My address: Department of Mathematics, Boise State University, 1900 University Drive, Boise, Idaho 83725
email: ukaiser@boisestate.edu
My research interests are in Geometric topology. I consider myself a Differential Topologist interested in all problems related to manifolds. These are questions of immersions and embeddings. I am interested in link theory in manifolds and in low dimensions in associated geometric and quantum invariants. I am also interested in all aspects of Quantum Computing. Here are some questions I am presently working on or interested in: Categorification of invariants of links in 3-manifolds (LMO-invariant, skein modules); Geometry of skein modules; Computation of quantum invariants in low-dimensional topology; representations of fundamental groups of 3-manifolds.
Selected presentations
- Rokhlin seminar (St. Petersburg, Russia, 05-17-2021) A survey of Bar-Natan skein theory
- Geometric topology seminar (Moscow, Russia, 04-30-2021) String topology and homotopy skein modules
- Joint AMS/MAA Meeting (2021, online, 01-06-2021) Kashaev and extended Kauffman summation; slides
- Knots in Washington XLIX (Washington DC, 02-09-2020) Kashaev invariant and Kauffman states; abstract
- CUNY Einstein Chair Seminar (New York, 04-23-2002) Skein modules and 3-manifolds
I am also giving regularly talks in Boise State’s Department of Mathematics TATERS seminar.
Publications
- A short survey of quantum computing; Journal of Knot Theory and it Ramifications 26, 2017, no.3, 19 pp.
- On the construction of generalized skein modules; Knots in Poland III, Part 1, Banach Center Publications 100, Polish Acad. Sci. Inst. Math., Warsaw, 2014
- Frobenius algebras and skein modules of surfaces in 3-manifolds; Algebraic Topology – old and new, 59-81, Banach Center Publications 85, Polish Acad. Sci. Inst. Math., Warsaw, 2009
- (with Nikos Apostolakis) Kauffman state sums and bracket deformation; Journal of Knot Theory and its Ramifications 16 (2007), no. 7, 809-831
- Link bordism skein modules; Fundamenta Mathematicae 184 (2004), 113-134
- Quantum deformations of fundamental groups of oriented 3-manifolds; Transactions of the AMS 356 (2004), 3869-3880
- Deformation of string topology into homotopy skein modules; Algebraic and Geometric Topology 3, 2003, no. 34, 1005-1035
- Presentations of q-homotopy skein modules of oriented 3-manifolds; Journal of Knot Theory and its Ramifications Vol. 10, No. 3 (May 2001), 461-491
- Link theory in manifolds; Lecture Notes in Mathematics 1669, 167 pp., Springer Verlag, Berlin 1997
- (with Nathan Habegger) Link homotopy in the 2-metastable range; Topology 37, No. 1, 1998, 75-93
- (with Nathan Habegger) Homotopy classes of two disjoint 2p-spheres in R^3p+1; Topology and its Applications 71, 1996, 1-8
- Link homotopy and skein modules; in Proceedings of the AMS-Israel Joint Workshop at Haifa, Contemp. Math Vol. 164, 1994, 59-77
- Homology boundary links and strong fusion; Osaka Journal of Mathematics 29, 1992, 573-593
- Geometric properties of strong fusion; Journal of Knot theory & its ramifications, Vol. 1, No. 3, 1992, 297-302
- Strong bandsum and dichromatic invariants; Manuscripta Mathematica 74, 1992, 317-336
- Bands, tangles and linear skein theory; Manuscripta Mathematica 71, 1991, 317-336
- Link homotopy in R^3 and S^3; Pacific Journal of Mathematics, Vol. 151, No. 2, 1991, 257-264
- (with Li Banghe) On the reflection of immersions in Euclidean space; Acta Mathematica Sinica, Vol. 11, No. 3, 1991, 257-264
- Verschlingungsabbildungen im Euklidischen Raum, Zentralblatt review; PhD thesis University of Siegen, 1989
- (with Li Banghe) Enumeration of immersions of m-manifolds in (2m-2)-manifolds; in Differential Topology, Proceedings, Siegen 1987, Lecture Notes in Mathematics Vol. 1350, Springer Verlag 1988, 171-188
- Immersions in codimension 1 up to regular homotopy; Archiv der Mathematik, Vol. 51, 1998, 371-377
STEM Education research: (with Louis S. Nadelson, Sharon McGuire, Kimberly Hardy, Kisten A. Davis, Arvin Farid and Yu-Chang Hsu) Am I a STEM Professional? Documenting STEM student professional identity development; Studies in Higher Education, July 2015
ArXiv & MATH Reviews & etc
- ArXiv Papers
- My Papers reviewed in Math Reviews
- My zbMATH entry
- My Math Reviews
- My zbMATH reviews
- Selected Works, Boise State University
- My CV