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BEGIN:VEVENT
SUMMARY:Brian Li (University of Toronto)
DTSTART:20210526T180000Z
DTEND:20210526T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/1
DESCRIPTION:Title: Cops and Robbers with Many Variants\nby Brian Li (
University of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nMat
hematics and games complement each other in both mathematical research and
learning. Cops and Robbers is a game played on graphs between a set of co
ps and a single robber. The cops begin the game by moving to a set of vert
ices\, with the robber then choosing a vertex to occupy. All players move
from vertex-to-vertex along edges. The cops win by successfully occupying
the robber’s vertex\, hence catching the robber. We will discuss theorem
s that help us better understand such games and unleash our creativity to
explore many different variants. No prior knowledge required.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker Glynn-Adey (University of Toronto)
DTSTART:20210602T180000Z
DTEND:20210602T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/2
DESCRIPTION:Title: The Probabilistic Method\nby Parker Glynn-Adey (Un
iversity of Toronto) as part of Undergraduate Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Chislett (University of Toronto)
DTSTART:20210609T180000Z
DTEND:20210609T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/3
DESCRIPTION:Title: Ray Tracing and the Light Transport Equation\nby B
enjamin Chislett (University of Toronto) as part of Undergraduate Seminar\
n\n\nAbstract\nRay Tracing is the primary technique for rendering photorea
listic images. Advancements in ray tracing techniques have enabled its use
in a variety of computer graphics applications\, from animated films to r
eal-time video games. In this talk\, we explore the Light Transport Equati
on\, Monte Carlo integration\, and some of the many optimizations that hav
e led to ray tracing's rapid rise in popularity.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Maltese (University of Toronto)
DTSTART:20210616T180000Z
DTEND:20210616T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/4
DESCRIPTION:Title: An Introduction to Mathematical Logic\nby Jesse Ma
ltese (University of Toronto) as part of Undergraduate Seminar\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schrittesser (University of Toronto)
DTSTART:20210630T180000Z
DTEND:20210630T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/5
DESCRIPTION:Title: Your life will be better with infinitesimals (Part 2)<
/a>\nby David Schrittesser (University of Toronto) as part of Undergraduat
e Seminar\n\n\nAbstract\nWhen Leibniz\, Newton\, and others first develope
d calculus\, they used the metaphor of infinitely small\, or infinitesimal
\, quantities to try to justify their methods. Later\, infinitesimals were
expelled from mathematics and calculus was made rigorous using the famili
ar notions of limit and epsilon-delta formulations.\n\nBut infinitesimals
have been making a come back! Using methods from logic\, in particular mod
el theory\, they have been restored as respected citizens in rigorous math
ematical arguments. This approach\, called non-standard analysis has been
described as ``the analysis of the future''. And indeed\, it sometimes all
ows 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 probl
em in statistics (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 course I will teach about this topic at U of T in this fall!)\
n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schrittesser (University of Toronto)
DTSTART:20210623T180000Z
DTEND:20210623T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/6
DESCRIPTION:Title: Your life will be better with infinitesimals\nby D
avid Schrittesser (University of Toronto) as part of Undergraduate Seminar
\n\n\nAbstract\nWhen Leibniz\, Newton\, and others first developed calculu
s\, they used the\nmetaphor of infinitely small\, or infinitesimal\, quant
ities to try to justify\ntheir methods. Later\, infinitesimals were expell
ed from mathematics and calculus was\nmade rigorous using the familiar not
ions of limit and epsilon-delta formulations.\n\nBut infinitesimals have b
een making a come back! Using methods from logic\, in particular model the
ory\, they have been restored as respected citizens in rigorous mathematic
al arguments. This approach\, called non-standard analysis has been descri
bed 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
statistics (namely giving a Bayesian interpretation of admissibility).\n\n
In this talk I will give an introduction to the non-standard method and de
scribe some applications. (And if I manage to spark your interest\, come t
o the course I will teach about this topic at U of T in this fall!)\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Santos (University of Toronto)
DTSTART:20210721T180000Z
DTEND:20210721T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/7
DESCRIPTION:Title: An Introduction to Group Theory through Puzzles\nb
y Kevin Santos (University of Toronto) as part of Undergraduate Seminar\n\
n\nAbstract\nThe concept of a group is a powerful tool that we can use to
understand the structures of mathematical objects. In this talk\, we’ll
use well-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 example
