PhD, University of Maryland, College Park
Interactions between topology, algebra and number theory. Moduli spaces of representations, and their quantization.

Professor Sikora's main research areas are: Interactions between topology, algebra and number theory. Moduli spaces of representations, and their quantization.

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