Home Page of Matilde Lalín
Matilde Lalín
Professeure titulaire / Professor
Adresse postale: Université de Montréal
Pavillon AndréAisenstadt,
Dépt. de mathématiques et de
statistique
CP 6128, succ. Centreville
Montréal, Québec, H3C 3J7, Canada
Bureau: Pavillon AndréAisenstadt 5145
Téléphone: (514)
3436689.
Courriel: mlalin@dms.umontreal.ca
Newererer!!! with
Olivier Mila,
Hyperbolic Heron triangles and elliptic curves,
submitted February 2021
Newerer!!! with
Chantal David
and
Alexandra Florea,
Nonvanishing for cubic Lfunctions,
submitted February 2021
Newer!!! with
Mikhail Belolipetsky,
Plinio G. P. Murillo,
and
Lola Thompson,
Counting Salem numbers of arithmetic hyperbolic 3orbifolds,
submitted August 2020
New!!! with
Chantal David
and
Alexandra Florea,
The mean values of cubic Lfunctions over function fields,
submitted March 2019
Personal Information:
Curriculum Vitae:
Preprints and Publications:
 Introduccion
a las
Curvas Elipticas (Introduction to Elliptic Curves), Tesis de Licenciatura, Universidad de Buenos
Aires (1999), in Spanish.
 Some
relations of Mahler measure with hyperbolic volumes and special values of
Lfunctions, Doctoral Dissertation,
University of Texas at Austin (2005).
 Some
examples of Mahler measures as multiple polylogarithms,
J. Number Theory 103
(2003), no. 1, 85108.
 Mahler
measure and volumes in hyperbolic space, Geom. Dedicata 107
(2004), no. 1, 211234.
 On certain combination of colored
multizeta values, J. Ramanujan Math. Soc. 21
(2006), no. 1, 115127.
 Mahler measure of some nvariable
polynomial families, J.
Number Theory 116 (2006), no. 1, 102139.
 with Carlos A. D'Andrea,
On the
Mahler measure of resultants in small dimensions,
J. Pure Appl. Algebra 209
(2007), no. 2, 393410.
 An
algebraic integration for Mahler measure, Duke Math.
J. 138 (2007), no. 3, 391422.
 with Mathew D. Rogers,
Functional equations for Mahler
measures of genusone curves, Algebra Number Theory 1
(2007), no. 1, 87117.
 Mahler measure and computations with
regulators
,
J.
Number Theory 128 (2008), no. 5,
12311271.
 with Oliver T. Dasbach,
On the
recurrence of coefficients in the
LückFugledeKadison determinant,
Proceedings of
the "Segundas Jornadas de Teoría de Números"
(Madrid 2007),
Bib. Rev. Mat. Iberoam. (2008), 119134.
(refereed)

with Nobushige Kurokawa and Hiroyuki
Ochiai ,
Higher Mahler measures and zeta functions,
Acta Arith. 135
(2008), no. 3,
269297.
 with Oliver T. Dasbach,
Mahler measure under variations of
the base group, Forum Math. 21
(2009), no. 4,
621637.

On a conjecture by Boyd,
Int. J. Number
Theory
6 (2010), no. 3, 705711.
 with
Pablo
Bianucci
, Marco
Leonardo Bianucci (also available: first draft, revised version,
journal proofs),
Royal Alex.
Hosp. Apr 30 (2009),
w. 4230, l. 560

with Alina Bucur, Chantal David, and
Brooke Feigon,
Statistics for traces of cyclic trigonal curves over finite
fields,
Int.
Math. Res. Not. IMRN 2010, no. 5,
932967.

with
Alina Bucur, Chantal David, and
Brooke Feigon,
Fluctuations in the number of points on smooth plane curves
over finite fields, J.
Number Theory 130 (2010), no. 11, 25282541.

with Alina Bucur, Chantal David, and
Brooke Feigon,
Biased statistics for traces of cyclic pfold covers over finite
fields,
WINWomen in Numbers, Fields Institute Communications, vol. 60,
Amer. Math. Soc., Providence, RI, 2011, pp. 121143.
(refereed)

with
Kaneenika
Sinha, Higher Mahler measure for
cyclotomic polynomials and Lehmer's question,
Ramanujan J. 26 (2011), no. 2, 257294.

with
Alina Bucur, Chantal David,
Brooke Feigon, and Kaneenika Sinha,
Distribution of zeta zeroes of ArtinSchreier
curves,
Math. Res. Lett. 19 (2012), no. 6, 13291356.