s of groups\, such as the Klein 4-group and the permutation groups. We’l
l then see how these ideas can be applied to understand the puzzles.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuveshen Mooroogen (University of Toronto)
DTSTART:20210707T180000Z
DTEND:20210707T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/8
DESCRIPTION:Title: Shining a rainbow-coloured light on the fundamental th
eorem of algebra\nby Yuveshen Mooroogen (University of Toronto) as par
t of Undergraduate Seminar\n\n\nAbstract\nThe graphs of real-valued functi
ons 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 f
unctions on the complex plane\, however\, are subsets of a four-dimensiona
l space. Good luck sketching that on a piece of paper.\n\nIn this presenta
tion\, I will introduce “domain colouring”\, which is a technique used
to illustrate functions of the complex numbers.\n\nThis talk will be in t
wo parts. In the first part\, I will explain how to read and construct dom
ain colouring plots\, focusing on a number of simple examples. In the seco
nd part\, I will discuss the Fundamental Theorem of Algebra (which states
that every nonconstant polynomial has a complex root) and explain how to v
isualise one of its proofs using domain colouring. This part of the talk w
ill draw heavily from D. J. Velleman’s beautiful expository article [1].
\n\nPrerequisites: Familiarity with the concept of dimension (for a vector
space) and with the complex numbers. (Basic principles only. You should k
now what the notation $x+iy$ means\, and how to convert it to modulus-argu
ment/polar form.) Knowledge of multivariable calculus and complex analysis
is not expected.\n\n[1] Velleman\, D.J. The Fundamental Theorem of Algebr
a: A Visual Approach. Math Intelligencer 37\, 12–21 (2015). https://doi.
org/10.1007/s00283-015-9572-7.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Lai (University of Toronto)
DTSTART:20210714T180000Z
DTEND:20210714T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/9
DESCRIPTION:Title: Partial orders and application to semantics of compute
r programs\nby Albert Lai (University of Toronto) as part of Undergrad
uate Seminar\n\n\nAbstract\nPartial orders generalize total orders. A fami
liar example is the subset relation over a family of sets. I will show a c
omputer-science application of partial orders to modelling recursive progr
ams. This will be a glimpse of denotational semantics\, the study of descr
ibing program behaviour by mapping programs to suitable mathematical struc
tures and partial order\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rakan Omar (York University)
DTSTART:20210728T180000Z
DTEND:20210728T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/10
DESCRIPTION:Title: Influence Centrality of Graphs\nby Rakan Omar (Yo
rk University) as part of Undergraduate Seminar\n\n\nAbstract\nIn graph th
eory and network analysis\, the notion of centrality refers to assigning n
odes in a network an index representing the extent to which each node is c
entral - important to the network\, or well positioned in it - based on so
me mathematical property.\nThere are a variety of measures of centrality\,
each of which measures ‘centrality’ differently\, based on (or result
ing in) a different definition of ‘importance’ or ‘prominence’.\n\
nI will define an original measure of centrality\, a variation of pageRank
centrality\, which i call ‘influence centrality’\, that measures the
extent to which a node contributes a relation (what is represented by the
arcs) to the graph in a directed weighted graph with a finite number of no
des\, which are initially labelled with values.\nI will discuss some prope
rties\, applications\, and extensions of influence centrality.\n\nI assume
some familiarity with graph theory terminology and linear algebra.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Fallone (York)
DTSTART:20210804T180000Z
DTEND:20210804T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/11
DESCRIPTION:Title: The Projected Number of Underreported COVID 19 Cases
in Canada\nby Andrew Fallone (York) as part of Undergraduate Seminar\n
\n\nAbstract\nAs Canada focuses more on mitigation strategies rather than
eradication ones\, mathematical modelling could play an important role in
preserving lives. The model used in this project is a modified SIR model w
hich retains a conservative calculation for COVID 19 cases while giving an
insight into how unreported COVID 19 cases are in Canada with the assumpt
ion that we have a limited amount of data. This approach seems to be the m
ost effective due to the uncertainty of COVID 19 progression in Canada. Fu
rthermore\, this modified SIR model uses a basic reproduction parameter
“to estimate the attack rate\, epidemic duration”\, and critical point
s of COVID 19 cases in Canada.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Midroni (University of Toronto)
DTSTART:20210811T180000Z
DTEND:20210811T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/12
DESCRIPTION:Title: Artificial neural networks: The fundamentals\nby
Julie Midroni (University of Toronto) as part of Undergraduate Seminar\n\n
\nAbstract\nArtificial neural networks (ANNs) are a powerful class of mach
ine learning algorithms that can be used for a variety of purposes\, inclu
