My primary research is in functional analysis, with a focus on operator algebras and their connections to fields such as ergodic theory and measured group theory.

I also hold a secondary research interest in computer vision, studying the use of differential invariant signatures for computerized object recognition and reconstruction.

- R. de Santiago, B. Hayes, D. Hoff, and T. Sinclair,
*Maximal rigid subalgebras of deformations and L*^{2}-cohomology**, Analysis & PDE, to appear. - D. Drimbe, D. Hoff, and A. Ioana,
*Prime II*_{1}factors arising from irreducible lattices in products of rank one simple Lie groups**, J. Reine Angew. Math.**757**(2019), 197–246. - L. Bowen, D. Hoff, and A. Ioana,
*Von Neumann's problem and extensions of non-amenable equivalence relations***, Groups Geom. Dyn.**12**(2018), no. 2, 399–448. - D. Hoff,
*Von Neumann Algebras of Equivalence Relations with Nontrivial One-Cohomology***, J. Funct. Anal.**270**(2016), no. 4, 1501–1536. - D. Hoff and P. J. Olver,
*Automatic solution of jigsaw puzzles***, J. Math. Imaging Vision**49**(2014), no. 1, 234–250. - D. Hoff and P. J. Olver,
*Extensions of invariant signatures for object recognition***, J. Math. Imaging Vision**45**(2013), no. 2, 176–185. - D. Hoff, C. R. Johnson, and S. Nasserasr,
*Totally positive shapes and TP*_{k}-completable patterns**, Linear Algebra Appl.**436**(2012), no. 12, 4412–4422.

- "Maximal Rigid Subalgebras of s-Malleable Deformations," Functional Analysis Seminar, University of California, Los Angeles, CA, January 29, 2020.
- "Maximal Rigid Subalgebras of s-Malleable Deformations," IPAM Quantitative Linear Algebra Reunion Conference, Lake Arrowhead, CA, December 5, 2019.
- "Rigid Components of s-Malleable Deformations," Functional Analysis Seminar, University of California, San Diego, CA, December 4, 2018.
- "Tensorial Relative Solidity," AMS Special Session on Advances in Operator Algebras, Joint Mathematics Meetings, San Diego, CA, January 13, 2018.
- "Between Popa's Intertwining and Measure Equivalence," Functional Analysis Seminar, University of California, Los Angeles, CA, November 15, 2017.
- "An Operator Algebraic Tool for Deducing Measure Equivalence of Groups," Logic Seminar, Caltech, Pasadena, CA, November 14, 2017.
- "Between Popa's Intertwining and Measure Equivalence," Special Session on Advances in Operator Algebras, AMS Fall Western Sectional Meeting, University of California, Riverside, CA, November 5, 2017.
- "Prime II
_{1}Factors Arising from Irreducible Lattices in Products of Simple Lie Groups of Rank One," Conference on Von Neumann Algebras and Measured Group Theory, Institut Henri Poincaré (IHP), Paris, France, July 7, 2017. - "Unique Factorization of II
_{1}Factors of Groups Measure Equivalent to Products of Hyperbolic Groups," Seminar in Operator Algebras, University of California, San Diego, CA, January 31, 2017. - "Unique Factorization of II
_{1}Factors of Groups Measure Equivalent to Products of Hyperbolic Groups," Functional Analysis Seminar, University of California, Los Angeles, CA, January 18, 2017. - "Von Neumann's Problem and Extensions of Non-Amenable Equivalence Relations," Spring Institute on Noncommutative Geometry and Operator Algebras (NCGOA), Hausdorff Research Institute for Mathematics (HIM), Bonn, Germany, May 23, 2016.
- "Unique Prime Factorization for II
_{1}Factors with Cartan Subalgebras," Subfactor Seminar, Vanderbilt University, Nashville, TN, December 4, 2015. - "Consequences of Spectral Gap Rigidity in Von Neumann Algebras of Non-Amenable Equivalence Relations," Operator Theory Seminar, University of Iowa, Iowa City, IA, December 1, 2015.
- "Von Neumann's Problem and Extensions of Non-Amenable Equivalence Relations," Operator Algebras Seminar, Purdue University, West Lafayette, IN, November 19, 2015.
- "Unique Prime Factorization for Von Neumann Algebras of Equivalence Relations," Special Session on von Neumann Algebras, AMS Fall Southeastern Sectional Meeting, University of Memphis, Memphis, TN, October 18, 2015.
- "Von Neumann's Problem and Extensions of Non-Amenable Equivalence Relations," West Coast Operator Algebra Seminar (WCOAS), University of California, San Diego, CA, October 10, 2015.
- "Unique Prime Factorization for Von Neumann Algebras of Equivalence Relations," East Coast Operator Algebras Symposium (ECOAS), University of Iowa, Iowa City, IA, October 3, 2015.
- "Unique Prime Factorization for Von Neumann Algebras of Equivalence Relations," Functional Analysis Seminar, University of California, Los Angeles, CA, May 11, 2015.
- "A Class of Von Neumann Algebras Which Admit Unique Prime Factorization," Seminar in Operator Algebras, University of California, San Diego, CA, April 24, 2015.
- "Von Neumann Algebras of Equivalence Relations with Nontrivial One-Cohomology," AMS Special Session on Classification Problems in Operator Algebras, Joint Mathematics Meetings, San Antonio, TX, January 12, 2015.
- "Von Neumann Algebras of Equivalence Relations with Nontrivial One-Cohomology," Workshop on Von Neumann Algebras and Ergodic Theory, University of California, Los Angeles, CA, September 24, 2014.