with
Mathew Rogers, Variations of the Ramanujan polynomials and remarks on
$\zeta(2j+1)/\pi^{2j+1}$, Funct. Approx. Comment.
Math. 48 (2013), part 1, 91111.

with
Chris
Smyth, Unimodularity
of zeros of selfinversive
polynomials,
Acta Math.
Hungar. 138 (2013), no.
12, 85101.
Addendum, Acta Math.
Hungar. 147 (2015), no.
1, 255257.
 with Zahraa Issa, A generalization of a theorem of
Boyd and Lawton,
Canad. Math. Bull. 56 (2013), no. 4, 759768.
 Equations for Mahler measure and isogenies,
Proceedings of the ``Cuartas jornadas de teoria de
numeros'' J. Théor. Nombres Bordeaux 25 (2013), no. 2, 387399.
(refereed)

with MarieJosé Bertin, Mahler measure of
multivariable polynomials,
Women in numbers 2: research directions in number theory, 125147, Contemp. Math., 606, Amer. Math. Soc., Providence, RI, 2013.
(refereed)

with MarieJosé Bertin, Amy Feaver, Jenny Fuselier, and Michelle
Manes, Mahler measure of some
singular
K3surfaces,
Women in numbers 2: research directions in number theory, 149169, Contemp. Math., 606, Amer. Math. Soc., Providence, RI, 2013.
(refereed)
 with
Pablo
Bianucci, Victor Alejandro Bianucci (also available: first draft, revised version,
journal proofs),
CHU St. Justine. Jun 27 (2013),
w. 4060, l. 530

with Francis Rodrigue and Mathew Rogers, Secant zeta functions, J. Math. Anal. Appl. 409 (2014),
no. 1, 197204.

Mahler measure and elliptic curve
Lfunctions at s=3,
J. Reine Angew. Math. 709 (2015), 201218.

with
JeanSébastien Lechasseur,
Higher Mahler measure of an nvariable family,
Acta Arith. 174
(2016), no. 1,
130.

with
Olivier Larocque,
The number of irreducible
polynomials with first two prescribed coefficients over a finite field,
Rocky Mountain J. Math.
46 (2016), no. 5, 15871618.

A new method for polylogarithmic Mahler measure formulas,
Res. Number Theory
2 (2016), 2:17.

with
Alina Bucur,
Chantal David,
Brooke Feigon,
Nathan Kaplan,
Ekin Ozman,
Melanie Matchett Wood
The distribution of F_qpoints on cyclic lcovers of genus g,
Int.
Math. Res. Not. IMRN 2016, no. 14, 42974340.

with
Alina Bucur, Chantal David, and
Brooke Feigon,
Statistics for ordinary
ArtinSchreier covers and other prank strata Trans. Amer. Math.
Soc.
368 (2016), 23712413.

with
Detchat Samart and Wadim Zudilin,
Further explorations of Boyd's
conjectures and a conductor 21 elliptic curve,
J. Lond. Math. Soc. (2)
93 (2016), no. 2, 341360.

with
Frank Ramamonjisoa,
The Mahler measure of a Weierstrass form,
Int. J. Number Theory
13 (2017), no. 8, 21952214.

with
Vincent Girard
and Sivasankar Nair,
Families of nonθcongruent numbers with arbitrarily many prime factors,
Colloq. Math. 152 (2018), no. 2, 255271.

with
JeanSébastien Lechasseur,
A reduction formula for lengthtwo polylogarithms and some applications,
Rev. Un. Mat. Argentina
59 (2018), no. 2, 285309.

