click on the title to read the abstract:
"Contemplating infinity: mathematics and mindfulness"
Faculty forum
Center for Excellence in Teaching
University of Southern California
February 2017
abstract:
USC's Luke Wolcott will share how mindfulness techniques can improve mathematics pedagogy, drawing on his own ongoing Wiki project and his recent ACMHE presentation (Association of Contemplative Mind in Higher Education).
"Interactive software for topological data analysis"
Joint Mathematics Meeting
Atlanta, GA
January 2017
abstract:
I will demo new software for playing with 2D data sets and persistence barcodes, meant to help develop intuition for what a barcode can tell us. One can save and load data sets, easily add and remove points, and watch how the barcode changes in realtime. The software builds on the JavaPlex demo written for Processing by Mikael VejdemoJohansson. I will discuss possble future development for interacting with 3D live data.
"The effects of altitude sickness on mathematical cognition"
Joint Mathematics Meeting
Atlanta, GA
January 2017
abstract:
The Berlin gallery HORSEANDPONY ran an October 2016 exhibition "Altitude Sickness" of artifacts derived from artistic actions conducted by artist Elizabeth McTernan and mathematician Luke Wolcott during a summer 2015 trip to the Indian Himalayas. There they investigated the effects of high altuude on mathematical cognition, informed by The Great Trigonometrical Survey, weightlessness and the genius myth. Luke will talk about the piece and show images.
"Contemplative Pedagogy and STEM: A Mathematics Example and Open Discussion"
8th Annual Meeting of the Association for Contemplative Mind in Higher Education
University of Massachusetts at Amherst
Amherst, MA
October 2016
abstract:
A unique set of challenges and opportunities presents itself when we attempt to introduce contemplative pedagogy into STEM classes such as mathematics, statistics, physics, chemistry, and engineering. The goal of this session is an open discussion of these issues, seeded by specific examples from mathematics. I will demo several practices that I’ve used in my math classes, and describe examples from other math faculty that have been contributed to our slowly growing disciplinespecific wiki site: contemplativemathematicspedagogy.wikispaces.com.
"An Interactive introduction to topological data analysis"
Math Colloquium
Northern Michigan University
Marquette, MI
April 2016
abstract:
Topology is the study of space and shapes. Topological data analysis is a new applied field of mathematics that uses topological tools to study "the shape of data". Although only a decade old, TDA has been applied widely, for example to understand new types of cancer, the shape of proteins, natural images, and even basketball positions. I'll tell the story of how topology  considered one of the most "pure" areas of mathematics  was harnessed to yield insights about highdimensional data sets. We'll start with simple examples of point clouds, but then I'll demo software that I've written to analyze more complex data sets. No knowledge of topology is assumed; if you can visualize shapes you should be able to follow (most of) the talk.
"The User's Guide Project: giving experiential context to research papers"
Joint Mathematics Meeting
Seattle, WA
January 2016
abstract:
A user's guide  at the same time humanistic and technical  is written to accompany a published or soontobepublished research article, providing further exposition and context for the results. Enchiridion is a new informal annual journal that brings together five mathematicians from a common subfield to write user's guides on their own papers, then work closely together to collaboratively groupedit and peerreview a compilation. The goal of this onlineonly journal is to make research mathematics more accessible, to explore unconventional expositional styles, and to augment rigor with humanistic metadata. My talk will describe and demo the project, which is up at mathusersguides.com.
"Gardens of Infinity: Cantor meets the real deep Web"
Joint Mathematics Meeting
Seattle, WA
January 2016
abstract:
The real deep Web  curated, visceral, profound  is an antidote to oversaturated Wikipedia pages of words, and to mindless viral videos. The content complements logical arguments with stories and meaningful prompts to contemplate. The format moves away from walls of text towards highconcept design that encourages deep thought.
The Gardens of Infinity project is a collaboration between a mathematician, an interaction designer and a programmer. We present five provocatove statements from Cantor's set theory, and the translation between rigorous mathematics and metaphor is articulated. Each statement branches down four paths: the user can read a rigorous proof of the statement, a shorter more accessible summary argument of the statement, the story of the people and events surrounding the statement, or a philosophical discussion of what it might mean. These last sections  sometimes presenting conventional philosophical interpretations, sometimes unapologetically metaphorical  are in a sense the real meat of the project, leading the user to contemplate infinity in new ways.
