# ESP Biography

## DANIEL GULOTTA, BU postdoc and MIT alum studying number theory

Major: Mathematics, Physics

College/Employer: MIT

Not Available.

## Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M15397: Tilings and Groups in Splash 2022 (Nov. 19 - 20, 2022)
Here is a problem that you may have seen before. Suppose you have a chessboard with two opposite corners removed. Can it be tiled with dominoes? The answer is no: each domino will cover one light square and one dark square, and there are different numbers of light squares than dark squares. Now consider the following problem. For which $m$ and $n$ can an $m \times n$ rectangle be tiled by tiles in the following shapes (rotations and reflections are allowed)? $$\begin{array}{ccc}& * & \\ {}* & * & * \\ & * & \end{array} \qquad \qquad \begin{array}{c} * \\ {}* \\ {}* \end{array} \qquad \qquad \begin{array}{cccc} * \\ {}* & * & * & * \\ & & & * \end{array}$$ If $mn$ is divisible by $3$, then it is easy to tile the rectangle with copies of the second tile. If $mn$ is not divisible by $3$, then you will find that tiling the rectangle seems to be impossible, yet there does not seem to be a coloring argument that proves that it is impossible to tile. I will describe a method of proving that a region cannot be tiled by drawing decorations along the edges of the tiles and the region, and explain how this method generalizes coloring arguments.

Creating Geometric Art in HSSP (2006)
We will examine the geometry behind the artwork of M. C. Escher, George Hart, and others, and then learn how ...

Creating Art With Geometric Transformations in SPLASH (2005)
We will take a look at the art of M. C. Escher and others who incorporated geometry into their work. ...

Simple Physics Experiments in SPLASH (2005)
We will perform some simple physics experiments and then try to figure out why they work.

String Theory in SPLASH (2005)
Are you curious about string theory but feel confused by descriptions involving a lot of advanced mathematics? In this class ...

Geometric Transformations in SPLASH (2004)
Often it is useful to think about problems in geometry in terms of transformations. In this class we will discuss ...