ding image classification\, function approximation\, and natural language
processing. This talk will present the mathematical basics of ANNs\, and b
riefly explore different ANN algorithms and their uses.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amalrose Vayalinkal (University of Toronto)
DTSTART:20210825T180000Z
DTEND:20210825T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/13
DESCRIPTION:Title: Virtual Ring Routing\nby Amalrose Vayalinkal (Uni
versity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nVirtua
l Ring Routing (VRR) schemes define a routing algorithm for communication
between devices by establishing a virtual network overlay given a physical
network of $N$ devices. Using graphs to model the physical network\, we i
ntroduce the algorithm and explore the pros and cons of VRR. Time permitti
ng\, 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 o
f an NSERC USRA this summer under the supervision of Professor Almut Burch
ard.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker and Lisa
DTSTART:20210901T180000Z
DTEND:20210901T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/14
DESCRIPTION:Title: TOWNHALL / ORGANIZATION\nby Parker and Lisa as pa
rt of Undergraduate Seminar\n\n\nAbstract\nWe are holding a special meetin
g to organize the seminar for the rest of the term.\n\nIf you have NEVER a
ttended 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* W
ould you like to give a talk?\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhekai Pang and Yuhong Zhang (University of Toronto)
DTSTART:20211110T160000Z
DTEND:20211110T165900Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/15
DESCRIPTION:Title: Matrix analysis with a focus on inequalities\nby
Zhekai Pang and Yuhong Zhang (University of Toronto) as part of Undergradu
ate Seminar\n\n\nAbstract\nMatrix inequalities are one of the key componen
ts in matrix analysis. They have a wide range of applications in statistic
s\, computer science\, economics\, and physics.\n\nIn this presentation\,
we focus on some classical matrix inequalities such as the Rayleigh-Ritz q
uotient\, the Courant Fischer theorem\, Weyl’s inequality\, the interloc
king eigenvalue lemma\, and the Woodbury matrix identity. In particular\,
some of these show the importance of the maximum and minimum of eigenvalue
s and singular values.\n\nRecommend Background: Linear Algebra and Calculu
s. (In the beginning of the presentation\, some definitions and key proper
ties such as positive definiteness will be reviewed.)\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathew Cater Benavides (University of Toronto)
DTSTART:20211117T190000Z
DTEND:20211117T200000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/16
DESCRIPTION:Title: An Introduction to the Fractional Brownian Motion
\nby Mathew Cater Benavides (University of Toronto) as part of Undergradua
te Seminar\n\n\nAbstract\nThe classical Brownian motion (or Wiener process
) serves as the fundamental object of probability theory with vast theoret
ical and practical applications in a plethora of fields. In the early 1940
’s Kolmogorov sought a natural one parameter extension of the process in
aims of modelling turbulence in liquids\, the extension consists of retai
ning the framework of the classical motion by constructing still a continu
ous centered Gaussian process that retains self similarity (of a now disti
nct index from that of the classical motion) and stationarity of increment
s but draws its distinction by parameterizing its specifying covariance st
ructure with what is known as the Hurst index\,$H \\in (0\,1)$\, resulting
in (for ‘most’ values of $H$) a non-Markov process allowing it to ser
ve as a popular model for dependent phenomena\; this extension has since b
een kept in common parlance as fractional Brownian motion (fBm). This talk
aims to provide discussion and (at times demonstration) of the fundamenta
l properties of the fBm as well as investigate sample path properties’ d
ependence on the Hurst parameter.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART:20211124T190000Z
DTEND:20211124T200000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/17
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Th
eorem Prover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE /
University of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHav
e you heard of automated and interactive theorem provers? Did you know tha
t American mathematician Alex Kontorovich predicts that the Lean Interacti
ve Theorem Prover will be so widely used that it will be as necessary as L
aTex 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 choose\, 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 numb
er game. Come join us and have some fun!\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART:20211201T190000Z
DTEND:20211201T200000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/18
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Th
eorem Prover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE /
University of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHav
e you heard of automated and interactive theorem provers? Did you know tha
t American mathematician Alex Kontorovich predicts that the Lean Interacti
ve Theorem Prover will be so widely used that it will be as necessary as L
