Adam Sikora Promotes Quantum Topology Worldwide

Portrait of Professor Adam Sikora who is helping advance and popularize the growing field of quantum topology, which connects topology and geometry with quantum physics through surprising cross-fertilization of ideas. He co-organized three international conferences and a summer school devoted to this area. The first three NSF-supported events were held at Vietnam Institute for Advanced Study in Mathematics and at the Centre International de Rencontres Mathématiques (CIRM) in Marseille, France, in summer 2025. Another meeting, exploring connections with Number Theory, will take place at the Mathematisches Forschungsinstitut Oberwolfach in Germany.

Adam Sikora, PhD

 

 

 

Professor Adam Sikora is helping advance and popularize the growing field of quantum topology, which connects topology and geometry with quantum physics through surprising cross-fertilization of ideas. Sikora co-organized three international conferences and a summer school devoted to this area. The first three NSF-supported events were held at Vietnam Institute for Advanced Study in Mathematics and at the Centre International de Rencontres Mathématiques (CIRM) in Marseille, France, in summer 2025. Another meeting, exploring connections with Number Theory, will take place at the Mathematisches Forschungsinstitut Oberwolfach in Germany.

Faculty Profile

Adam S. Sikora

PhD

Adam S. Sikora.

Adam S. Sikora

PhD

Adam S. Sikora

PhD

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