely $k=\\omega(\\frac{p-1}{\\rm{ord}_p(a)})
$\, $k=\\Omega(\\frac{p-1}\n{\\rm{ord}_p(a)})$ and $k=\\omega(p-1)-\\omega
(\\rm{ord}_p(a))$\, and present\nconditional results analogous to Hooley's
in all three cases and for all\ninteger $k$. From this\, we will derive c
onditionally the expectation for these\nquantities.\n\nFurthermore we will
provide partial unconditional answers to some of these\nquestions.\n\nThi
s is joint work with Leo Goldmakher and Greg Martin.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (University of Lethbridge)
DTSTART:20250130T200000Z
DTEND:20250130T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/7
DESCRIPTION:Title: Classification of some Galois fields with a fixed Polya index\nby
Abbas Maarefparvar (University of Lethbridge) as part of Calgary Algebra a
nd Number Theory Seminar\n\nLecture held in MS 337.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubhodip Mondal (UBC)
DTSTART:20250206T200000Z
DTEND:20250206T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/8
DESCRIPTION:Title: Zeta 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 337.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Olechnowicz (Concordia University)
DTSTART:20250213T200000Z
DTEND:20250213T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/9
DESCRIPTION:Title: Bad reduction of rational maps.\nby Matt Olechnowicz (Concordia Un
iversity) 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 en
domorphism modulo a discrete valuation naturally takes the form of a set-t
heoretic correspondence. This raises the possibility of classifying "reduc
tion types" of such dynamical systems\, reminiscent of the additive/multip
licative dichotomy for elliptic curves. These correspondences facilitate t
he exact evaluation of certain integrals of dynamical Green's functions\,
which arise as local factors in the context of counting rational points or
dered by the Call-Silverman canonical height. No prior knowledge of arithm
etic dynamics will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20250227T200000Z
DTEND:20250227T210000Z
DTSTAMP:20260404T111134Z
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://stable.researchseminars.org/talk/ANTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Talk
DTSTART:20250220T200000Z
DTEND:20250220T210000Z
DTSTAMP:20260404T111134Z
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://stable.researchseminars.org/talk/ANTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Quesada-Herrera (University of Lethbridge)
DTSTART:20250306T200000Z
DTEND:20250306T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/12
DESCRIPTION:Title: Fourier optimization and the least quadratic non-residue\nby Emil
y Quesada-Herrera (University of Lethbridge) as part of Calgary Algebra an
d Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will ex
plore how a Fourier optimization framework may be used to study two classi
cal problems in number theory involving Dirichlet characters: The problem
of estimating the least character non-residue\; and the problem of estimat
ing the least prime in an arithmetic progression. In particular\, we show
how this Fourier framework leads to subtle\, but conceptually interesting\
, improvements on the best current asymptotic bounds under the Generalized
Riemann Hypothesis\, given by Lamzouri\, Li\, and Soundararajan. Based on
joint work with Emanuel Carneiro\, Micah Milinovich\, and Antonio Ramos.\
n
LOCATION:https://stable.researchseminars.org/talk/ANTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Leudière (University of Calgary)
DTSTART:20250313T190000Z
DTEND:20250313T200000Z
DTSTAMP:20260404T111134Z
UID:ANTS/13
DESCRIPTION:Title: Elliptic curves\, Drinfeld modules\, and computations\nby Antoine
Leudière (University of Calgary) as part of Calgary Algebra and Number T
heory Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will talk about D
rinfeld modules\, and how they compare to elliptic curves for algorithms a
nd computations.\n\nDrinfeld modules can be seen as function field analogu
es of elliptic curves. They were introduced in the 1970's by Vladimir Drin
feld\, to create an explicit class field theory of function fields. They w
ere instrumental to prove the Langlands program for GL2 of a function fiel
d\, or the function field analogue of the Riemann hypothesis.\n\nElliptic
curves\, to the surprise of many theoretical number theorists\, became a f
undamental computational tool\, especially in the context of cryptography
(elliptic curve Diffie-Hellman\, isogeny-based post-quantum cryptography)
and computer algebra (ECM method).\n\nDespite a rather abstract definition
\, Drinfeld modules offer a lot of computational advantages over elliptic
curves: one can benefit from function field arithmetics\, and from objects
called Ore polynomials and Anderson motives.\n\nWe will use two examples
to highlight the practicality of Drinfeld modules computations\, and menti
on some applications.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Hoi Yip (Georgia Institute of Technology)
DTSTART:20250327T190000Z
DTEND:20250327T200000Z
DTSTAMP:20260404T111134Z
UID:ANTS/14
DESCRIPTION:Title: Diophantine tuples and their generalizations\nby Chi Hoi Yip (Geo
rgia Institute of Technology) as part of Calgary Algebra and Number Theory
Seminar\n\nLecture held in MS 337.\n\nAbstract\nA set {a1\,a2\,…\,am}
of distinct positive integers is a Diophantine m-tuple if the product of a