aTex 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 choose\, 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 numb
er game. Come join us and have some fun!\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parker Glynn-Adey (University of Toronto)
DTSTART:20220202T190000Z
DTEND:20220202T200000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/20
DESCRIPTION:Title: ORGANIZATIONAL MEETING\nby Parker Glynn-Adey (Uni
versity of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nWe are
holding a special meeting to organize the seminar for the rest of the ter
m.\n\nIf you have NEVER attended Undergraduate Seminar\, this is a great t
ime 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 o
n a specific topic?\n\n* Would you like to give a talk?\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE / University of
Toronto)
DTSTART:20220209T190000Z
DTEND:20220209T200000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/21
DESCRIPTION:Title: Getting Started: Proving with the Lean Interactive Th
eorem Prover\nby Kitty Yan\, Japleen Anand\, and Logan Murphy (OISE /
University of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nHav
e you heard of automated and interactive theorem provers? Did you know tha
t American mathematician Alex Kontorovich predicts that the Lean Interacti
ve Theorem Prover will be so widely used that it will be as necessary as L
aTex 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 choose\, 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 numb
er game. Come join us and have some fun!\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Santos (University of Toronto)
DTSTART:20220316T180000Z
DTEND:20220316T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/22
DESCRIPTION:Title: Modelling Mathematics with Knitting and Crochet\n
by Kevin Santos (University of Toronto) as part of Undergraduate Seminar\n
\n\nAbstract\nWhen studying subjects like geometry and topology\, it can b
e difficult to visualize or understand certain abstract concepts. Being ab
le to hold and manipulate a physical model of a mathematical object can gi
ve deeper intuition into its properties. The process of constructing such
an object also offers further insight. In this talk\, we will investigate
how geometric and topological objects can be constructed using the crafts
of knitting and crochet\, which offer unique advantages in creating models
. We will describe how the hyperbolic plane can be modelled with crochet a
nd we will explore how topological surfaces such as the sphere\, the torus
\, and the Klein bottle can be knitted. No prior knowledge in geometry\, t
opology\, knitting\, or crochet is required.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Logan Lim (University of Toronto)
DTSTART:20220323T180000Z
DTEND:20220323T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/23
DESCRIPTION:Title: Why Geometric Algebra Should be in the Standard Linea
r Algebra Curriculum\nby Logan Lim (University of Toronto) as part of
Undergraduate Seminar\n\n\nAbstract\nGeometric algebra is an extension of
$\\mathbb{R}^n$ that includes as special cases: The complex numbers\, quat
ernions\, exterior algebras\, dual numbers\, split-complex numbers\, dual
quaternions and more! When applied to multivariable calculus\, it generali
zes the fundamental theorem of calculus on manifolds to include the diverg
ence theorem\, curl theorem\, and gradient theorem\, and as a result Green
’s and Stoke’s theorem\, as special cases of a single statement. It al
so simplifies many geometric operations in computer graphics by eliminatin
g the need for matrices in projections\, rotations\, and reflections. Thou
gh we can only cover the ‘main idea’ of geometric algebra in the allot
ted time\, this talk will be a buffet of ideas you can explore for this fa
scinating and deceptively simple algebraic object.\n\nMathematicians hate
him!!!! See how Clifford generalized rotations and orthogonal complements
in n-dimensions with this one simple trick! \n\n$$\\mathbf{uv} = \\mathbf{
u} \\cdot \\mathbf{v} + \\mathbf{u} \\wedge \\mathbf{v}$$\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Teeter (University of Toronto)
DTSTART:20220330T180000Z
DTEND:20220330T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/24
DESCRIPTION:Title: Seifert Surfaces and Knots Genus\nby Alex Teeter
(University of Toronto) as part of Undergraduate Seminar\n\n\nAbstract\nKn
ot Theory\, a field of mathematics born from a misguided model for atoms\,
has since grown to become an important subfield of Topology. Not only doe
s it have much of mathematical interest\, but also numerous connections to
fields such as graph theory\, the study of manifolds\, and applications t
o Biology and Physics. We will analyze the connection between Knot Theory
and the Topology of Surfaces. Along the way\, we will cover the Euler Char
acteristic\, Genus and the beautiful Classification Theorem of Surfaces. T
hrough 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 also be vital in establishing fundamental properties of prime and co
mposite Knots. No prior background in Knot Theory or Topology is assumed.\
n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zack Wolske
DTSTART:20220921T170000Z
DTEND:20220921T180000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/25