with
Tushant Mittal,
The Mahler measure for arbitrary tori,
Res. Number Theory
4, no. 2, (2018), 4:16.
 with
Abhijit Champanerkar and
Ilya Kofman,
Mahler measure and the VolDet conjecture,
J. Lond. Math. Soc. (2)
99 (2019), no. 3, 872900.
 with
Gang Wu,
Regulator proofs for Boyd's indentities on genus 2 curves,
Int. J. Number Theory
15 (2019), no. 5, 945967.
 with
Xinchun Ma,
θtriangle and ωparallelogram pairs with common area and common perimeter,
J. Number Theory 202
(2019), 126.
 with
Gang Wu,
The Mahler measure of a genus 3 family,
Ramanujan J., to appear
 with
Debmalya Basak and
Nicolas DegréPelletier,
Multiple zeta functions and polylogarithms over global function fields,
J. Théor. Nombres Bordeaux 32
(2020), no. 2, 403438.
 with
Chantal David and
Jungbae Nam,
Conjectures for moments associated with cubic twists of elliptic curves,
Exp. Math., to appear
 with
Jeanne Laflamme,
On Ceva points of (almost) equilateral triangles,
J. Number Theory 222
(2021), 4874.
 with
Jarry Gu,
The Mahler measure of a threevariable family and an application to the BoydLawton formula,
Res. Number Theory
7, no. 1, (2021), 1:13.
Talks (not up to date):
 Examples of Mahler Measures as Multiple Polylogarithms, notes,
slides
and video
from my talk at The many
aspects of Mahler's measure, a workshop organized by PIMS in Banff.
Here is a picture of the
participants of the workshop.
 Examples of Mahler Measures as special values of the Riemann Zeta
fucntion and Lseries, notes and
slides
from my talk at Mahler's Measure of
Polynomials, a workshop organized by PIMS and SFU in Vancouver.
 Introduction to Mahler Measure, notes from my
talk at Universidad de Buenos Aires.
 On Mahler measures of severalvariable
polynomials and polylogarithms, notes
and slides from my talk at the Zeta
Functions Seminar at UC Berkeley.
 Some aspects of Mahler measure, notes
and slides
from my talk at University of Colorado at Boulder.
 Some aspects of Mahler
measure, notes
and slides
from my talk at Texas A&M University.
 An
algebraic integration for Mahler measure, slides from my talk at Variations on Mahler's
Measure, a workshop at CIRM in Luminy.
 I've also gave a couple of talks at
the Oberseminar Geometrie at the University of Fribourg, Switzerland.
 Slides from
my last talk at Universidad de Buenos Aires.
 Mahler
measure and values of regulators, slide show from my short
talk at IAS
 Regulators and computations of Mahler measure notes and slide
show from my talk at Mahler
Measure in Mobile, Alabama
 On the Mahler measure of resultants in small dimensions, notes and
slide
show from my talk at AMS Joint
Mathematics Meetings, San Antonio, Texas
 Mahler measures as values of regulators, notes and slide show
from my talk at University of British
Columbia, Vancouver, BC, Canada
 My talk at the
Topology seminar at Louisiana State
University
 My talk at the
Members seminar at IAS
 My talk at the GeometryTopology seminar at
Georgia Institute of Technology
(GaTech)
 My talk at
the Postdoc Seminar at MSRI
 My talk at the
MSRI Number Theory Seminar at UC
Berkeley
 My talk at the
Barcelona Number
Theory Seminar
 Notes and
some slides
from my talk in Paris
 Functional equations for Mahler measures of genusone curves, slides and notes from my
talk at MPIfM
 Slides and notes from my talk at
Bristol
 Mahler
measure of multivariable polynomials, my talk at Norwich
 My talk at SFUBCPIMS
Number Theory seminar
 I crashed into a topology class in
Louisiana State University and
gave an Introduction to modular
forms!!!
 A few hours after I gave a talk at the Topology seminar!!!
 My talk at Alberta
 My talk at Chicago
 My talk Mahler measure under
variations of the base group at the conference A second time
around the Volume Conjecture in LSU
 Notes and slides from
Polylogarithms and Hyperbolic Volumes, my EXPOSITORY talk at Hyperbolic
Volume 2007 at Fribourg
 Slides from my talk
at the 25th Journ?s
Arithm?iques
 Slides from my talk
at the Lunch Number Theory Seminar in MPIfM
 Slides
from my talk at Segundas
Jornadas de Teoria de Numeros
 My talk at the
Lowdimensional Topology and Number Theory workshop in
Banff

My talks
at the Mahler measures conference at the
Tokyo
Institute of Technology

Slide show from my talk about the
history of the Riemann Hypothesis at the GAME Seminar here at U of
A.

Slide show from my talk at
the Colloquium in Calgary

Slide show from my talk at
the AMS
2008 Spring Southeastern Sectional Meeting, Baton Rouge, Louisiana

Slide show from my talk at
the ABC
Algebra Workshop, Simon Fraser University
 Slide show from my talk at
the Annual
North/South Dialogue in Mathematics, University of Calgary
 Slide show from my talk
at
the Number
Theory Day at the University of Lethbridge
 My talk at the CNTA
 My talk at the Université de
Montréal

