Research Interests

Low Dimensional Topology, Knot Theory, Categorification

Grants

Conferences Organized

Advances in Quantum and Low-Dimensional Topology (co-organized with Heather M. Russell, Ben Cooper and Maggy Tomova) held at The University of Iowa in March 11-13, 2016.
2019 Pacific Math Alliance Conference (co-organized with Andrea Arauza Rivera, Maribel Bueno, Ricardo Cordero Soto, Jessica De Silva, Cynthia Flores, Tamas Forgacs, Omayra Ortega, Oscar Vega) held at California State University, East Bay, on October 12, 2019.

 Publications and  Preprints

  1. Book (in Romanian): Matematici speciale pentru ingineri. Colectie de probleme (Collection of problems), The "Politehnica" Publishing House, 1999 (with M.D. Rendi, I. Mihut, D. Popescu).
  2. On the stability of mappings and an answer to a problem of Th.M. RassiasAnn. Math. Blaise Pascal, Vol.2, nr.2, (1995) 55-66 (with P. Gavruta, M. Hossu, D. Popescu). pdf
  3. An sl(2) tangle homology and seamed cobordisms, preprint 2007; arXiv:math.GT/0707.3051
  4. sl(2) tangle homology with a parameter and singular cobordismsAlgebraic and Geometric Topology 8 (2008) 729-756.
  5. The universal sl(2) cohomology using webs and foamsTopology and its Applications 156 (2009) 1684-1702; arXiv:math.GT/0802.2848
  6. Universal Khovanov-Rozansky sl(2) cohomologyJ. Knot Theory Ramifications 19(2010), No. 6, 739-761; arXiv:math.GT/0805.2755
  7. On the sl(2) foam cohomology computationsJ. Knot Theory Ramifications 18 (2009), No. 9, 1313-1328; arXiv:math.GT/0805.4651
  8. Twin TQFTs and Frobenius algebrasJournal of Mathematics, vol. 2013, Article ID 407068, 25 pages, (2013). doi:10.1155/2013/407068; arXiv:math.GT/0901.2979
  9. The sl(2) foam cohomology via extended TQFTs, New York Jornal of Mathematics 19 (2013) 61-90; http://nyjm.albany.edu/j/2013/19-6.html
  10. On the quantum filtration of the universal sl(2) foam cohomology, J. Knot Theory Ramifications 21, (2012) No. 3, 1250023, 12 pages; arXiv:math.GT/1006.2575
  11. The Kauffman polynomial and trivalent graphs (with James Tipton), Kyungpook Mathematical Journal 55 (2015) No. 4, 779-806; arXiv:math.GT/1107.1210
  12. A cohomology theory for colored tangles, Banach Center Publications 100 (2014), 13-25; Proceedings of Knots in  Poland III, Warsaw-Bedlewo 2013; arXiv:math.GT/1207.3373
  13. On a state model for the SO(2n) Kauffman polynomial (with David Heywood and Dionne Ibarra), Involve-A Journal of Mathematics, Vol. 7, No.4 (2014), 547-563. DOI 10.2140/involve.2014.7.547; arXiv:math.GT/1304.4665
  14. The singular Temperley-Lieb category (with Joel Smith), ISRN Geometry, vol. 2014, Article ID 321509, (2014) 9 pages. DOI 10.1155/2014/321509; http://www.hindawi.com/journals/isrn/2014/321509/
  15. Singular links and Yang-Baxter state models (with Tsutomu Okano and Danny Orton), Rocky Mountain Journal of Mathematics, Vol. 46, No. 6 (2016) 1867-1898. DOI:10.1216/RMJ-2016-46-6-1867; arXiv:1406.3853[Math.GT]
  16. Three approaches to a bracket polynomial for singular links (with Alex Chichester and Patrick Chu), Involve-A Journal of Mathematics, Vol. 10, No. 2 (2017) 197-218; DOI 10.2140/involve.2017.10.197.
  17. A formula for the Dubrovnik polynomial of rational knots (with Katherine Urabe), Publicacions Matemātiques 61 (2017), 105-134; DOI: 10.5565/PUBLMAT 61117 04; arXiv:1503.09134[Math.GT]
  18. Virtual singular braids and links (with Andrew de la Pena and Sarah McGahan), Manuscripta Mathematica (September 2016) 151, Issue 1, 147-175; arXiv:1504.01086v2[Math.GT]
  19. Movie moves for singular link cobordisms in 4-dimensional space, J. Knot Theory Ramifications 25, No 2 (2016), 23 pages. DOI: 10.1142/S0218216516500139; arXiv:1507.04077[Math.GT].
  20. On the Kauffman-Jones polynomial for virtual singular links (with Kelsey Friesen), Missouri J. Math. Sci. 31, No. 1, (2019), 79-104; arXiv:1610.02691[Math.GT].
  21. On the virtual singular braid monoid (with Sarah Zepeda), 21 pages, preprint 2017; arXiv:1710.05416[Math.GT].
  22. Alexander- and Markov-type theorems for virtual trivalent braids (with Abigayle Dirdak, Rita Post and Erica Sawyer), J. Knot Theory Ramifications (online ready) doi.org/10/1142/S0218216519500032; arXiv:1804.09919[Math.GT].
  23. Invariants for trivalent tangles and handlebody-tangles, New York Journal of Mathematics 25 (2019), 156-167; arXiv:1806.06435[Math.GT].
  24. The L-move and Markov theorems for trivalent braids (with Gabriel Coloma and Marguerite Davis), Involve, a Journal of Mathematics 13, No 1 (2020), 21--50. DOI 10.2140/involve.2020.13.21 arXiv:1807.08095[Math.GT].
  25. On Khovanov homology and related invariants (with Nicolle Gonzalez, Christine Ruey Shan Lee, Adam M. Lawrance, Radmila Sazdanovic, Melissa Zhang); arXiv:2002.05247 [math.GT].

Students Papers

 Selected Talks

 


My Erdös number is less or equal to 4.

- Erdös, Paul ; Volkmann, Bodo; Additive Gruppen mit vorgegebener Hausdorffscher Dimension (German). J. Reine Angew. Math. 221 1966 203--208.

- Volkmann, Bodo ; Jung, Soon-Mo; Remarks on a paper of Wagner. (English summary). J. Number Theory 56 (1996), no. 2, 329--335.

- Gavruta, Pasc; Jung, Soon-Mo; Lee, Ki-Suk; Remarks on the Pexider equations modulo a subgroup. (English summary). Far East J. Math. Sci. (FJMS) 19 (2005), no. 2, 215--222.

- Gavruta, Pasc; Hossu, M.; Popescu, D.; Caprau, Carmen; On the stability of mappings and an answer to a problem of Th. M. Rassias. (English, French summary). Ann. Math. Blaise Pascal 2 (1995), no. 2, 55--60.

 

My math genealogy:


Erhard Weigel

Gottfried Leibniz

Jacob Bernoulli

Johann Bernoulli

Leonhard Euler

Joseph Lagrange

Simeon Poisson

Michel Chasles

H. A. Newton

E. H. Moore

Oswald Veblen

R. L. Moore

Raymond Wilder

Frank Raymond

Allan Edmonds

Charles Frohman

Me!!


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