DESCRIPTION:Title: An Introduction to Combinatorial Games\nby Zack W
olske as part of Undergraduate Seminar\n\n\nAbstract\nWe’ll introduce a
collection of two player games that anyone can play – they’re fun for
all ages. Some games have strategy patterns we can find quickly\, some hav
e well-hidden patterns that we can uncover with more tools\, and others ha
ve patterns that no one in the world has found. We will play and analyze t
hose games and share currently open problems.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART:20221005T170000Z
DTEND:20221005T180000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/26
DESCRIPTION:Title: Permutations with quipu\nby Scott Carter as part
of Undergraduate Seminar\n\n\nAbstract\nAccording to Wikipedia\, a quipu i
s an accounting system in which knots are tied in a sequence of strings. T
hey were used as a method of storing tax and other financial records. Here
we consider cyclic subgroups of groups and catalogue the cosets by means
of a string bundle (the English word\, not the mathematical word is intend
ed). The quipu are elements in the cyclic subgroups. The traditional metho
ds of multiplying braids by means of vertical juxtaposition is mimicked in
the case of permutations-with-quipu. The quipu are allowed to pass upward
s through the crossings of transverse strings. So a permutation-with-quipu
represents an element in a semi-direct product.\n\nWe have developed appe
aling diagrams that represent the elements in the dihedral groups\, and es
pecially in the finite subgroups of SU(2). Have no fear! The groups in que
stion will be described explicitly\, and we’ll play with the diagrams in
ways that allow easy computations. In fact\, the permutations-with-quipu
can be thought of as matrices in disguise. I will show how to go between t
he quipu and the corresponding matrices. Emphasis will be upon examples.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blake Madill
DTSTART:20221019T170000Z
DTEND:20221019T180000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/27
DESCRIPTION:Title: An Algebraic Proof of the Fundamental Theorem of Alge
bra\nby Blake Madill as part of Undergraduate Seminar\n\n\nAbstract\nR
ecall that the Fundamental Theorem of Algebra states that every non-consta
nt polynomial over the complex numbers completely factors as a product of
linear terms. In a typical undergraduate experience\, students will see pr
oofs of this theorem using topology and/or complex analysis. In this talk\
, we will explore a completely algebraic (with the exception of some basic
calculus) proof of this algebraic theorem. Students will be introduced to
aspects of group theory\, Sylow theory\, field theory\, and Galois theory
. No prior knowledge of abstract algebra will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Brewer
DTSTART:20221026T170000Z
DTEND:20221026T180000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/28
DESCRIPTION:Title: Star rosettes in GeoGebra: constructing traditional p
atterns with contemporary technologies\nby Sarah Brewer as part of Und
ergraduate Seminar\n\n\nAbstract\nStar rosette patterns are ubiquitous in
geometric architectural ornament of the Islamic world. These patterns are
traditionally built on a mathematically elegant system of polygons and tan
gent circles in their underlying Euclidean compass and straightedge constr
uctions. Of particular interest are star rosette patterns built on univale
nt circle packings whose intersection graph is any k-uniform tiling\, wher
e varying the angle of the star rosette pattern lines serves as the transi
tion between a tiling and its dual. In simple terms\, you’ll learn how t
o make some pretty patterns in GeoGebra.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Teeter
DTSTART:20221102T170000Z
DTEND:20221102T180000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/29
DESCRIPTION:Title: Spheres\, Donuts and Crazy Bottles: An Introduction t
o The Classification Theorem of Surfaces\nby Alex Teeter as part of Un
dergraduate Seminar\n\n\nAbstract\nMathematicians love to classify mathema
tical structures in order to understand them better. In this presentation\
, I will take you on a journey through the World of Surfaces and prove the
ir classification. We will see many examples of Surfaces\, such as the one
-sided Mobius Strip\, the Torus\, and the Klein Bottle\, a bizarre surface
that cannot be embedded in 3-dimensional space. We will also cover how to
construct surfaces easily and conveniently using surgery\, and prove that
all surfaces (that fulfill certain conditions) can be constructed from su
ch surgery. I hope you are excited as I am to delve into the wonderful wor
ld of Topology!\n\nNo prior knowledge of Topology is needed.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Briggs
DTSTART:20221109T180000Z
DTEND:20221109T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/30
DESCRIPTION:Title: What’s the deal with Homological Algebra?\nby B
en Briggs as part of Undergraduate Seminar\n\n\nAbstract\nBack in the 70
’s\, David Mumford accused algebraic geometry of “secretly plotting to
take over all the rest of mathematics”. While that battle was raging\,
the topologists attacked from the side and annexed most of algebra (as wel
l as a good deal of number theory\, combinatorics\, statistics\, physics).