My talks in Okinawa

My talk at the MIT Women in
Mathematics Lecture Series

My talk at the Workshop
on Discovery
and Experimentation in Number Theory

My talk at the 2009 CMS Winter
Meeting

My talk at the
AMS 2010 Joint Mathematics Meetings
 My talk at the
West End Number Theory Seminar
 My talk at CNTA XI
 My talk at
the Conf?ence
Qu?ecMaine
 My talk at the Number theory seminar at
Rochester
 My talk at the 2010 CMS Winter
Meeting
 My talk at the Colloque des math?atiques de Montr?l CRMISM
 Pr?entation sur le cube de Rubik
pour le
club
mathé:atique.
Voici quelques notes. Si vous avez des corrections,
ditesle moi, je serai heureuse de corriger mon francais! (et les
mathéatiques)
 Des triangles, des quadrilatères et des courbes elliptiques(club mathématique)
Seminar Talks at UT:
 Dilogarithm,
a cool function , Junior Number Theory Seminar.
 On
certain examples of Mahler Measures as Multiple Polylogarithms , the
candidacy talk that I gave at the Number Theory Seminar.
 Every
Positive Integer is the Sum of Four Squares! (and other exciting
problems) , about Lagrange's Theorem and Waring's problem at the
Sophex Seminar.
 A nice
condition for linearity, Sophex Seminar.
 The zeta
function strikes back!!!, a talk I gave about an example of a
fivevariable polynomial whose Mahler measure is esentially zeta(5) at the
Junior Algebra / Number Theory Seminar.
 Mahler Measure and Hyperbolic Volumes, notes and slides
from my talk at the Junior Number Theory Seminar.
 An algebraic
integration for Mahler Measure, my talk at the Junior Number Theory
Seminar.
 On the
friendship between Mahler measure and polylogarithms, notes and slides of my
talk at the Number Theory Seminar. Don't miss the bonus
slide!!!
 There's something about Mahler measure, notes and
slides
from my talk at the Junior Number Theory Seminar.
 My defense.
 My last talk as a student at UT was about Bernoulli
Numbers at the Junior Number Theory Seminar.
Teaching, organizing, etc:
 Past teaching:
MAT6684w Formes modulaires/Modular Forms
(Fall 2017, U de M, in English)
MAT6630
Courbes elliptiques et formes modulaires/Elliptic Curves and Modular Forms
(Winter 2017, U de M, in English)
MAT1410 Calcul 2 (Automne 2017, Hiver 2015, U de M)
MAT1500
Mathématiques discrètes (Hiver 2020, Hiver 2018, Automne 2016, Hiver 2013, U de M)
MAT2600 Algèbre (Automne 2020, Automne 2019, Automne 2018, Automne 2012, U de M)
MAT2130 Variable complexe (Hiver 2011,
U de M)
MAT3632 Théorie des nombres (Autonme 2012, Autonme 2011,
U de M)
MAT3661 Théorie de Galois (Hiver 2019, Hiver 2017, Hiver 2011,
U de M)
MAT6650 Théorie algébrique des nombres/Algebraic Number Theory (Fall 2020, U de M, in English)
MAT6617 Théorie des nombres/Algebraic Number Theory (Fall 2019, Fall 2018, Fall
2014, Fall 2010, U de M, in English)
Math 228 Introduction to Ring
Theory (Winter 2010, U of A)
Math 228 Introduction to Ring
Theory (Winter 2009, U of A)
Math 512 Algebraic
Number Theory (Fall 2008, U of A)
Math 682 Introduction to Elliptic
Curves (Winter 2008, U of A)
Math 324 Elementary
Number Theory (Fall 2007, U of A)
Math 103 Integral Calculus with Applications to Life Sciences
(Spring 2007 UBC)
M427K
Advanced Calculus for applications I (Fall 2005 UT Austin)
Other Stuff:
 Cool places to learn Math: Arxivs, MathSciNet, Mathworld
 My favorite number is 127
 My favorite comic strips: Ph.D,
the unfeasible adventures of
Beaver and Steve, and Order of the stick
 My favorite blog is
Female Science Professor
 I am very fond of Mathematical Olympiads
 If I
were a SpringerVerlag Graduate Text in Mathematics...
 Visit Matilde, the
Danish Mathematical Society's newsletter!!!
 I
got married on
July 23rd, 2004!!!
 42
 Cute
Overload for cute pictures.
 Nerdy stuff: News for nerds, Thinkgeek (this is where I get my
cool Tshirts)
 Getting info: Google, Standard repository of human knowledge
and wisdom aka Wikipedia! (at least until I get some copies of the
Encyclopedia Galactica or the HHG2G).
 Massive (geeky
music). Here
is one for music with Physics lyrics. I think this song should be my
favorite. Pandora for more
conventional music.
 Movies: imdb, rotten tomatoes, and the movie spoiler
Last updated August 10, 2016 (or later).
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September 17,
2005