# Jacob "Bat Conjurer" Turner

Office:
418 McAllister Building
University Park, PA 16802

E-mail: turner at math dot psu dot edu

I am originally from Hazard, a small town in eastern Kentucky. I went to school at Western Kentucky Universerity with the plan of being an engineer, like several of my family members. I had this crazy idea that I was going to design roller coasters. But after an internship and the realization that roller coaster designers are not in high demand, I decided to rethink my life. So I grew a beard and took up mathematics and computer science instead. I did two REU's in cryptography which was my first introduction to Algebraic Geometry, of the applied sort. In 2009, I attended the MASS program at Penn State and decided to return there in 2010 for graduate school. I was lucky enough to find an advisor in applied Algebaic Geometry. Apart from math, my main interests are music (I play a few instruments, though I won't claim to be amazing at them), Vikings and their mythologies, kitty cats, I am avid player of video games, and puzzles of any sort (I have quite the collection of Rubik's products).

Research Interests:

 The fundamental objects that I study are tensor networks. These can be viewed as diagrams from the category of finite dimensional vector spaces of the complex numbers. There are several different problems associated with tensor networks that I am interested in.     The first revolves around the fact that a tensor network, if it is closed, represents a scalar. However, finding this scalar is #P-hard to compute. This makes tensor networks interesting from the point of view of complexity theory. One of the natural things to do is to restrict the tensors that are allowed to some variety or to perhaps make restrictions on the underlying graph. This leads to connections to algebraic geometry.     Tensor networks also show up in physics where they can be used to approximate the ground states of Hamiltonians where the specific interaction of particles in the stae can be specified. Tensor networks admit a natural action of direct products of general linear groups. Physicists are concerned with properties of quantum states that are invariant under these "local groups", e.g. entropy. A popular approach to this problem is via Invariant theory.     I am also interested in Invariant theory applied to other problems. Geometric invariant theory has recently been used to try and resolve to problem of FP vs. #P. The problem is to try and understand the relationship of the orbits of the polynomials described by the determinant and permanent under a particular group action.

Papers

Talks

Curriculum Vitae