Adam S. Sikora
PhD
Associate Professor
Research Interests
Professor Sikora's main research areas are: Interactions between topology, algebra and number theory. Moduli spaces of representations, and their quantization.
Education
PhD, University of Maryland, College Park
Interactions between topology, algebra and number theory. Moduli spaces of representations, and their quantization.
Research Summary
Professor Sikora's main research areas are: Interactions between topology, algebra and number theory. Moduli spaces of representations, and their quantization.
Selected Publications
SO(2n,C)-character varieties are not varieties of characters, arXiv: 1503.08279
G-Character varieties for G=SO(n,C) and other not simply connected groups, Journal of Algebra vol. 429, 2015, 324--341, arXiv: 1303.7181
Character Varieties of Abelian Groups, Mathematische Zeitschrift, vol. 277, Issue 1-2, 2014, 241--256, arXiv: 1207.5284
Generating sets for coordinate rings of character varieties , Journal of Pure and Applied Algebra, 217(11), (2013), 2076--2087.
Distributive Products and Their Homology, with J.H. Przytycki, Communications in Algebra, 42 , no 3, (2014), 1258--1269.
Character varieties, Trans. of AMS 364 (2012) 5173--5208.
Quantizations of Character Varieties and Quantum Knot Invariants
"Topology on the spaces of orderings of groups," Bull. London Math. Soc. 36 (2004) 519--526., arXiv: 0111002.
A. Sikora, Analogies between group actions on 3-manifolds and number fields Comm. Math. Helv 78 (2003), no. 4, 832--844, http://arxiv.org/abs/math.GT/0107210
A. Sikora, Character varieties,Trans. of AMS 364 (2012) 5173--5208., http://arxiv.org/abs/0902.2589