David Jordan's Homepage – UT Mathematics
I am an NSF postdoctoral fellow in the Department of Mathematics at the University of Texas. I received my Ph.D. from MIT, under the advisement of Pavel Etingof. Here you can find information about me, my research, and my teaching.
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Research InterestsI study various algebraic systems which lie between representation theory and physics. More precisely, my research falls roughly into three distinct areas: Firstly, I study tensor categories in their various flavors (fusion, braided, symmetric, stable oo-…) - their classification, and their representation theory. Secondly, I study the interplay between non-commutative algebra and algebraic geometry. Finally, I study quantization problems involving quantum groups, quantum orbit spaces, and their geometry. My Ph.D. thesis constructed a deformation quantization of rational and multiplicative quiver varieties, by applying the theory of quantum groups and quantum Hamiltonian reduction. TeachingIn Spring 2013, I am teaching the course “Quantum groups and geometric representation theory”. Course notes can be found here. In Fall 2012 I taught Math 427L: Advanced Calculus II, and Math 341: Linear Algebra. My C.V. can be found here. SeminarsTogether with James Pascaleff, I co-organize the Current Literature in Geometry and Topology seminar, and the Back Porch Seminar. |
Publications and current projects
Here is a list of my work to date, and on-going projects with links to the arXiv versions of each paper. Click here for a slightly more detailed informal description of each work.
Quantum groups, quantum D-modules
Quantized Multiplicative Quiver Varieties - my Ph.D. thesis.
Link: arxiv:1010.4076. Submitted.Quantum symmetric pairs and representations of double affine Hecke algebras of type C^C_n, with Xiaoguang Ma.
Link: arXiv:0908.3013. Published in Selecta Mathematica, 2011.Quantum D-modules, elliptic braid groups, and double affine Hecke algebras.
Link: arXiv:0805.2766. Published in International Math Research Notes, 2008.In progress: Kohno-Drinfeld theorem for the KZB connection, with Adrien Brochier, and An explicit description of the center of
, with Sammy Black.
Fusion and tensor categories
Cyclic extensions of fusion categories via the Brauer-Picard groupoid, with Pinhass Grossman & Noah Snyder.
Link: http://arxiv.org/abs/1211.6414. Submitted.On the classification of certain fusion categories, with Eric Larson.
Link: arXiv:0812.1603. Published in Journal of Noncommutative Geometry, 2008.In progress: Representation theory for pivotal tensor categories, with David Ben-Zvi.
Lower central series and Poisson homology
Lower central series of a free associative algebra over the integers and finite fields, with Surya Bhupatiraju, Pavel Etingof, William Kuszmaul, and Jason Li.
Link: arXiv: 1203.1893. To appear in Journal of Algebra.Poisson traces in positive characteristic, with Yongyi Chen, Pavel Etingof, & Mike Zhang.
Link: arXiv:1112.6385. Submitted.The lower central series of the symplectic quotient of a free associative algebra, with Ben Bond.
Link: arXiv: 1111.2316. To appear in Journal of Pure and Applied Algebra, 2012.Lower central series of free algebras in a symmetric tensor category, with Asilata Bapat.
Link: arXiv:1001.1375. To appear in Journal of Algebra, 2012.New results on the lower central series quotients of a free associative algebra, with Noah Arbesfeld.
Link: arXiv:0908.3013. Published in Journal of Algebra, 2009.In progress: Lower central series via commutative formal geometry, with Hendrik Orem.
Disambiguation
Please note that there are several arXiv and print articles published by another David A. Jordan. I did not, in fact, publish mathematics before I was born, nor am I the head of Pure Mathematics at Sheffield University (yet…). I am also, unfortunately, not the British pop sensation David Jordan. If you know of any other David Jordan's who I am not, please let me know!