Talks

Upcoming talks:

• Joint Mathematics Meetings, AMS Special Session (January 10)
  
  
• Southern Illinois University Edwardsville (January 15)
  
  
• Indiana University, Geometry Seminar (January 17)
  
  
• Harvard University, Geometry & Dynamics Seminar (February 6)
  
  
• Yale University, Geometry & Topology Seminar (February 11)
  
  
• ICERM, Brown University (Fall semester 2013)

• Oxford University (UK), Graduate student seminar (December 3, 2012).
  
  
• Freie Universität Berlin (Germany), Discrete Geometry seminar (November 8, 2012).
  
  
• University of Bristol (UK), Dynamics Seminar (February 2012).
  
  
• Colby College, Colloquium (March 2012).
  
  
• Brown University, Graduate Student Seminar (March 2012).
  
  
• Brown University, Graduate Student Seminar (September 2011).
  
  
• Brown University, Graduate Student Seminar (April 2010).

• Summer @ ICERM REU, Brown University, July 2012: How to give a math talk
  Some ideas on how to give a good talk, how to avoid giving a bad talk, and how to learn from others' talks. Handout from talk (pdf).

• CWIC session, Phillips Exeter Academy math conference, June 2012: Dancing about math
  Some things in math are much better when explained through pictures, rather than in words. Could we take it one step further and explain it through dance, rather than pictures? I recently made a video for the "Dance Your PhD" competition, which explains my PhD thesis through interpretive dance. I'll show how I turned my theorem into a compelling video, and then as a group, we'll turn a better-known geometry theorem into a dance.

• CWIC session, Phillips Exeter Academy math conference, June 2012: Exeter math from both sides of the Harkness table
  (same as last year)

• Colloquium, Colby College, March 2012: Geodesic paths and cutting sequences on polygon surfaces
  If you glue together opposite edges of a square, you get a torus (the surface of a donut). What happens if you travel forever in a straight line on the square torus surface? I'll discuss this, and the associated "cutting sequences" that arise, for the square torus and for other polygon surfaces.

• Dynamics seminar, University of Bristol (UK), February 2012: Shearing, twisting and geodesics on polygon surfaces
  We create a surface by identifying opposite parallel edges of a polygon, and then we consider an interesting "twisting" automorphism of the surface. We will discuss the miraculous property that allows us to do this twist for all regular polygons, and then introduce some other surfaces that can also be twisted.

• Graduate student seminar, Brown University, September 2011: The modulus miracle: Cylinder decomposition in regular polygons and beyond
  If you have a regular polygon (or two), you can divide the polygons into parallelograms. The miracle is that if you calculate the ratio width/height (the modulus) of all these parallelograms in a regular polygon, they are all the same! This allows us to do the cutting and shearing magic described in my previous talks. This talk will have lots of pictures and will be completely accessible.

• CWIC session, Phillips Exeter Academy math conference, June 2011: Bugs, bagels, surfaces and topology
  The world is flat! Or maybe it's spherical -- or is it a torus? We will learn to determine the shape of our world using only string, paper, and common breakfast foods. This talk will be a gentle introduction to the subject of topology. You will also learn an entertaining topological party trick to amaze your friends (or students).

• CWIC session, Phillips Exeter Academy math conference, June 2011: Exeter math from both sides of the Harkness table
  To date, exactly one person has both learned math using Exeter's word-problem-based curriculum, and returned to teach math at Exeter. I'll talk about my experience on each side of the curriculum, and the differences between being a successful Exeter math student and an effective teacher.

• Graduate student seminar, Brown University, September 2010: Veech groups: Cutting Polygons into Puzzles
  If you have a parallelogram, you can cut off a right triangle and rearrange the pieces to make a rectangle. Veech groups generalize this idea for many different polygons. I'll give some examples with pictures, and explain how Veech groups relate to cutting sequences. Photo of talk.

• Topics exam, Brown University, April 2010
  This talk discussed Smillie and Ulcigrai's recent paper, Symbolic coding for linear trajectories in the regular octagon. It was very similar to the seminar I gave about octagons the previous week (see below). On the basis of this talk, I was admitted to candidacy. Celebratory octagonal cakes.

• Graduate student seminar, Brown University, April 2010: Cutting sequences on the octagon
  If we identify opposite sides of the octagon, we get a surface (actually the two-hole torus) on which we can draw straight paths. If we write down the edges of the octagon that our path crosses, we get a "cutting sequence" of letters. I'll start with the simpler case of the square torus, and then explain some recent results about cutting sequences on the octagon, using lots of pictures. Photo of talk (above).

• Graduate student seminar, Brown University, May 2009: Simple geometric proofs using pictures
  Abstract: [I gave this talk on 24 hours' notice when someone else cancelled.] First, we will give President James A. Garfield's original proof of the Pythagorean Theorem. Then we will derive the angle-addition formulas using a right triangle inscribed in a rectangle. Finally, we will use a cylinder and a cone to find the volume of a hemispherical bowl filled with water up to a certain height. The latter two constructions are found in PEA math 2.

• Thesis defense, Williams College, May 2007: Alpha-Regular Stick Knots
  Abstract: A stick knot is a closed chain of line segments attached end to end. An alpha-regular stick knot has unit-length segments where the angle at each vertex is the same, some angle that we call alpha. If we have found an example of a stick knot that is very nearly alpha-regular, with sticks that are very close to unit length and angles that are very close to alpha, we would like to say that a stick knot exists of the same knot type, where the sticks are exactly unit length and the angles are exactly alpha. I will discuss my results on this problem.

• Undergraduate colloquium, Williams College, September 2006: An elementary proof of Krull's Intersection Theorem
  Abstract: To do analysis on commutative rings, we need a metric, and to prove that the distance function we have is actually a metric, we need to show that it satisfies the three conditions for a metric. Two are easy to prove, but the third requires Krull's Intersection Theorem. Standard proofs of this theorem require advanced knowledge and complicated lemmas, but I'll explain a new, simpler proof that requires only abstract algebra. Photo of talk.

• Hudson River Undergraduate Math Conference, April 2006: Isoperimetric Regions in Sectors of the Gauss Plane: Eliminating Monsters
  Abstract: The cheapest way to enclose area in the Euclidean plane is by a circle, but what if the plane has varying density? What if we only consider a pie-shaped sector of the plane with varying density? I'll show how to eliminate shapes (such as the circle) that we now know cannot be minimizing, and give conjectures and evidence for the best shape.

• Phillips Exeter Academy Math Club, 2005: What is math research?
  Abstract: What do mathematicians work on? What does "math research" really mean, and what opportunities are there for high school and college students to do it? To explain the answers, I'll talk about some research I did last summer.

• MathFest 2005, Albuquerque, NM: Curvature in the Gauss Plane and Minimizing Curves
  Abstract: We consider constant-curvature curves in the Euclidean plane with Gaussian density. [I won the AMS student speaker prize for this talk.]

• MAA regional meeting at Bates College, June 2005: The Hutchings function in Gauss space
  Abstract: Current work on double bubbles in Gauss space (Euclidean space with Gaussian density) requires showing that a certain "Hutchings" function is positive.

• Hudson River Undergraduate Math Conference, April 2005: Latin squares: permutations inside the box
  Abstract: A Latin square is an nxn grid of symbols in which each of n symbols appears once in each row and each column. We will discuss orthogonality, Cayley tables, and you will discover how Latin squares apply to tire rotation.

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