My talk will explain and demo this web project, which is up at gardensofinfinity.com.
"The mathematics of walking in the Himalayas"
Science Hall Colloquium
Lawrence University
Appleton, WI
October 2015
abstract:
Walking uphill is a metaphor for doing mathematics. Walking uphill at high altitude under the influence of thin air addresses aptitude and effort, models the move from grounded subjective perspective to objective aerial view, and puts mathematics back into the moving body.
I'll tell the story of my summer trip to the Indian Himalayas, to perform artistic actions  involving shaved heads, boiling water, sketchbooks, and lots of long division  with my collaborator, Berlinbased artist Elizabeth McTernan.
I'll also tie our project in with the fascinating story of the Great Trigonometrical Survey of 19th century India, a 60year application of the law of sines to the British mapping and imperial control of the Indian subcontinent.
"Bousfield lattice invariants of triangulated symmetric monoidal categories"
AMS/EMS/SPM International Meeting
Porto, Portugal
June 2015
abstract:
If T is a well generated triangulated category with a symmetric monoidal structure, or any localizing subcategory of such a category, the Bousfield class of an object X is the collection of Y such that X tensor Y = 0. In such a category, the collection of Bousfield classes is a set and has the structure of a lattice. We discuss recent work in analyzing the structure of this lattice, in particular when considering a localizing subcategory that does not include the tensor unit.
"A classification of mathart work"
AMS/EMS/SPM International Meeting
Porto, Portugal
June 2015
abstract:
We present a rough classification of mathart pieces, based mainly on the relationship between math and art that they employ and demonstrate, as well as their subsequent functionalities. Hermann Hesse's 1946 novel "The Glass Bead Game" is invoked to clarify and illustrate our classification. This is a collaboration between Luke Wolcott, a mathematician at Lawrence University, Wisconsin, and Elizabeth McTernan, an exhibiting fine artist based in Berlin, Germany.
Panel discussion on "Math, poetry, and improvisations" collaboration
Math tea
Lawrence University
Appleton, WI
February 2015
This was a panel discussion  involving mathematicians, poets, and musicians  about the collaboration leading up to the concert performance. See "Past Projects" for more information.
"Conditional convergence in the process of math and art: a case study"
Science Hall Colloquium
Lawrence University
Appleton, WI
November 2014
abstract:
Wading into the Danish sea to measure the fractal dimension of a small island's coastline, by hand. Measuring the farthest distances traveled by various emotions communicated across the Gobi Desert in sun and darkness. Chopping down a tree in Maine and gathering witnesses to listen for its sound, at the right time and in the right direction, in a park in Sweden. Walking into a wall repeatedly to try to quantum tunnel through. Guiding participants through thought experiments and ritual circle dance, with the aim of inducing the experience of contemplating negative dimensional space. Electronic dance music based on category theory, an Indian raga, and a pen hitting a ceiling fan. A movement workshop inspired by topological data analysis. Come hear stories about these experiments at the interface of mathematics and art.
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"Report on the Bodies of Data workshops"
MAA MathFest
Portland, OR
August 2014
abstract:
Concurrent with MathFest this year, I'm running a Bodies of Data workshop with Portlandarea dancers, clowns, and theater performers. The workshop introduces the subject of topological data analysis  a fascinating and accessible approach to understanding the "shape" of data, and its persistent qualitative structure. The point of the workshop is to use TDA  the mathematical ideas and metaphors, and their vernacular counterparts  as a jumpingoff point for movement activities and exploratory performance. My talk will report on this workshop.
"A topological localizing subcategory that isn't a Bousfield class"
BIREP Seminar
University of Bielefeld
Bielefeld, Germany
April 2014
abstract:
The stable homotopy category of spectra is a nice compactly generated tensor triangulated category. In this talk I'll look at a quotient of this category, the HFplocal category. I will calculate the Bousfield lattice, and give an example of a localizing subcategory that isn't a Bousfield class. Almost all the methods used make sense in other tensor triangulated categories, so anyone familiar with this concept should be able to follow.
"A gentle introduction to category theory: architecture of the universe of abstract nonsense?"