- "Invariants for Object Recognition and Automatic Puzzle Assembly," Honors Thesis Presentation, University of Minnesota, Twin Cities, MN, May 3, 2011.
- "Totally Positive Shapes and TP
_{k}-Completable Patterns," REU Research Presentation, College of William and Mary, Williamsburg, VA, June 26, 2010.

- "Absolute Continuity for States on C*-Algebras," Participating Functional Analysis Seminar, University of California, Los Angeles, CA, May 11 & 15, 2020.
- "Mathematical Amenability, from the Banach-Tarski Paradox to Operator Algebras," Invited Professor Talk for the Undergraduate Mathematics Student Association, University of California, Los Angeles, CA, February 5, 2020
- "Mathematical Amenability, from the Banach-Tarski Paradox to Operator Algebras," Invited Professor Talk for the Undergraduate Mathematics Student Association, University of California, Los Angeles, CA, April 24, 2018
- "C*-Simplicity and the Unique Trace Property," Operator Algebras Working Seminar, University of California, San Diego, CA, November 10, 2015; January 19 & 26, 2016.
- "Hyperbolic Groups," C*-Algebra Learning Seminar following Brown and Ozawa, University of California, San Diego, CA, May 19 & 20, 2015.
- "Creutz-Peterson Character Rigidity for Lattices and Commensurators," Poisson Boundary Seminar, University of California, San Diego, CA, January 22 & 29 and February 5 & 12, 2015.
- "Nuclear and Exact C*-Algebras," C*-Algebra Learning Seminar following Brown and Ozawa, University of California, San Diego, CA, October 16 & 23, 2014.
- "Measured Equivalence Relations," Arbeitsgemeinschaft: Superrigidity, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, March 31, 2014.
- "Proper Analytic NC-Functions," Seminar in Free Analysis, University of California, San Diego, CA, January 30, 2013.
- "Symbols and Oscillatory Integrals," Pseudo-Differential Operator Reading Course, University of California, San Diego, CA, August 15, 2012.
- "The Stone-Von Neumann Theorem," Pseudo-Differential Operator Reading Course, University of California, San Diego, CA, July 16 & 18, 2012.