Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                                Spring 2019

   Organizers: Anna Marie Bohmann, Rares Rasdeaconu and Larry Rolen

   Fridays, 3:10-4:00pm in SC 1310 (unless otherwise noted)

                  Thursday, February 21st, 3:10p-4:00p, Room SC1310 (not the usual day)

Speaker:  Joshua Males, University of Cologne (Germany)

Title:  Constructing quantum modular forms of depth two

Abstract: Work of Bringmann, Kaszian and Milas in 2017 introduced the concept of higher depth quantum modular forms
(qmfs), and therein provided one such example of a qmf of depth two, related to characters of vertex algebras. In this talk
we see how to generalise their work to obtain an infinite family of non-trivial qmfs of depth two. To show this, we relate our
constructed function F asymptotically to double Eichler integrals on the lower half plane, and further to non-holomorphic
theta functions with coefficients given by double error functions.  (Contact Person: Larry Rolen)

                  Friday, February 22nd

Speaker:  Laurentiu Maxim, University of Wisconsin-Madison

Title:  Euclidean distance degree of algebraic varieties 

Abstract: The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry.
It has direct applications in geometric modeling, computer vision, and statistics. I will first describe a new topological
interpretation of the Euclidean distance degree of an affine variety in terms of Euler characteristics. As a concrete application,
I will present a solution to the open problem in computer vision of determining the Euclidean distance degree of the affine
multiview variety. Secondly, I will present a solution to a conjecture of Aluffi-Harris concerning the Euclidean distance
degree of projective varieties (Joint work with J. Rodriguez and B. Wang.)  (Contact Person: Rares Rasdeaconu)

                  Friday, March 8th -- no meeting (Spring Break)

                  Friday, March 15th

Speaker:  Kate Ponto, University of Kentucky

Title:  Fixed point invariants are maps

Abstract: Thinking about fixed point invariants as generalizations of the Euler characteristic suggests structure we would
want these invariants to have - additivity on subcomplexes and multiplicativity on fibrations being the first examples. Using
classical perspectives this structure can be hard to see (and may not exist) but if we think of invariants as maps rather than
numbers (or elements of groups) the desired structure follows from formal constructions.  (Contact Person: Anna Marie Bohmann)

April 13-14th, 2019 Shanks Workshop on Homotopy Theory

Location: Stevenson Center 1308 (Contact Person: Anna Marie Bohmann)


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