Lawrence University
Appleton, WI
March 2014
abstract:
Some people call mathematics the language of nature. Some mathematicians call category theory the language of mathematics. This broad theory attempts to capture the shape of all of mathematics, and is notoriously abstract. (Search "general abstract nonsense" on Wikipedia and category theory comes up!) But category theory is also remarkably simple. I'll give a gentle introduction to this very important and powerful theory, and will show with lots of examples how simple and natural it is. At the same time, you'll get a taste of what higher mathematics is about. Anyone who's seen some group theory, ring theory, or linear algebra should be able to follow along.
"Telescope conjectures and Bousfield lattices for localized categories of spectra"
Homotopy Theory Satellite Conference
Joint Mathematics Meeting, January 2014
and
Algebraic Topology Seminar
Radboud University, Nijmegen, NL, May 2014
abstract:
We investigate several versions of the telescope conjecture on localized categories of spectra, and implications between them. Generalizing the "finite localization" construction, we show that on such categories, localizing away from a set of strongly dualizable objects is smashing. We classify all smashing localizations on the harmonic category, HFplocal category, and Ilocal category, where I is the BrownComenetz dual of the sphere spectrum; all are localizations away from strongly dualizable objects, although these categories have no nonzero compact objects. The Bousfield lattices of these categories are also computed.
"Bousfield lattices and smashing localizations of local categories"
Young Topologists' Meeting
EPFL, Lausanne, Switzerland
July 2013.
abstract:
Given an object X in a well generated tensor triangulated category C (such as the stable homotopy category, or its localizations), the Bousfield class of X is the collection of objects that tensor with X to zero. The set of Bousfield classes, ordered by reverse inclusion, forms a lattice called the Bousfield lattice. The structure of this lattice gives insight into localizations, nilpotents, and subcategories of C.
We will describe quotient functors that allow us to relate quotients of Bousfield lattices to Bousfield lattices of quotient categories. Specifically, we will discuss the Bousfield lattice of the E(n)local, K(n)local, and harmonic categories, and lattice morphisms between them. We will also discuss the telescope conjecture and generalized smashing conjecture on these local categories, and the relevance of Bousfield lattices to these questions.
"Exquisite failure: The telescope as lived object"
Bridges conference: Mathematics, Music, Art, Architecture, Culture.
Enschede, the Netherlands.
July 2013.
abstract:
We describe an exquisite mathematical failure, arrived at after hundreds of hours of solitary mathematical research, and offering no hope for mathematical redemption. The mathematical object at the center of the failure, the telescope denoted Tel, becomes a focal point for an ideabased art piece exploring the human relationship with darkness, history, and utopia. In this larger mathart theoretical space, Tel is reclaimed as a tool for critiquing mathematical ontology and reevaluating the terms of engagement of creative production.
"The coevolution of math and mathematicians"
Mathematical Practice seminar
Center for Philosophy of Science of the University of Lisbon
February 2013.
abstract:
I will discuss the coevolution of the content of mathematics and the community of mathematicians. The claim is that math is what it is, because the culture of mathematicians is that it is, and vice versa. I will give three specific examples of characteristics of mathematics; conjecture characteristics of mathematical practice that may have brought these about; then conjecture how these aspects of mathematics encourage certain math practices; and suggest ideas for how we could do math differently, to make math different.
"Bousfield lattices, quotients, ring maps, and nonNoetherian rings"
Algebra seminar, Instituto Superior Técnico, Lisbon, Portugal, January 2013.
Algebra seminar, University of Seville, May 2013.
Topology seminar, University of Copenhagen, May 2013.
Homotopy Methods in Algebra, Geometry and Topology conference, Barcelona, May 2013.
abstract:
Given an object X in a compactly generated tensor triangulated category C (such as the derived category of a ring, or the stable homotopy category), the Bousfield class of X is the collection of objects that tensor with X to zero. The set of Bousfield classes forms a lattice, called the Bousfield lattice BL(C). First, we look at examples of when a functor F: C> D induces a lattice map BL(C) > BL(D), and will describe several lattice quotients and lattice isomorphisms. Second, we will focus on homological algebra: a ring map f: R > S induces, via extension of scalars, a functor D(R) > D(S), and this induces a map on Bousfield lattices. Third, we specialize to specific maps between some interesting nonNoetherian rings.
Slides from this talk are available here.
