Spin Structures and Quadratic Enhancements on Number Fields

Speaker

Dr. Artane Siad (Princeton University)

Time

Wed., 10:30-11:30 am, Sept. 4, 2024

Venue

C654, Shuangqing Complex Building A

Oragnizer

Heng Du (Tsinghua University)

Spin Structures and Quadratic Enhancements on Number FieldsI will report on joint work in progress with Akshay Venkatesh. Motivated by anomalous class group statistics, we propose an arithmetic analogue of the topological story of quadratic enhancements associated with spin structures on closed oriented $2$- and $3$-manifolds: a choice of spin structure gives, respectively, a quadratic refinement of the mod $2$ intersection form and of the linking pairing on the first torsion homology. Time permitting, I will clarify the sense in which our construction can be viewed as a candidate determinant-of-cohomology for number fields.

About the speaker

I am currently an Instructor at Princeton University and a member of the Institute for Advanced Study (IAS). My research is partially supported by a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council of Canada (NSERC-PDF). I am co-organizing the joint Princeton University and IAS Number Theory seminar with Sam Mundy and Griffin Wang.

At Princeton, my mentors are Prof. Peter Sarnak and Prof. Manjul Bhargava. At the Institute my mentor is Prof. Akshay Venkatesh. I obtained my PhD from the University of Toronto in the fall of 2021 and my advisor was Arul Shankar.