## Lecture notes “Aspects of the Monster Tower Construction”

Here are lecture notes and slides from the 4-lecture series delivered by me and Susan Colley at the Workshop on Nash Blow-up and Semple Tower, II in June 2019 at KU Leuven. The full title is “Aspects of the Monster Tower Construction: Geometric, Combinatorial, Mechanical, Enumerative.” The notes will serve as the kernel of a book that we are now (slowly) writing along with Corey Shanbrom.

Here’s a link to the full 51-page lecture notes:

Leuven lecture notes

Here are the lecture slides

Leuven Lecture 1

Leuven Lecture 2

Leuven Lecture 3

Leuven Lecture 4

Everything in the notes is built on the “Basic construction.” At the lectures we handed out this one-page reminder of the construction:

Basic construction

Here is our Introduction:

In these lectures we survey the construction and use of the monster tower (also known as the Semple tower) in three distinct areas of mathematics.

Lecture 1: The Monster Tower (Kennedy) — This lecture will explain how three seemingly different situations lead to the same construction:

1. Compactifying curvilinear data (algebraic geometry)
2. Studying Goursat distributions (differential geometry)
3. Analyzing a truck with trailers (mechanics and control theory)

Lecture 2: Combinatorial Aspects (Colley) — We explain a natural system of coordinate charts on the monster space. We show how to lift (prolong) a curve in the base into the tower. We explain a natural coarse stratification of the monster, catalogued by a simple system of code words.

Lecture 3: Mechanical Aspects (Kennedy) — A version of the monster tower construction creates the natural configuration space for a truck with trailers. We explain the model and survey some important features, including Lie brackets of its basic vector fields, its singular configurations, and its dynamics.

Lecture 4: Enumerative Aspects (Colley) — We begin with an introduction (via examples) to the subjects of enumerative geometry and intersection theory. Specializing to the enumeration of contacts between plane curves, we present a strategy for counting such contacts and illustrate it with a quadruple contact formula we once proved. The ideas behind this formula lead to a discussion of the orbits of the monster space, and to the idea of appropriately lifting a family of curves.

## In Vista Winds

In Vista Winds will present a concert on Saturday, September 30 at 2:00 p.m. in the John and Pearl Conard Performance Hall, located in Riedl Hall on the Mansfield campus. The program is free and open to the public.

In Vista Winds is a woodwind quintet (flute, oboe, clarinet, French horn and bassoon) based out of Cincinnati. Their program will feature three pieces by composer Rick Sowash, a Richland County native who served as the founding Executive Director of the Renaissance Theatre. The quintet will also perform pieces by Lefebvre, Ibert, Washburn, and Bernstein.

PROGRAM

Lefebvre, Charles – Suite Op. 57

Ibert, Jacques – Trois Pieces Breves

Washburn, Robert – Suite for Woodwind Quintet

Sowash, Rick – Three pieces

• The Piper at the Gates of Dawn
• Hope Is Kindled
• Ragtime

Bernstein, Leonard (arr. By Don Stewart) – Overture to Candide

PERFORMERS

Glenn Gollobin, flute

Tim Vincze, oboe

Ken Poleyeff, clarinet

Danielle Cain, horn

Wendy Haas, bassoon

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## The Janus String Quartet with Suzanne Newcomb

The Janus String Quartet, together with pianist Suzanne Newcomb, will present a concert on Sunday, October 23 at 7:30 p.m. in the John and Pearl Conard Performance Hall, located in Riedl Hall on the Mansfield campus. They will perform works by Karen Sunabacka and Antonin Dvořák.

PROGRAM

• Mama’s Painting, Louis Riel’s Dream — Karen Sunabacka
• Piano Quintet in A major, Op. 81 — Antonín Dvořák

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## Classical music concert series at the Mansfield campus 2022–2023

The Mansfield campus is hosting a 2022–2023 series of classical music performances in The John and Pearl Conard Performance Hall (151 Riedl Hall) on the OSU Mansfield campus. All concerts are free and open to the public.

