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BEGIN:VEVENT
SUMMARY:Brian Li (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210526T180000Z
DTEND;VALUE=DATE-TIME:20210526T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/1
DESCRIPTION:Title: Cops and Robbers with Many Variants\nby Brian Li (Univers
ity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nMathematic
s and games complement each other in both mathematical research and learni
ng. Cops and Robbers is a game played on graphs between a set of cops and
a single robber. The cops begin the game by moving to a set of vertices\,
with the robber then choosing a vertex to occupy. All players move from ve
rtex-to-vertex along edges. The cops win by successfully occupying the rob
ber’s vertex\, hence catching the robber. We will discuss theorems that
help us better understand such games and unleash our creativity to explore
many different variants. No prior knowledge required.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker Glynn-Adey (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210602T180000Z
DTEND;VALUE=DATE-TIME:20210602T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/2
DESCRIPTION:Title: The Probabilistic Method\nby Parker Glynn-Adey (Universit
y of Toronto) as part of Undergraduate Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Chislett (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210609T180000Z
DTEND;VALUE=DATE-TIME:20210609T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/3
DESCRIPTION:Title: Ray Tracing and the Light Transport Equation\nby Benjamin
Chislett (University of Toronto) as part of Undergraduate Seminar\n\n\nAb
stract\nRay Tracing is the primary technique for rendering photorealistic
images. Advancements in ray tracing techniques have enabled its use in a v
ariety of computer graphics applications\, from animated films to real-tim
e video games. In this talk\, we explore the Light Transport Equation\, Mo
nte Carlo integration\, and some of the many optimizations that have led t
o ray tracing's rapid rise in popularity.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Maltese (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210616T180000Z
DTEND;VALUE=DATE-TIME:20210616T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/4
DESCRIPTION:Title: An Introduction to Mathematical Logic\nby Jesse Maltese (
University of Toronto) as part of Undergraduate Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schrittesser (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210630T180000Z
DTEND;VALUE=DATE-TIME:20210630T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/5
DESCRIPTION:Title: Your life will be better with infinitesimals (Part 2)\nby
David Schrittesser (University of Toronto) as part of Undergraduate Semin
ar\n\n\nAbstract\nWhen Leibniz\, Newton\, and others first developed calcu
lus\, they used the metaphor of infinitely small\, or infinitesimal\, quan
tities to try to justify their methods. Later\, infinitesimals were expell
ed from mathematics and calculus was made rigorous using the familiar noti
ons of limit and epsilon-delta formulations.\n\nBut infinitesimals have be
en making a come back! Using methods from logic\, in particular model theo
ry\, they have been restored as respected citizens in rigorous mathematica
l arguments. This approach\, called non-standard analysis has been describ
ed as ``the analysis of the future''. And indeed\, it sometimes allows us
to do miraculous things. A recent case in point is my joint result with D.
Roy and H. Duanmu\, with which we solve a long-standing open problem in s
tatistics (namely giving a Bayesian interpretation of admissibility).\n\nI
n this talk I will give an introduction to the non-standard method and des
cribe some applications. (And if I manage to spark your interest\, come to
the course I will teach about this topic at U of T in this fall!)\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schrittesser (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210623T180000Z
DTEND;VALUE=DATE-TIME:20210623T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/6
DESCRIPTION:Title: Your life will be better with infinitesimals\nby David Sc
hrittesser (University of Toronto) as part of Undergraduate Seminar\n\n\nA
bstract\nWhen Leibniz\, Newton\, and others first developed calculus\, the
y used the\nmetaphor of infinitely small\, or infinitesimal\, quantities t
o try to justify\ntheir methods. Later\, infinitesimals were expelled from
mathematics and calculus was\nmade rigorous using the familiar notions of
limit and epsilon-delta formulations.\n\nBut infinitesimals have been mak
ing a come back! Using methods from logic\, in particular model theory\, t
