Mihai Staic

Professor and Undergraduate Coordinator

Phone: 419-372-6657
Email: mstaic@bgsu.edu
Address: Office: 426 Mitchell B. McLeod Hall
Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, OH 43403-0206

Research Interests

• Quantum Groups
• Low dimensional Topology
  
• Homology
  
• Homotopy

Education

• Ph.D. SUNY at Buffalo 2007

Publications

Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$, arXiv:2407.13959, submitted (2024) (with Matthew J. Fyfe, Steven R. Lippold, and Alin Stancu)

The $r$-equilibrium Problem, arXiv:2405.10407, submitted (2024).

Existence of the Map $det^{S^3}$, Linear Algebra and its Applications, 689 (2024), 1--33. (with Steven R. Lippold)

Existence of the $det^{S^2}$ map, Bulletin of the London Mathematical Society, 55 (4) (2023), 1685--1699.

Conditional Probability Matrix and the $S^2$-rank, arXiv:2205.02183, submitted.

The Exterior Graded Swiss-Cheese Operad $\Lambda^{S^2}_V$ , (with an appendix by Ana Lorena Gherman and Mihai D. Staic), Comm. Algebra, 51 (7) (2023), 2705--2728.

Pseudo symmetric tensor categories and Pseudo-triangular Hopf Algebras, submitted, (with Florin Panaite).

Partitions of the complete hypergraph $K_3^6$ and a determinant like function,   Journal of Algebraic Combinatorics, 56 (2022), no. 3, 969–1003.  (with Steven R. Lippold)

Edge partitions of the complete graph and a determinant like function, Monatshefte fur Mathematik, 198 (4) (2022), 819--858. (with Steven R. Lippold, and Alin Stancu)

A Geometric Application for the $det^{S^2}$ Map, arXiv:2009.13641, Communications in Algebra,  50 (3) (2022), 1106--1117, (with Jacob Van Grinsven)

G-algebra structure on the higher Hochschild cohomology H_{S^2}(A,A), Algebra Colloqium,  29 (1) (2022), 113--124. (with Samuel Carolus)

A Simplicial Construction for Noncommutative Settings, Homology, Homotopy and Applications, 23 (2021), 49–60.(with Samuel Carolus, and Jacob Laubacher)

Automorphisms of the k-algbera k[X_1,...,X_m], Journal of Algebra and its Applications, Vol 18  (2019) 1950046, 9  (with Alina Petrescu Nita)

Hom tensor categories and the Hom Yang Baxter Equation, Applied categorical Structures, Vol 27 (2019) 323-363.  (with Florin Panaite and Paul Schrader)

Bar Simplicial Modules and Secondary Cyclic (Co)homology, (with Jacob Laubacher, and Alin Stancu) Journal of Noncommutative Geometry, Vol 12, (2018), 865-887  

Higher Order and Secondary Hochschild Cohomology, Comptes Rendus Mathematique. Vol 354, (2016) 1049-1054 (with Bruce R. Corrigan-Salter)  

Secondary Hochschild Cohomology, Algebra and Representation Theory, 19 (2016), 47-56. arXiv

Operations on the Secondary Hochschild Cohomology, Homology Homotopy Appl., 17 (2015), 129-146.(with Alin Stancu)  

Classification of a class of nonrigid Carnot groups, Journal of Lie Theory 25 (2015), 717-732. (with Mike Hughes and Xie Xiangdong) 

Symmetry group of two special types of carbon nanotori, Acta Crystallographica section A 69 (4) (2013), 435-439 (with Alina Nita-Petrescu) 

More examples of pseudosymmetric braided categories, Journal of Algebra and its Applications 12(4) (2013). arXiv (with Florin Panaite)

An explicit description of the simplicial group K(A,n), J. Austr. Math Soc. 95 (2013) 133-144.  

Secondary Cohomology and k-invariants, Bull. Belg. Math. Soc. 19(3) (2012), 561-572.  

Some notes on (1+1) dimensional HQFT, Algebraic and Geometric Topology 10 1367-1393 (2010). (with Vladimir Turaev).  

A quotient of the braid group related to pseudosymmetric braided categories, Pacific Journal of Mathematics, 144, (2010), 155-167. (with Florin Panaite )  

Pseudosymmetric braidings, twines and twisted algebras, Journal of Pure and Appl. Algebra, 244, (2010) 864-887. (with Florin Panaite and Freddy Van Oystaeyen)  

From 3-algebras to $\Delta$-groups and symmetric cohomology. Journal of Algebra 322(4), (2009), 1360-1378.  

Symmetric Cohomology for Groups in low dimension, Arch. der Mathematik (Basel) 93 (2009), 205--211.

On some classes of lazy cocycles and categorical structures. Journal of Pure and Appl. Algebra, 209 (2007), 687-701. (with Florin Panaite and Freddy Van Oystaeyen)  

Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category. Israel J. Math. 158 (2007), 349-365. (with Florin Panaite)  

A note on anti-Yetter-Drinfeld modules, Contemp. Math. 441, AMS Providence (2007), 149-153.

Pure-braided Hopf Algebras and knot invariants, Journal of Knot Theory and it's Ramifications, 13(3), 385-400, (2004).

Pseudo-qusitriangular subbialgebras of quantum systems, Communications in Algebra, 30 (2002), no5, 2133-2141.

On the dimension of irreducible modules of a semisimple Hopf algebra, Communications in Algebra, 30 (2002), no. 1, 437--442.