jrm53

Jason Morton is an Associate Professor at Penn State.

He studies applied algebraic geometry and tensor networks in statistics, computer science, and quantum information. Information-processing systems described as networks (e.g. Bayesian networks, quantum circuits) in seemingly disparate fields in fact have common mathematical foundations. They are connected by variations on the graphical modeling language of tensor networks, or more generally monoidal categories with various additional properties. Basic questions about each type of information-processing system (such as what probability distributions or quantum states can be represented, or what word problems can be solved efficiently) quickly become interesting problems in shared algebraic geometry, representation theory, polyhedral geometry, and category theory.

Publications

• Dimensions of marginals of Kronecker product models

• .  With G. Montufar. To appear in SIAM Journal on Applied Algebra and Geometry.
   
• Computing the Tutte polynomial of lattice path matroids using determinantal circuits. With Jacob Turner. Theoretical Computer Science, Available online 29 July 2015, http://dx.doi.org/10.1016/j.tcs.2015.07.042.
   
• An operad-based normal form for morphism expressions in a closed compact category (Extended abstract). With David I. Spivak. HDRA 2015.
   
• When does a mixture of products contain a product of mixtures? With Guido Montufar.  SIAM Journal on Discrete Mathematics 29(1), 321-347. (2015).
   
• Tensor network contractions for #SAT.  With J. Turner and J. Biamonte. Journal of Statistical Physics 160(5), 1389-1404 (2015).
   
• Polynomial-time solvable #CSP problems via algebraic models and pfaffian circuits. With Susan Margulies.  Journal of Symbolic Computation, Available online 19 June 2015, http://dx.doi.org/10.1016/j.jsc.2015.06.008.
   
• Discrete restricted Boltzmann machines. With G. Montufar.  Journal of Machine Learning Research 16:653-672 (2015).
   
• Generalized counting constraint satisfaction problems with determinantal circuits. With Jacob Turner.  Linear Algebra and its Applications 466(0), 357-381 (2014).
   
• Belief propagation in monoidal categories, QPL 2014
• and EPTCS
• .
   
• Algebraic geometry of matrix product states
• . With Andrew Critch
  • .  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 10 (2014), 095, 10 pages.

   

  Teaching

  Fall 2015: Introduction to Applied Algebraic Geometry.

  Summer 2015: Math 436 Linear Algebra (taught online).

  Spring 2015: Stat 553, Asymptotic Tools.

  Fall 2014: Reading Course on Computational Commutative Algebra.

  Spring 2014: Stat 504, Analysis of Discrete Data.

  Spring 2014: Reading Course on Algebraic Geometry.

  Fall 2013: Math 436, Linear Algebra.

  Fall 2013: Stat 501, Regression Analysis (taught online). 

  Spring 2013: Reading Course on Tensor Networks.

  Spring 2012: Math 597C, Topics in Representation Theory

  Fall 2010: Math 518, Probability Theory II.

  Spring 2010: Math 311W, Concepts of Discrete Mathematics.