hey have been restored as respected citizens in rigorous mathematical argu
ments. This approach\, called non-standard analysis has been described as
``the analysis of the future''. And indeed\, it sometimes allows us to do
miraculous things. A recent case in point is my joint result with D. Roy a
nd H. Duanmu\, with which we solve a long-standing open problem in statist
ics (namely giving a Bayesian interpretation of admissibility).\n\nIn this
talk I will give an introduction to the non-standard method and describe
some applications. (And if I manage to spark your interest\, come to the c
ourse I will teach about this topic at U of T in this fall!)\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Santos (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210721T180000Z
DTEND;VALUE=DATE-TIME:20210721T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/7
DESCRIPTION:Title: An Introduction to Group Theory through Puzzles\nby Kevin
Santos (University of Toronto) as part of Undergraduate Seminar\n\n\nAbst
ract\nThe concept of a group is a powerful tool that we can use to underst
and the structures of mathematical objects. In this talk\, we’ll use wel
l-known puzzles such as Peg Solitaire\, the 15 puzzle\, and Rubik’s cube
to motivate a brief introduction to the concepts of group theory. We’ll
explore how groups are related to symmetry and give some examples of grou
ps\, such as the Klein 4-group and the permutation groups. We’ll then se
e how these ideas can be applied to understand the puzzles.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuveshen Mooroogen (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210707T180000Z
DTEND;VALUE=DATE-TIME:20210707T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/8
DESCRIPTION:Title: Shining a rainbow-coloured light on the fundamental theorem o
f algebra\nby Yuveshen Mooroogen (University of Toronto) as part of Un
dergraduate Seminar\n\n\nAbstract\nThe graphs of real-valued functions on
the real line are subsets of a two-dimensional space. As a result\, we can
sketch them on a piece of paper.\n\nThe graphs of complex-valued function
s on the complex plane\, however\, are subsets of a four-dimensional space
. Good luck sketching that on a piece of paper.\n\nIn this presentation\,
I will introduce “domain colouring”\, which is a technique used to ill
ustrate functions of the complex numbers.\n\nThis talk will be in two part
s. In the first part\, I will explain how to read and construct domain col
ouring plots\, focusing on a number of simple examples. In the second part
\, I will discuss the Fundamental Theorem of Algebra (which states that ev
ery nonconstant polynomial has a complex root) and explain how to visualis
e one of its proofs using domain colouring. This part of the talk will dra
w heavily from D. J. Velleman’s beautiful expository article [1].\n\nPre
requisites: Familiarity with the concept of dimension (for a vector space)
and with the complex numbers. (Basic principles only. You should know wha
t the notation $x+iy$ means\, and how to convert it to modulus-argument/po
lar form.) Knowledge of multivariable calculus and complex analysis is not
expected.\n\n[1] Velleman\, D.J. The Fundamental Theorem of Algebra: A Vi
sual Approach. Math Intelligencer 37\, 12–21 (2015). https://doi.org/10.
1007/s00283-015-9572-7.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Lai (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210714T180000Z
DTEND;VALUE=DATE-TIME:20210714T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/9
DESCRIPTION:Title: Partial orders and application to semantics of computer progr
ams\nby Albert Lai (University of Toronto) as part of Undergraduate Se
minar\n\n\nAbstract\nPartial orders generalize total orders. A familiar ex
ample is the subset relation over a family of sets. I will show a computer
-science application of partial orders to modelling recursive programs. Th
is will be a glimpse of denotational semantics\, the study of describing p
rogram behaviour by mapping programs to suitable mathematical structures a
nd partial order\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rakan Omar (York University)
DTSTART;VALUE=DATE-TIME:20210728T180000Z
DTEND;VALUE=DATE-TIME:20210728T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/10
DESCRIPTION:Title: Influence Centrality of Graphs\nby Rakan Omar (York Univ
ersity) as part of Undergraduate Seminar\n\n\nAbstract\nIn graph theory an
d network analysis\, the notion of centrality refers to assigning nodes in
a network an index representing the extent to which each node is central
- important to the network\, or well positioned in it - based on some math
