Research Interests

Low Dimensional Topology, Invariants of Knots and Links

Grants

• NSF grant, DMS # 0906401; August 1, 2009 - July 31, 2012.

 Publications and  Preprints

1. Book: 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. Rassias, Ann. 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, Ph.D thesis, University of Iowa. pdf
4. An sl(2) tangle homology and seamed cobordisms, preprint 2007, arXiv:math.GT/0707.3051
5. sl(2) tangle homology with a parameter and singular cobordisms, Algebraic and Geometric Topology 8 (2008), 729-756.
6. The universal sl(2) cohomology using webs and foams, Topology and its Applications 156 (2009), 1684-1702, preprint 2008, arXiv:math.GT/0802.2848
7. Universal Khovanov-Rozansky sl(2) cohomology, J. Knot Theory Ramifications 19, Issue 6 (2010), 739-761, preprint 2008, arXiv:math.GT/0805.2755
8. On the sl(2) foam cohomology computations, J. Knot Theory Ramifications 18, Issue 9 (2009), 1313-1328, preprint 2008, arXiv:math.GT/0805.4651
9. Twin TQFTs and Frobenius algebras, preprint 2009, arXiv:math.GT/0901.2979
10. The sl(2) foam cohomology via extended TQFTs, preprint 2010, arXiv:math.GT/1001.1797
11. On the quantum filtration of the universal sl(2) foam cohomology, will be published in the J. Knot Theory Ramifications, preprint 2010, arXiv:math.GT/1006.2575
12. The Kauffman polynomial and trivalent graphs, preprint 2011, arXiv:math.GT/1107.1210

 Selected Talks 

• The Kauffman polynomial and trivalent graphs, AMS Sectional Meeting, University of Nebraska-Lincoln, October 14-16, 2011. 
• Trivalent graphs and the Kauffman polynomial, "Knots in Washington XXXII", George Washington University, Washington D.C., April 29-May 1, 2011.
• A polynomial invariant of 3-valent graphs embedded in R^3, AMS Sectional Meeting, University of Iowa, March 2011. 
• sl(n) link homology, AMS Sectional Meeting, University of California Los Angeles, October 2010. 
• On a categorification of the colored Jones polynomial, "KNOTS in Poland III", Conference and Workshop on Knot Theory and its Ramifications, Warsaw, Poland, July 18-24, 2010.
• Link cohomology and extended TQFTs, AMS Sectional Meeting, New Jersey Institute of Technology, Newark, NJ, May 2010. pdf
• The universal sl(2) foam cohomology for links, Connections for Women: Homology Theories of Knots and Links, MSRI, January 2010.
• The universal sl(2) foam cohomology for links via extended TQFTs, AMS Sectional Meeting, UC Riverside, November 2009.
• On the filtered sl(2) foam cohomology for links, AMS Sectional Meeting, Florida Atlantic University, Boca Raton, FL, October 2009.
• On the universal sl(2) foam cohomology, "Claremont Topology Seminar", Claremont Colleges, March 24, 2009.
• Twin TQFTs and Frobenius algebras, AMS National Meeting, Washington D.C., January 2009. pdf
• TQFTs defined on singular 2-cobordisms, The Topology and Geometry of Physics - The 8th Annual Red Raider Mini Symposium, Texas Tech University, October 2008.
• On the Khovanov-Rozansky cohomology, AMS Sectional Meeting, Louisiana State University, Baton Rouge, March 2008. pdf
• On a generalized version of the Khovanov-Rozansky Homology for n = 2, Workshop on Knots and Quantum Computing, University of Texas at Dallas, December 2007.
• The universal sl(2)-link cohomology via webs and foams, ''Knotting Mathematics and Art'', University of South Florida, Tampa, November 2007. pdf
• On the universal sl(2)-link cohomology, "Cascade Topology Seminar", Boise State University, October 2007. pdf
• An sl(2) tangle homology and seamed cobordisms, AMS Sectional Meeting, Miami University, Oxford, Ohio, March 2007. pdf
• An sl(2) tangle homology for dotted, seamed cobordisms, CMS, Toronto, December 2006. 
• An sl(2) tangle homology for seamed cobordisms with polynomial coefficients, "Knots in Washington", George Washington University, Washington D.C., November 2006. 
• Khovanov homology for tangles and cobordisms, Low Dimensional Topology Seminar, University of Iowa, October 2006. 
• The Alexander polynomial, Graduate And Undergraduate Student Seminar (GAUSS), University of Iowa, March 2006.
• Triply graded link homology, Topology Seminar, University of Iowa, February 2006.
• Introduction to Khovanov-Rozansky homology, Workshop on Khovanov and Hochschild homology, University of Iowa, October 2005.
• Introduction to "Macaulay 2", Low Dimensional Topology Seminar, University of Iowa, April 2005.

My Erdös number is less or equal to 4.

My math genealogy:

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