Nowadays you cannot go outside without stepping in homology or cohomology
\, or some kind of homotopy. All of this started from homological algebra
(the Trojan horse?)\, which sort of began with David Hilbert and Emmy Noet
her way back in the 1890’s\, but which really got going in the 50’s. I
will explain what homological algebra is in very gentle terms\, starting
with chain complexes\, and I’ll give a lot of concrete examples of the c
ool things you can do with it. I might also give a less concrete idea of h
ow it ended up everywhere (or at least\, in math I do).\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgür Esentepe
DTSTART:20221116T180000Z
DTEND:20221116T190000Z
DTSTAMP:20260404T095901Z
UID:UndergraduateSeminar/31
DESCRIPTION:Title: What caused Coxeter many restless nights?\nby Öz
gür Esentepe as part of Undergraduate Seminar\n\n\nAbstract\n“Frieze pa
tterns” kept Coxeter up at night. This talk will introduce these surpris
ingly ubiquitous grids of integers. We will discuss some basic properties
and how they appear in representation theory. We will assume almost zero b
ackground.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Zhengyu Li
DTSTART:20221123T180000Z
DTEND:20221123T190000Z
DTSTAMP:20260404T095901Z
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 foundati
ons of quantum mechanics is the Kochen-Specker (KS) theorem\, a `no-go’
theorem that states that contextuality is an essential feature of any hidd
en-variable theory. The theorem hinges on the existence of a mathematical
object called a KS vector system. While the existence of a KS vector syste
m was first established by Kochen and Specker\, the problem of the minimum
size of such a system has stubbornly remained open for over 50 years. In
this paper\, we present a new method that is based on a combination of a S
AT solver and a computer algebra system (CAS) to address this problem. Usi
ng our approach\, we improve the lower bound from 22 to 23\, with a signif
icant speed-up over the most recent computational methods. Finding the min
imum KS system could enable applications in security of quantum cryptograp
hic protocols\, zero-error classical communication\, and dimension witness
ing.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Maltese
DTSTART:20221130T180000Z
DTEND:20221130T190000Z
DTSTAMP:20260404T095901Z
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 t
wo new operators are added.\nReferred to as modal operators and denoted
□ and ◊ (‘box’ and ‘diamond’ respectively)\, these operators c
hange the truth value of a proposition\, allowing one to reason about moda
lities such as necessity\, knowledge\, and time.\nThis talk will first pre
sent some of the historical development of modal logic\, and then introduc
e the Kripke semantics. We will talk briefly of some alternative semantics
\, before presenting other modal logics\, specifically temporal\, epistemi
c\, and doxastic. We will conclude with a discussion of the applications o
f these systems of logic to computer science. Specifically\, how they are
used to reason about distributed systems and concurrent programs\, and for
verifying correctness of software. Throughout\, we will make note of the
philosophical applications.\n\nThis talk will assume an understanding of f
irst-order logic.\n
LOCATION:https://stable.researchseminars.org/talk/UndergraduateSeminar/33/
END:VEVENT
END:VCALENDAR