ematical property.\nThere are a variety of measures of centrality\, each o
f which measures ‘centrality’ differently\, based on (or resulting in)
a different definition of ‘importance’ or ‘prominence’.\n\nI will
define an original measure of centrality\, a variation of pageRank centra
lity\, which i call ‘influence centrality’\, that measures the extent
to which a node contributes a relation (what is represented by the arcs) t
o the graph in a directed weighted graph with a finite number of nodes\, w
hich are initially labelled with values.\nI will discuss some properties\,
applications\, and extensions of influence centrality.\n\nI assume some f
amiliarity with graph theory terminology and linear algebra.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Fallone (York)
DTSTART;VALUE=DATE-TIME:20210804T180000Z
DTEND;VALUE=DATE-TIME:20210804T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/11
DESCRIPTION:Title: The Projected Number of Underreported COVID 19 Cases in Cana
da\nby Andrew Fallone (York) as part of Undergraduate Seminar\n\n\nAbs
tract\nAs Canada focuses more on mitigation strategies rather than eradica
tion ones\, mathematical modelling could play an important role in preserv
ing lives. The model used in this project is a modified SIR model which re
tains a conservative calculation for COVID 19 cases while giving an insigh
t into how unreported COVID 19 cases are in Canada with the assumption tha
t we have a limited amount of data. This approach seems to be the most eff
ective due to the uncertainty of COVID 19 progression in Canada. Furthermo
re\, this modified SIR model uses a basic reproduction parameter “to est
imate the attack rate\, epidemic duration”\, and critical points of COVI
D 19 cases in Canada.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Midroni (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210811T180000Z
DTEND;VALUE=DATE-TIME:20210811T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/12
DESCRIPTION:Title: Artificial neural networks: The fundamentals\nby Julie M
idroni (University of Toronto) as part of Undergraduate Seminar\n\n\nAbstr
act\nArtificial neural networks (ANNs) are a powerful class of machine lea
rning algorithms that can be used for a variety of purposes\, including im
age classification\, function approximation\, and natural language process
ing. This talk will present the mathematical basics of ANNs\, and briefly
explore different ANN algorithms and their uses.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amalrose Vayalinkal (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210825T180000Z
DTEND;VALUE=DATE-TIME:20210825T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/13
DESCRIPTION:Title: Virtual Ring Routing\nby Amalrose Vayalinkal (University
of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nVirtual Ring
Routing (VRR) schemes define a routing algorithm for communication between
devices by establishing a virtual network overlay given a physical networ
k of $N$ devices. Using graphs to model the physical network\, we introduc
e the algorithm and explore the pros and cons of VRR. Time permitting\, we
take a closer look at the simpler case where the physical network is also
a ring (circle) and discuss future directions. This work is part of an NS
ERC USRA this summer under the supervision of Professor Almut Burchard.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker and Lisa
DTSTART;VALUE=DATE-TIME:20210901T180000Z
DTEND;VALUE=DATE-TIME:20210901T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/14
DESCRIPTION:Title: TOWNHALL / ORGANIZATION\nby Parker and Lisa as part of U
ndergraduate Seminar\n\n\nAbstract\nWe are holding a special meeting to or
ganize the seminar for the rest of the term.\n\nIf you have NEVER attended
Undergraduate Seminar\, this is a great time to hop in.\n\n* What do you
want from the Undergrad Seminar?\n\n* What times / days of the week should
it run on?\n\n* Would you like to focus on a specfic topic?\n\n* Would yo
u like to give a talk?\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhekai Pang and Yuhong Zhang (University of Toronto)
DTSTART;VALUE=DATE-TIME:20211110T160000Z
DTEND;VALUE=DATE-TIME:20211110T165900Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/15
DESCRIPTION:Title: Matrix analysis with a focus on inequalities\nby Zhekai
Pang and Yuhong Zhang (University of Toronto) as part of Undergraduate Sem
inar\n\n\nAbstract\nMatrix inequalities are one of the key components in m
atrix analysis. They have a wide range of applications in statistics\, com
puter science\, economics\, and physics.\n\nIn this presentation\, we focu
s on some classical matrix inequalities such as the Rayleigh-Ritz quotient