ny two distinct elements in the set is one less than a square. In this tal
k\, I will discuss some recent results related to Diophantine tuples and t
heir generalizations. Joint work with Ernie Croot\, Seoyoung Kim\, and Sem
in Yoo.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemehzahra Janbazi (University of Toronto)
DTSTART:20250410T190000Z
DTEND:20250410T200000Z
DTSTAMP:20260404T111134Z
UID:ANTS/15
DESCRIPTION:Title: Extensions of Birch-Merriman and Related Finiteness Theorems\nby
Fatemehzahra Janbazi (University of Toronto) as part of Calgary Algebra an
d Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nA classica
l theorem of Birch and Merriman states that\, for fixed $n$\, the set of i
ntegral binary $n$-ic forms with fixed nonzero discriminant breaks into fi
nitely many $\\mathrm{GL}_2(\\mathbb{Z})$-orbits. In this talk\, I’ll pr
esent several extensions of this finiteness result. \n\nIn joint work with
Arul Shankar\, we study a representation-theoretic generalization to tern
ary $n$-ic forms and prove analogous finiteness theorems for $\\mathrm{GL}
_3(\\mathbb{Z})$-orbits with fixed nonzero discriminant. We also prove a s
imilar result for a 27-dimensional representation associated with a family
of K3 surfaces. \n\nIn joint work with Sajadi\, we take a geometric persp
ective and prove a finiteness theorem for Galois-invariant point configura
tions on arbitrary smooth curves with controlled reduction. This result un
ifies classical finiteness theorems of Birch–Merriman\, Siegel\, and Fal
tings.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Ram Murty (Queen's University)
DTSTART:20250424T190000Z
DTEND:20250424T200000Z
DTSTAMP:20260404T111134Z
UID:ANTS/17
DESCRIPTION:Title: UNIMODAL SEQUENCES: From Isaac Newton to the Riemann Hypothesis\
nby M. Ram Murty (Queen's University) as part of Calgary Algebra and Numbe
r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will give an e
xposition on the recent progress in the study of unimodal sequences\, begi
nning with the work of Isaac Newton and then to the contemporary papers of
June Huh. We will also relate this topic to the Riemann hypothesis. In t
he process\, we will connect many areas of mathematics ranging from number
theory\, commutative algebra\, algebraic geometry and combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juanita Duque Rosero (Boston University)
DTSTART:20251023T190000Z
DTEND:20251023T200000Z
DTSTAMP:20260404T111134Z
UID:ANTS/18
DESCRIPTION:Title: Triangular modular curves\nby Juanita Duque Rosero (Boston Univer
sity) as part of Calgary Algebra and Number Theory Seminar\n\nLecture held
in MS 337.\n\nAbstract\nTriangular modular curves are a generalization of
modular curves and arise as quotients of the complex upper half-plane by
congruence subgroups of hyperbolic triangle groups. These curves naturally
parameterize hypergeometric abelian varieties\, making them interesting a
rithmetic objects. In this talk\, we will focus on the Borel-kind triangul
ar modular curves. We will show that when restricting to prime level\, the
re are finitely many such curves of any given genus\, and there is an algo
rithm to enumerate them. Time permitting\, we will explore generalizations
to composite level. This is joint work with John Voight.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tangli Ge (Princeton University)
DTSTART:20251113T210000Z
DTEND:20251113T220000Z
DTSTAMP:20260404T111134Z
UID:ANTS/19
DESCRIPTION:Title: Sparsity of intersections with group subschemes within an abelian sch
eme\nby Tangli Ge (Princeton University) as part of Calgary Algebra an
d Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nI will tal
k about a unification of two bounded height results around abelian varieti
es. The first is Silverman’s specialization theorem\, which states for a
n abelian scheme A/C with no fixed part over a curve C\, that the set of p
oints on C where the generic Mordell—Weil group fails to specialize inje
ctively has bounded height. The second is by Habegger in an abelian variet
y: a suitable subvariety intersected with all torsion cosets up to complem
entary dimension gives a set of bounded height. I will take the point of v
iew from unlikely intersections and discuss the key idea of the arithmetic
part of the proof by homomorphism approximations using Ax—Schanuel resu
lts.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jit Wu Yap (MIT)
DTSTART:20251120T200000Z
DTEND:20251120T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/20
DESCRIPTION:Title: Ultrafilters in Arithmetic Dynamics\nby Jit Wu Yap (MIT) as part
of Calgary Algebra and Number Theory Seminar\n\nLecture held in MS 337.\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Villagra Torcomian (Simon Fraser University)
DTSTART:20260212T200000Z
DTEND:20260212T210000Z
DTSTAMP:20260404T111134Z
UID:ANTS/21
DESCRIPTION:Title: The role of hyperelliptic curves in the modular method\nby Lucas
Villagra Torcomian (Simon Fraser University) as part of Calgary Algebra an
d Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nIn this ta
lk we will briefly review the modular method\, the strategy used by Wiles
to prove Fermat’s Last Theorem. We will then explain how hyperelliptic c
urves have emerged as an important tool in recent years to approach genera
lized Fermat equations\, and summarize the current state of the art result
s.\n
LOCATION:https://stable.researchseminars.org/talk/ANTS/21/
END:VEVENT
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