"Different sizes of infinity"
Madam M's Berlin Salon
Berlin, Germany
December 2012.
abstract:
In a comfortable and open setting I'll introduce the basic set theory ideas needed to understand some miraculous statements and proofs about different sizes of infinite sets. We'll discuss a range of different sets, and prove which are the same size and which are different sizes. There are no prerequisites besides an open mind and an ability to focus on complicated ideas and lines of reasoning. Plenty of time will be allowed for questions, disagreements, and discussion of implications.
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"A nonNoetherian graded mess: some Bousfield lattice products and quotients"
BIREP Seminar
University of Bielefeld
Beilefeld, Germany
October 2012.
abstract:
A map of rings induces adjoint functors between derived categories of modules. We investigate the induced operations on Bousfield lattices, focusing on a particular setting in which these operations give nice quotient lattices. We apply this theory to a toy example involving maps between several nonNoetherian rings, and establish a splitting of the Bousfield lattices into a product. We also apply the theory to the case of a surjection onto a Noetherian ring, and are able to pull back some of the Noetherian structure to the nonNoetherian setting.
"Not every object in the derived category of a ring is Bousfield equivalent to a module"
Algebra Seminar
University of Washington
June 2012.
abstract:
Given W and X in a tensor triangulated category, we say W is Xacyclic if W tensors with X to zero. Two objects X and Y are called Bousfield equivalent if they have the same acyclics. In this talk we give a (nonconstructive) proof that there exist objects in the derived category of graded modules over a certain graded nonNoetherian ring Lambda that are not Bousfield equivalent to any module. This contrasts with the Noetherian case, and has consequences for subcategory classification.
"A tensortriangulated approach to derived categories of nonNoetherian rings"
Final Exam
University of Washington
May 2012.
abstract:
We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending work previously done under a Noetherian hypothesis. Maps between rings R > S induce adjoint functors between unbounded derived categories D(R) and D(S), and we explore the induced relationships between thick and localizing subcategories, and Bousfield lattices. Several specific nonNoetherian rings are studied in depth. We also contextualize these results within the human dimensions in which they occurred.
"It's not right, but it's okay: New mathart works"
Current Topics Seminar
University of Washington
January 2012.
abstract:
We discuss notions of collaboration and interdisciplinary creation, while exhibiting a range of mathart works done by the speaker in collaboration. Pieces include video, music, installation, performance, actions, and performance/lecture.
"Three stories from the mathart frontier"
AMS/MAA Joint Meetings
Boston, MA
January 2012
abstract:
I’ll outline three recent mathart collaborations. Media involved: illustration and dance, electronic pop music, and ritual performance. Themes explored: my PhD research in stable homotopy theory, the research mathematics experience, and negativedimensional space.
"Ring maps, derived categories, and the Bousfield lattice"
(abbreviated version)
AMS/MAA Joint Meetings
Boston, MA
January 2012
abstract:
A ring map between commutative rings induces adjoint maps between their derived categories. We investigate how thick and localizing subcategories, and the Bousfield lattice, behave with respect to these maps. This gives new information about the derived categories of several nonNoetherian rings. The work connects to classifications given by Neeman, Thomason, and Balmer, and complements the stratification construction of Benson, Iyengar, and Krause.
"Recent stories from the mathart frontier"
Workshop 11w5070: Mathematics: Muse, Maker, and Measure of the Arts
Banff International Research Station
Banff, Canada
December 2011
abstract:
I will show and tell about several recent mathart collaborations. Media involved: illustration and dance, electronic pop music, and ritual performance. Themes explored: my PhD research in stable homotopy theory, the research mathematics experience, and negativedimensional space.
"Ring maps, derived categories, and the Bousfield lattice"
Algebra seminar
University of Washington
October 2011
abstract:
Given a map of commutative rings f: R > S, extension of scalars and the forgetful functor give an induced adjoint pair of functors between the derived categories D(R) and D(S). I'll describe new work, using these functors to relate the Bousfield lattices, and thick and localizing subcategories, of D(R) and D(S). One consequence is new information about the structure of derived categories of nonNoetherian rings. Most of this talk will be accessible to anyone who has taken an introductory homological algebra class.