\, the Courant Fischer theorem\, Weyl’s inequality\, the interlocking ei
genvalue lemma\, and the Woodbury matrix identity. In particular\, some of
these show the importance of the maximum and minimum of eigenvalues and s
ingular values.\n\nRecommend Background: Linear Algebra and Calculus. (In
the beginning of the presentation\, some definitions and key properties su
ch as positive definiteness will be reviewed.)\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathew Cater Benavides (University of Toronto)
DTSTART;VALUE=DATE-TIME:20211117T190000Z
DTEND;VALUE=DATE-TIME:20211117T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/16
DESCRIPTION:Title: An Introduction to the Fractional Brownian Motion\nby Ma
thew Cater Benavides (University of Toronto) as part of Undergraduate Semi
nar\n\n\nAbstract\nThe classical Brownian motion (or Wiener process) serve
s as the fundamental object of probability theory with vast theoretical an
d practical applications in a plethora of fields. In the early 1940’s Ko
lmogorov sought a natural one parameter extension of the process in aims o
f modelling turbulence in liquids\, the extension consists of retaining th
e framework of the classical motion by constructing still a continuous cen
tered Gaussian process that retains self similarity (of a now distinct ind
ex from that of the classical motion) and stationarity of increments but d
raws its distinction by parameterizing its specifying covariance structure
with what is known as the Hurst index\,$H \\in (0\,1)$\, resulting in (fo
r ‘most’ values of $H$) a non-Markov process allowing it to serve as a
popular model for dependent phenomena\; this extension has since been kep
t in common parlance as fractional Brownian motion (fBm). This talk aims t
o provide discussion and (at times demonstration) of the fundamental prope
rties of the fBm as well as investigate sample path properties’ dependen
ce on the Hurst parameter.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART;VALUE=DATE-TIME:20211124T190000Z
DTEND;VALUE=DATE-TIME:20211124T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/17
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Theorem P
rover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / Univers
ity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHave you h
eard of automated and interactive theorem provers? Did you know that Ameri
can mathematician Alex Kontorovich predicts that the Lean Interactive Theo
rem Prover will be so widely used that it will be as necessary as LaTex in
doing mathematics? This seminar series will take you on a journey\, using
Lean to give you insights on how to go about proving\, which route to cho
ose\, how to check for errors\, and how to verify a computation or a proof
. Particularly\, you will be learning to use Lean by playing a number game
. Come join us and have some fun!\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART;VALUE=DATE-TIME:20211201T190000Z
DTEND;VALUE=DATE-TIME:20211201T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/18
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Theorem P
rover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / Univers
ity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHave you h
eard of automated and interactive theorem provers? Did you know that Ameri
can mathematician Alex Kontorovich predicts that the Lean Interactive Theo
rem Prover will be so widely used that it will be as necessary as LaTex in
doing mathematics? This seminar series will take you on a journey\, using
Lean to give you insights on how to go about proving\, which route to cho
ose\, how to check for errors\, and how to verify a computation or a proof
. Particularly\, you will be learning to use Lean by playing a number game
. Come join us and have some fun!\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker Glynn-Adey (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220202T190000Z
DTEND;VALUE=DATE-TIME:20220202T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/20
DESCRIPTION:Title: ORGANIZATIONAL MEETING\nby Parker Glynn-Adey (University
of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nWe are holdin
g a special meeting to organize the seminar for the rest of the term.\n\nI
f you have NEVER attended Undergraduate Seminar\, this is a great time to
hop in.\n\n* What do you want from the Undergrad Seminar?\n\n* What times
/ days of the week should it run on?\n\n* Would you like to focus on a spe
cific topic?\n\n* Would you like to give a talk?\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART;VALUE=DATE-TIME:20220209T190000Z
DTEND;VALUE=DATE-TIME:20220209T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/21
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Theorem P
