# Michael Zhao Memorial Student Colloquium

Fall 2019

Each week, the Michael Zhao Memorial Student Colloquium holds 45-minute talks by Columbia mathematics faculty about their own research.

The talks are intended for current PhD students in mathematics at Columbia. If you are an undergraduate student or external graduate student and would like to come, please email me at nguyen.dung@math.columbia.edu

The colloquium meets at **6:00pm, Wednesdays in Mathematics Room 507.**
The talks will be followed by dinner.

Date |
Speaker |
Title of talk |

September 18 | Mikhail Khovanov | ## What is categorification?Categorification lifts numbers to vector spaces and vector spaces to categories. In the talk we'll give a couple of examples and sketch more general setups where categorification works. |

September 25 | Alisa Knizel | ## Random tilingsRandom tilings of large planar domains by simple shapes (domino tiles or rhombuses obtained by gluing two unit triangles of the triangular lattice together) have many surprising features. They develop deterministic limit shapes, and the fluctuations around those shapes reveal universal laws of probability. The aim of the talk is to give an introduction to this topic. (slides) |

October 2 | Francesco Lin | ## Spectral geometry and the topology of hyperbolic 4-manifoldsThe Atiyah-Patodi-Singer index theorem describes, for a given Riemannian manifold with boundary, a relation between its geometry, topology and the spectral theory of the boundary. In this talk, we introduce the main protagonists of the theorem, and discuss some applications due to Long and Reid to the study of hyperbolic 4-manifolds. |

October 9 | Andrei Okounkov | ## Why is it interesting to think about elliptic cohomology ?Elliptic cohomology, especially equivariant elliptic cohomology, can be a very technical and not particularly intuitive subject. Yet I will try to argue that there is something one can gain from a better understand of elliptic cohomology, and its place in geometric representation theory and enumerative geometry. |

October 15 (Tuesday) | Chao Li | ## From quadratic forms to arithmetic intersection numbersWe begin with the classical theory of quadratic forms and illustrate its link to modular forms and intersection theory. We then motivate the notion of arithmetic intersection numbers, discuss their relation with the BSD conjecture and end with recent results concerning them. |

October 23 | Kyler Siegel | |

October 30 | Gus Schrader | |

November 6 | Michael Harris | |

November 13 | Carolyn Abbott | |

November 20 | ||

November 27 | No talk (Thanksgiving break) | |

December 4 | ||

December 11 |

Fall 2018