To attend the conference, please register by October 27th.
Tara Holm Cornell University Symplectic Embeddings and Infinite StaircasesMcDuff and Schlenk determined when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional ball. They found that if the ellipsoid is close to round, the answer is given by an ``infinite staircase" determined by the odd index Fibonacci numbers, while if the ellipsoid is sufficiently stretched, all obstructions vanish except for the volume obstruction. Infinite staircases have also been found when embedding ellipsoids into polydisks (Frenkel - Muller, Usher) and into the ellipsoid E(2, 3) (Cristofaro-Gardiner -Kleinman). In this talk, we will see how the sharpness of ECH capacities for embedding of ellipsoids implies the existence of infinite staircases for these and three other target spaces. We will then discuss the relationship with toric varieties, lattice point counting, and the Philadelphia subway system. This is joint work with Dan Cristofaro-Gardiner, Alessia Mandini, and Ana Rita Pires. The talk will be based on pictures and examples.
Dandrielle Lewis High Point University Wolfgang and Luise Kappe Alumni Speaker Reflections on Undergraduate Research
After I got my Ph.D., I joined the University of Wisconsin-Eau Claire, which is an undergraduate institution known for undergraduate research. I had a few ideas for projects, but I did not know exactly how to guide students through a year-long, summer, or semester research project. However, I learned how to navigate this guidance in my first year. Being flexible, meeting students where they are in their mathematical and sometimes other areas of interest journeys, and setting realistic goals is key to making a project accessible. In this talk, I will share how I do undergraduate research, and I will share projects I have worked on with undergraduates.
Inna Zakharevich Cornell University From topological spaces to categories and back again
One of the most powerful techniques in mathematics is the use of algebra to model geometric phenomena. By turning a geometric problem (often difficult) into an algebraic problem (often easier, sometimes even solvable by computer) we can analyze the problem without understanding what is happening "geometrically." Unfortunately, homotopy types cannot be modeled in this way: algebra is simply too rigid. For example, consider a point and a disk. A point is 0-dimensional, while a disk is 2-dimensional; in order to describe them algebraically different numbers of variables are required. However, from the point of view of homotopy they are the same. Thus if we want to make algebraic models of homotopy types we need algebraic objects which have some kind of "floppiness" built in. Categories, with their possibility of multiple copies of each object, are perfect for this. In this talk we will explore this connection in detail, discussing topological interpretations of category-theoretic models and different methods of modeling familiar spaces using categories