rover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / Univers
ity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHave you h
eard of automated and interactive theorem provers? Did you know that Ameri
can mathematician Alex Kontorovich predicts that the Lean Interactive Theo
rem Prover will be so widely used that it will be as necessary as LaTex in
doing mathematics? This seminar series will take you on a journey\, using
Lean to give you insights on how to go about proving\, which route to cho
ose\, how to check for errors\, and how to verify a computation or a proof
. Particularly\, you will be learning to use Lean by playing a number game
. Come join us and have some fun!\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Santos (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220316T180000Z
DTEND;VALUE=DATE-TIME:20220316T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/22
DESCRIPTION:Title: Modelling Mathematics with Knitting and Crochet\nby Kevi
n Santos (University of Toronto) as part of Undergraduate Seminar\n\n\nAbs
tract\nWhen studying subjects like geometry and topology\, it can be diffi
cult to visualize or understand certain abstract concepts. Being able to h
old and manipulate a physical model of a mathematical object can give deep
er intuition into its properties. The process of constructing such an obje
ct also offers further insight. In this talk\, we will investigate how geo
metric and topological objects can be constructed using the crafts of knit
ting and crochet\, which offer unique advantages in creating models. We wi
ll describe how the hyperbolic plane can be modelled with crochet and we w
ill explore how topological surfaces such as the sphere\, the torus\, and
the Klein bottle can be knitted. No prior knowledge in geometry\, topology
\, knitting\, or crochet is required.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Logan Lim (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220323T180000Z
DTEND;VALUE=DATE-TIME:20220323T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/23
DESCRIPTION:Title: Why Geometric Algebra Should be in the Standard Linear Algeb
ra Curriculum\nby Logan Lim (University of Toronto) as part of Undergr
aduate Seminar\n\n\nAbstract\nGeometric algebra is an extension of $\\math
bb{R}^n$ that includes as special cases: The complex numbers\, quaternions
\, exterior algebras\, dual numbers\, split-complex numbers\, dual quatern
ions and more! When applied to multivariable calculus\, it generalizes the
fundamental theorem of calculus on manifolds to include the divergence th
eorem\, curl theorem\, and gradient theorem\, and as a result Green’s an
d Stoke’s theorem\, as special cases of a single statement. It also simp
lifies many geometric operations in computer graphics by eliminating the n
eed for matrices in projections\, rotations\, and reflections. Though we c
an only cover the ‘main idea’ of geometric algebra in the allotted tim
e\, this talk will be a buffet of ideas you can explore for this fascinati
ng and deceptively simple algebraic object.\n\nMathematicians hate him!!!!
See how Clifford generalized rotations and orthogonal complements in n-di
mensions with this one simple trick! \n\n$$\\mathbf{uv} = \\mathbf{u} \\cd
ot \\mathbf{v} + \\mathbf{u} \\wedge \\mathbf{v}$$\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Teeter (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220330T180000Z
DTEND;VALUE=DATE-TIME:20220330T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/24
DESCRIPTION:Title: Seifert Surfaces and Knots Genus\nby Alex Teeter (Univer
sity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nKnot Theo
ry\, a field of mathematics born from a misguided model for atoms\, has si
nce grown to become an important subfield of Topology. Not only does it ha
ve much of mathematical interest\, but also numerous connections to fields
such as graph theory\, the study of manifolds\, and applications to Biolo
gy and Physics. We will analyze the connection between Knot Theory and the
Topology of Surfaces. Along the way\, we will cover the Euler Characteris
tic\, Genus and the beautiful Classification Theorem of Surfaces. Through
this consideration\, we develop an algorithm to associate each Knot with a
surface\, and uncover an important invariant\, the Genus of a Knot. This
will not only allow us to distinguish between different Knots\, but will a
lso be vital in establishing fundamental properties of prime and composite
Knots. No prior background in Knot Theory or Topology is assumed.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zack Wolske
DTSTART;VALUE=DATE-TIME:20220921T170000Z