"Set theory questions in homotopy theory"
Advanced Course on LargeCardinal Methods in Homotopy
University of Barcelona
September 2011
abstract:
We present a survey of the relevance of large cardinals and set theory to homotopy theory. In 1979, Bouseld proved the existence of homological localizations (essentially a set theory issue), and began an investigation into what is now a deep theory of homological Bouseld classes (HBCs) and Bouseld lattices. The analogous question of the existence of cohomological localizations is tied to large cardinal principles, and any subsequent investigation of cohomological Bouseld classes (CBCs) presents more set theory questions. We will give an overview of HBCs, CBCs, and their relationship to localizing subcategories, and present the main open problems in the area.
"Structure within Bousfield lattices"
West Coast Algebraic Topology Summer School
University of Washington
August 2011
abstract:
Bousfield localization gives a natural equivalence relation on any axiomatic stable homotopy category. The equivalence classes are called Bousfield classes, and the collection of Bousfield classes (when it is a set) is called the Bousfield lattice. We will explain some of the nice structure with the Bousfield lattice of the stable homotopy category and the derived category of a commutative ring, show the utility of this concept, and present new results and open questions.
"Cohomological Bousfield classes in stable homotopy categories"
General Exam
University of Washington
June 2010.
General exam paper available here. The introduction is a short summary of the talk and paper.
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"The codependent arising of math and mathematicians, and where do we go from here?"
Washington State Community College Math Conference, 2010 Annual Meeting
Yakima Valley Community College
May 2010.
abstract:
Mathematicians create mathematics, but mathematics also creates mathematicians. The body of knowledge we call mathematics and the community that does mathematics have been codependently evolving for millennia. I'll try to describe, from a sociological perspective, several prominent characteristics of the math culture, and suggest how aspects of math itself may have helped to bring about these characteristics. Conversely, I'll suggest ways that our methods of doing math have affected the development of mathematical knowledge. Along the way, I'll discuss possible implications for the future of mathematics.
For the talk I wrote up a Selected Bibliography of excellent articles and books that comment on the nature of the mathematical community. Check it out!
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"The codependent arising of math and mathematicians"
Pacific Northwest MAA, 2010 Annual Meeting
Seattle University
April 2010.
abstract:
Mathematicians create mathematics, but mathematics also creates mathematicians. The body of knowledge we call mathematics and the community that does mathematics have been codependently evolving for millennia. I'll try to describe, from a sociological perspective, several prominent characteristics of the math culture, and suggest how aspects of math itself may have helped to bring about these characteristics. Conversely, I'll suggest ways that our methods of doing math have affected the development of mathematical knowledge.
"An introduction to the category of spectra"
Current Topics Seminar
University of Washington
January 2010.
abstract:
Algebraic Topologists study functors between topological categories and algebraic categories. The topological category of Spectra  generalizations of topological spaces  has beautiful global and local structure, as well as powerful applicability to topological and algebraic questions. This talk will be a somewhat historical survey of what algebraic topology is about. Category theory junkies should prepare for a solid dose of elegance and abstraction. If you've met the fundamental group of a topological space, you'll be able to understand (at least the starting point of) this talk.
"A gentle introduction to category theory: architecture of the universe or abstract nonsense?"
1. Undergraduate Mathematical Sciences Seminar
University of Washington
January 2010.
2. Undergraduate Math Club
University of Washington
November 2010.
abstract:
Some people call mathematics the language of nature. Some mathematicians call category theory the language of mathematics. This broad theory attempts to capture the shape of all of mathematics, and is notoriously abstract. (Search "general abstract nonsense" on Wikipedia and category theory comes up!) But it is also remarkably simple. I'll give you a gentle introduction to this very important and powerful theory, and will show with lots of examples how simple and natural it is. At the same time, you'll get a taste of what higher mathematics is about. I'll also mention some of the recent applications of category theory to theoretical computer science.
"Where arithmetic comes from"
The Mathematical Experience Seminar
University of Washington
April 2008 and April 2010.
abstract:
In the past few decades, cognitive scientists have made several discoveries about how we construct and conceptualize abstract ideas. There has been a recent attempt to apply these results to mathematics, searching for empirical (rather than philosophical) answers to questions such as: Where does mathematics come from? What cognitive mechanisms allow us to construct mathematics that seems so universal, stable, generalizable, and applicable? I will sketch some of these ideas, using the familiar example of arithmetic, and discuss some of their implications for a theory of "embodied mathematics". This is not a math talk; it is a talk about mathematics. Prerequisite: familiarity with arithmetic.
