Wednesdays, 7:30pm; Room 507, Mathematics

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*ums* [at] *math.columbia.edu*

Date | Speaker | Title | Abstract |

October 5 | Raymond Cheng |
Grothendieck Ring of Varieties |
Since the time of Euler, we have known that the alternating sum of the number of vertices, edges and faces of a polytope is, somewhat remarkably, always 2. In this talk, I will discuss invariants of geometric objects called "motivic invariants". As a main example, I discuss motivic invariants in the context of algebraic geometry where the invariants will take values in the so-called Grothendieck ring of varieties, or more affectionately, the ring of "baby motives". Despite being a rather mysterious object, we will see that this ring will allow us to make many interesting calculations and find amazing ways to encode facts we already know. |

October 12 | Sam Mundy |
Bernoulli Numbers and Arithmetic |
I will discuss the role Bernoulli numbers play in modern Number Theory. |

October 19 | Shizhang Li | Poncelet's Closure Theorem | Let C and D be two plane conics intersecting transversely. For a point c on C, consider the following procedure: find a tangent line of D passing through c, which would cut C at another point, say, c'. Now consider the chain of points on C: c, c', c'',.... The theorem says: if you could find one point c on C such that after n times of procedure described above it coincides with the original point c, then for any point on C same thing would happen. I will introduce a little bit about elliptic curves and prove this (fantastic) theorem. |

October 26 | George Drimba | Eigenvalue Problems in Geometry | In this talk, we will explore Elliptic PDE theory and discuss tools from geometric analysis in the context of Eigenvalue problems. |

November 2 | Michael Thaddeus | Schubert Calculus | |

November 9 | TBD | ||

November 16 | Math Department Open House | ||

November 23 | TBD | ||

November 30 | TBD | ||

December 7 | TBD | ||

December 14 | Daniel Litt | ||

December 21 | TBD |

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