DTEND;VALUE=DATE-TIME:20220921T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/25
DESCRIPTION:Title: An Introduction to Combinatorial Games\nby Zack Wolske a
s part of Undergraduate Seminar\n\n\nAbstract\nWe’ll introduce a collect
ion of two player games that anyone can play – they’re fun for all age
s. Some games have strategy patterns we can find quickly\, some have well-
hidden patterns that we can uncover with more tools\, and others have patt
erns that no one in the world has found. We will play and analyze those ga
mes and share currently open problems.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART;VALUE=DATE-TIME:20221005T170000Z
DTEND;VALUE=DATE-TIME:20221005T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/26
DESCRIPTION:Title: Permutations with quipu\nby Scott Carter as part of Unde
rgraduate Seminar\n\n\nAbstract\nAccording to Wikipedia\, a quipu is an ac
counting system in which knots are tied in a sequence of strings. They wer
e used as a method of storing tax and other financial records. Here we con
sider cyclic subgroups of groups and catalogue the cosets by means of a st
ring bundle (the English word\, not the mathematical word is intended). Th
e quipu are elements in the cyclic subgroups. The traditional methods of m
ultiplying braids by means of vertical juxtaposition is mimicked in the ca
se of permutations-with-quipu. The quipu are allowed to pass upwards throu
gh the crossings of transverse strings. So a permutation-with-quipu repres
ents an element in a semi-direct product.\n\nWe have developed appealing d
iagrams that represent the elements in the dihedral groups\, and especiall
y in the finite subgroups of SU(2). Have no fear! The groups in question w
ill be described explicitly\, and we’ll play with the diagrams in ways t
hat allow easy computations. In fact\, the permutations-with-quipu can be
thought of as matrices in disguise. I will show how to go between the quip
u and the corresponding matrices. Emphasis will be upon examples.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blake Madill
DTSTART;VALUE=DATE-TIME:20221019T170000Z
DTEND;VALUE=DATE-TIME:20221019T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/27
DESCRIPTION:Title: An Algebraic Proof of the Fundamental Theorem of Algebra
\nby Blake Madill as part of Undergraduate Seminar\n\n\nAbstract\nRecall t
hat the Fundamental Theorem of Algebra states that every non-constant poly
nomial over the complex numbers completely factors as a product of linear
terms. In a typical undergraduate experience\, students will see proofs of
this theorem using topology and/or complex analysis. In this talk\, we wi
ll explore a completely algebraic (with the exception of some basic calcul
us) proof of this algebraic theorem. Students will be introduced to aspect
s of group theory\, Sylow theory\, field theory\, and Galois theory. No pr
ior knowledge of abstract algebra will be assumed.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Brewer
DTSTART;VALUE=DATE-TIME:20221026T170000Z
DTEND;VALUE=DATE-TIME:20221026T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/28
DESCRIPTION:Title: Star rosettes in GeoGebra: constructing traditional patterns
with contemporary technologies\nby Sarah Brewer as part of Undergradu
ate Seminar\n\n\nAbstract\nStar rosette patterns are ubiquitous in geometr
ic architectural ornament of the Islamic world. These patterns are traditi
onally built on a mathematically elegant system of polygons and tangent ci
rcles in their underlying Euclidean compass and straightedge constructions
. Of particular interest are star rosette patterns built on univalent circ
le packings whose intersection graph is any k-uniform tiling\, where varyi
ng the angle of the star rosette pattern lines serves as the transition be
tween a tiling and its dual. In simple terms\, you’ll learn how to make
some pretty patterns in GeoGebra.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Teeter
DTSTART;VALUE=DATE-TIME:20221102T170000Z
DTEND;VALUE=DATE-TIME:20221102T180000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/29
DESCRIPTION:Title: Spheres\, Donuts and Crazy Bottles: An Introduction to The C
lassification Theorem of Surfaces\nby Alex Teeter as part of Undergrad
uate Seminar\n\n\nAbstract\nMathematicians love to classify mathematical s
tructures in order to understand them better. In this presentation\, I wil
l take you on a journey through the World of Surfaces and prove their clas
sification. We will see many examples of Surfaces\, such as the one-sided
Mobius Strip\, the Torus\, and the Klein Bottle\, a bizarre surface that c
annot be embedded in 3-dimensional space. We will also cover how to constr
uct surfaces easily and conveniently using surgery\, and prove that all su