The series will begin on Sunday, October 23 at 7:30 with a performance by the Janus String Quartet together with pianist Suzanne Newcomb. Additional concerts are in the planning stage.

Anyone who wants to receive e-mail announcements of our concerts can sign up for our mailing list. Please write to me at kennedy.28@osu.edu or call me at 419-565-0561. I can also be contacted if you want further information about the concert series.

## The Janus Quartet with guest artist Kia-Hui Tan

This concert has been cancelled. We hope to host the Janus Quartet in the future.

The Janus Quartet, together with guest artist Kia-Hui Tan, will present a concert on Tuesday, April 7 at 7 p.m. in the John and Pearl Conard Performance Hall, located in Riedl Hall on the Mansfield campus. They will perform quintets by Mozart and Schnittke.

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## In Vista Winds

This concert has been cancelled. We hope to host the In Vista Winds in the future.

In Vista Winds, a woodwind quintet from Cincinnati, will present a concert on Sunday, April 19 at 3 p.m. in the John and Pearl Conard Performance Hall, located in Riedl Hall on the Mansfield campus.

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## The Aviatori Trio

This concert has been cancelled. We hope to host the Aviatori Trio in the future.

The Aviatori Trio, a piano trio from the University of Dayton, will present a concert in the autumn of 2020 in the John and Pearl Conard Performance Hall, located in Riedl Hall on the Mansfield campus. The date and time are still to be determined. This announcement will be updated when that information becomes available.

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## The Mühlfeld Quartet

We were pleased to host the Mühlfeld Quartet, who inaugurated our campus classical music series with a concert on Sunday, December 8 in the John and Pearl Conard Performance Hall. The quartet is an ensemble of  young musicians based out of Columbus. Its members are:

• Yi Chieh Anita Chiu, violin
• Noah Wise, clarinet
• Thomas LaMon, cello
• Sunghwan Kim, piano

They performed Walter Rabl’s Opus 1 and a transcription of Mozart’s Piano Quartet in g minor.

They were semifinalists in the Coltman National Chamber Music Competition in 2019, and they were recipients of the annual Brahms Chamber Music Scholarship. The Mühlfeld Quartet is dedicated to programming diverse music, including recording a new commissioned piece written by Cooper Wood coming in early 2020. The group is named after Richard Mühlfeld, the clarinetist that inspired Brahms to come out of retirement and to continue writing music in the early 1890s.

For further information, contact me at kennedy.28@osu.edu or 419-565-0561.

## Classical music at the Mansfield campus

Our 2020 and 2021 concerts have been cancelled. Our series will resume in 2022, we hope.

The Mansfield campus is hosting a 2019–2020 series of chamber music performances in Riedl Hall on the OSU Mansfield campus. All concerts are free and open to the public.

The series began on Sunday, December 8 with a performance by the Mühlfeld Quartet, an ensemble of young musicians based out of Columbus.

In spring 2020, the series will host two additional performances:

• In Vista Winds (wind quintet from Cincinnati) — performance on Sunday April 19 at 3 p.m.
• Janus Quartet (string quartet of OSU School of Music faculty) together with guest artist Kia-Hui Tan — performance on Tuesday April 7 at 7 p.m. of quintets by Mozart and Schnittke

Anyone who wants to receive e-mail announcements of our concerts can sign up for our mailing list. Please write to me at kennedy.28@osu.edu or call me at 419-565-0561. I can also be contacted if you want further information about the concert series.

In autumn 2020, the series will resume. Among others, we expect to present the Aviatori Trio, a piano trio from the University of Dayton.

## Gallery essay for “In the Realm of Forms”

In 2015, I had the pleasure of curating an exhibition of mathematical art, along with my Art Professor colleagues Kate Shannon and John Thrasher. Here’s an essay I wrote to accompany the show.