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SUMMARY:Edmund Harriss (University of Arkansas)
DTSTART;VALUE=DATE-TIME:20240628T153000Z
DTEND;VALUE=DATE-TIME:20240628T163000Z
DTSTAMP;VALUE=DATE-TIME:20240910T005653Z
UID:CompMath/1
DESCRIPTION:Title: Mappings between abstract and physical spaces\nby Edmund Harriss (Uni
versity of Arkansas) as part of Compassionate Math Seminar\n\n\nAbstract\n
I work as a mathematician and artist\, and within the Illustrating Mathema
tics group\, at the heart of this work lie ideas about translation and map
ping between physical and abstract spaces\, in different ways to just mode
lling. In particular thinking about ideas in art and mathematical illustra
tion where physical spaces are being used to understand the abstract world
(rather than science that normally goes the other way). Images\, models a
nd experiences can reveal aspects of the abstract that we do not yet under
stand and thus drive research. I will introduce some ideas about this and
then open the question of how category theory might be useful to understan
ding the mapping and conversion that is happening between the abstract and
the physical and thus how it can be validated and potentially checked for
errors.\n\nThe talk will be moderated by Namista Tabassum who joined our
comp math group recently. Namista is an interdisciplinary researcher and b
usiness advisor who has worked with diverse organizations in Canada and Ba
ngladesh\, notably leading research projects and facilitating social impac
t events. Her interest in mathematics and science communication stems from
her belief in compassionate mathematics\, bridging her passion for art an
d logic to make complex concepts accessible and engaging.\n
LOCATION:https://researchseminars.org/talk/CompMath/1/
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SUMMARY:Irfan Alam (U. Pennsylvania)
DTSTART;VALUE=DATE-TIME:20240531T160000Z
DTEND;VALUE=DATE-TIME:20240531T170000Z
DTSTAMP;VALUE=DATE-TIME:20240910T005653Z
UID:CompMath/2
DESCRIPTION:Title: How will mathematics education change with the rise of A.I. tutors?\n
by Irfan Alam (U. Pennsylvania) as part of Compassionate Math Seminar\n\n\
nAbstract\nI have been advising two students\, Tomas Nepala and Tunga Bayr
ak\, who have created MotionShark\, which is a software that generates vid
eo explanations of mathematical problems. This type of technology prompts
significant questions about the future role of mathematics educators and t
he evolution of teaching methods. \n\nAfter Tomas and Tunga exhibit the cu
rrent capabilities of their evolving technology\, I will give a presentati
on on some challenges that I think the mathematics education community mus
t brace itself for in the wake of this type of technology. Navigating such
challenges requires an active input of mathematicians and this talk is me
ant to start that conversation at an international level. I will share my
vision on how to integrate this type of technology into lower-level mathem
atics classes in healthy ways\, and how I see the scope of such classes ad
apting and evolving in a future where I argue the context of mathematics w
ill become more important to teach than actual methods of problem solving.
\n\nMy goal is to start this conversation that will hopefully keep going
offline after the talk has ended\, since we as a community ought to better
understand in a timely manner the directions in which mathematics educati
on will change in the wake of this and similar technologies in near future
. \nThe talk will be moderated by Daniel Filonik who is a postdoc at Carne
gie Mellon University (CMU) and foreign guest researcher at the National I
nstitute of Standards and Technology (NIST). Daniel specializes in data vi
sualization and human computer interaction. His current work is focused on
natural interfaces for interactive data modeling and analysis with formal
foundations in category theory.\n
LOCATION:https://researchseminars.org/talk/CompMath/2/
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SUMMARY:Niels Voorneveld (Cybernetica)
DTSTART;VALUE=DATE-TIME:20240425T160000Z
DTEND;VALUE=DATE-TIME:20240425T170000Z
DTSTAMP;VALUE=DATE-TIME:20240910T005653Z
UID:CompMath/3
DESCRIPTION:Title: Relational Molecules: Using games to interact with formal structures\
nby Niels Voorneveld (Cybernetica) as part of Compassionate Math Seminar\n
\n\nAbstract\nI love video games\, and I love mathematics. For the longest
time\, I saw them as separate. But as time went on\, I realized their sim
ilarities: both define worlds besides our own which we can explore and int
eract with. Combined\, games can give a powerful tool to learn about and p
lay with mathematical structures in a non-standard way. In this talk\, we
look at an idea I have been thinking about in the past few months\, that o
f the search for relational molecules. These are relations which look like
and share symmetries with molecules\, and are inspired by the works of 19
th century philosopher Peirce. We look at examples of such molecules\, whe
re they may turn up\, and see how a simple game allows people to interact
with them to learn their behavior. After the talk\, we will have an open d
iscussion about the ideas covered.\n
LOCATION:https://researchseminars.org/talk/CompMath/3/
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SUMMARY:David Spivak (Topos Institute)
DTSTART;VALUE=DATE-TIME:20240802T153000Z
DTEND;VALUE=DATE-TIME:20240802T163000Z
DTSTAMP;VALUE=DATE-TIME:20240910T005653Z
UID:CompMath/4
DESCRIPTION:Title: How the Yoneda lemma applies\nby David Spivak (Topos Institute) as pa
rt of Compassionate Math Seminar\n\n\nAbstract\nWhat is the relationship b
etween your web of concepts about the world and all the examples you've se
en of these concepts? And what is the relationship between a generic flowe
r and all the particular flowers or a generic bicycle and all the particul
ar bicycles? A formal answer to this was given by Nobuo Yoneda in a privat
e letter to a founder of Category Theory\, Saunders Mac Lane\, and this an
swer has become the most fundamental concept in category theory: the Yoned
a lemma.\n\nIn this talk\, I'll begin by explaining schemas and instances
—concept-webs and the system of examples that live in them—in terms of
categories C and set-valued functors F:C-->Set. Then I'll explain how eac
h concept (each node in the web) determines a generic instance: the generi
c flower\, the generic bicycle\, etc. \n\nSo given a concept\, how is the
generic instance of it related to all the other examples of it? The answer
is that the generic instance of flower can be overlaid perfectly onto any
particular flower\, and all its generic features will be given particular
values. This is the content of the Yoneda lemma: given any schema C and f
unctor (system of examples) F: C-->Set\, the Yoneda lemma says that "apply
ing F to concept c"\, i.e. the set of c-examples\, is the same as the set
of all ways that the generic instance for c can be overlaid onto the syste
m of examples. And this is how the Yoneda lemma "applies"!\n
LOCATION:https://researchseminars.org/talk/CompMath/4/
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SUMMARY:Nathan Haydon
DTSTART;VALUE=DATE-TIME:20240830T153000Z
DTEND;VALUE=DATE-TIME:20240830T163000Z
DTSTAMP;VALUE=DATE-TIME:20240910T005653Z
UID:CompMath/5
DESCRIPTION:Title: Peirce's Existential Graphs and String Diagrams for First-Order Logic
\nby Nathan Haydon as part of Compassionate Math Seminar\n\n\nAbstract\nTh
e Existential Graphs are the result of C.S. Peirce's studies in the logic
of relations and his concern for developing a better logical notation. In
this talk I give an accessible introduction to Peirce's graphs that emphas
izes the intuitions behind these notational choices and the resulting infe
rence rules. Along the way I discuss how Peirce's work has been the inspir
ation for recent advances in categorical logic and show examples of how th
e graphs help us present and clarify some of our logical concepts.\n
LOCATION:https://researchseminars.org/talk/CompMath/5/
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