rfaces (that fulfill certain conditions) can be constructed from such surg
ery. I hope you are excited as I am to delve into the wonderful world of T
opology!\n\nNo prior knowledge of Topology is needed.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Briggs
DTSTART;VALUE=DATE-TIME:20221109T180000Z
DTEND;VALUE=DATE-TIME:20221109T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/30
DESCRIPTION:Title: What’s the deal with Homological Algebra?\nby Ben Brig
gs as part of Undergraduate Seminar\n\n\nAbstract\nBack in the 70’s\, Da
vid Mumford accused algebraic geometry of “secretly plotting to take ove
r all the rest of mathematics”. While that battle was raging\, the topol
ogists attacked from the side and annexed most of algebra (as well as a go
od deal of number theory\, combinatorics\, statistics\, physics). Nowadays
you cannot go outside without stepping in homology or cohomology\, or som
e kind of homotopy. All of this started from homological algebra (the Troj
an horse?)\, which sort of began with David Hilbert and Emmy Noether way b
ack in the 1890’s\, but which really got going in the 50’s. I will exp
lain what homological algebra is in very gentle terms\, starting with chai
n complexes\, and I’ll give a lot of concrete examples of the cool thing
s you can do with it. I might also give a less concrete idea of how it end
ed up everywhere (or at least\, in math I do).\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgür Esentepe
DTSTART;VALUE=DATE-TIME:20221116T180000Z
DTEND;VALUE=DATE-TIME:20221116T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/31
DESCRIPTION:Title: What caused Coxeter many restless nights?\nby Özgür Es
entepe as part of Undergraduate Seminar\n\n\nAbstract\n“Frieze patterns
” kept Coxeter up at night. This talk will introduce these surprisingly
ubiquitous grids of integers. We will discuss some basic properties and ho
w they appear in representation theory. We will assume almost zero backgro
und.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Zhengyu Li
DTSTART;VALUE=DATE-TIME:20221123T180000Z
DTEND;VALUE=DATE-TIME:20221123T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/32
DESCRIPTION:Title: A SAT Solver + Computer Algebra Attack on the Minimal Kochen
-Specker Problem\nby Brian Zhengyu Li as part of Undergraduate Seminar
\n\n\nAbstract\nOne of the most fundamental results in the foundations of
quantum mechanics is the Kochen-Specker (KS) theorem\, a `no-go’ theorem
that states that contextuality is an essential feature of any hidden-vari
able theory. The theorem hinges on the existence of a mathematical object
called a KS vector system. While the existence of a KS vector system was f
irst established by Kochen and Specker\, the problem of the minimum size o
f such a system has stubbornly remained open for over 50 years. In this pa
per\, we present a new method that is based on a combination of a SAT solv
er and a computer algebra system (CAS) to address this problem. Using our
approach\, we improve the lower bound from 22 to 23\, with a significant s
peed-up over the most recent computational methods. Finding the minimum KS
system could enable applications in security of quantum cryptographic pro
tocols\, zero-error classical communication\, and dimension witnessing.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Maltese
DTSTART;VALUE=DATE-TIME:20221130T180000Z
DTEND;VALUE=DATE-TIME:20221130T190000Z
DTSTAMP;VALUE=DATE-TIME:20221209T115707Z
UID:UndergraduateSeminar/33
DESCRIPTION:Title: An Introduction to Modal Logic and Its Applications\nby
Jesse Maltese as part of Undergraduate Seminar\n\n\nAbstract\nModal logic
refers to an extension of the language of classical logic wherein two new
operators are added.\nReferred to as modal operators and denoted □ and
◊ (‘box’ and ‘diamond’ respectively)\, these operators change th
e truth value of a proposition\, allowing one to reason about modalities s
uch as necessity\, knowledge\, and time.\nThis talk will first present som
e of the historical development of modal logic\, and then introduce the Kr
ipke semantics. We will talk briefly of some alternative semantics\, befor
e presenting other modal logics\, specifically temporal\, epistemic\, and
doxastic. We will conclude with a discussion of the applications of these
systems of logic to computer science. Specifically\, how they are used to
reason about distributed systems and concurrent programs\, and for verifyi
ng correctness of software. Throughout\, we will make note of the philosop
hical applications.\n\nThis talk will assume an understanding of first-ord
er logic.\n
LOCATION:https://researchseminars.org/talk/UndergraduateSeminar/33/
END:VEVENT
END:VCALENDAR