My current projects are in the analysis problems (mostly involving measure theory and functional analysis) arising in rigorously constructing interacting quantum field theories. However, I am and have been interested in many other topics as well. Below is a list of my papers and preprints in reverse chronological order.
- “A Devil’s Staircase to Urysohn’s Lemma”, Math. Mag, Vol. 97, no. 5, (2024), pp 547-550, draft.
- “Yang-Mills as a Constrained Gaussian”, Adv. Theor. Math. Phys., 27, No. 2 (2023), pp. 563-581, arXiv:2207.06069 [math-ph].
- “On the Construction of Euclidean Invariant and Reflection Positive Measures on the Cylindrical Compactification of Distributions”, J. Math. Phys. 63, 082301, (2022), arXiv:2206.08131 [math.FA].
- “A Construction of Euclidean Invariant, Reflection Positive Measures on a Compactification of Distributions”, J. Math. Phys. 62, no. 6, 062301, (2021), arXiv:2101.01427 [math.FA].
- “On the Preservation of Quasilocality by the Integration-Out Transformation”, arXiv:2012.14747 [math-ph].
- “Bump Functions With Monotone Fourier Transforms Satisfying Decay Bounds”, J. Approx. Theory 278, 105742, (2022), arXiv:2003.12364 [math.CA].
- “Big Free Groups are Almost Free”, Internat. J. Algebra Comput. 25, no. 5, (2015), arXiv: 1312.4750 [math.GR].
- “On the Ashtekar-Lewandowski Measure as a Restriction of the Product One”, J. Math. Phys. 55, no. 12, 122302, (2014), arXiv: 1312.3603 [math.FA].
- “On the Holonomic Equivalence of Two Curves”, Internat. J. Math. 27, no. 6, 1650055, (2016), arXiv: 1311.6611 [math.DG].
- “Nonstandard Proofs of Herglotz, Bochner and Bochner-Minlos Theorems”, J. Fourier Anal. Appl. 21, (2015), draft.
- (With D. Oriti) “Encoding simplicial quantum geometry in group field theories”, Class. Quant. Grav. 27, 135018 (2010), arXiv: 0912.1546 [gr-qc].
- (With D. Oriti) “A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity”, Class. Quant. Grav. 25, 085011 (2008), arXiv: gr-qc/0710.2679.
- (With D. Oriti) “Causality and matter propagation in 3d spin foam quantum gravity”, Phys. Rev. D 74, 104021 (2006), arXiv: gr-qc/0608116.