Iva Halacheva's Homepage

Research interests: Quantum algebra, geometric and combinatorial representation theory, knot theory, low-dimensional topology.

I completed my PhD at the University of Toronto in 2016, my advisors were Dror Bar-Natan and Joel Kamnitzer. For some more information, you can have a look at my CV.

Research Papers

Shift of argument algebras and the cactus group, with J. Kamnitzer, L. Rybnikov, and A. Weekes. (In preparation)
Extensions of the Multivariable Alexander Polynomial. (In preparation)
Alexander type invariants of tangles, skew Howe duality for crystals and the cactus group . (PhD thesis, slides)
Gromov width of the coadjoint orbits of the symplectic group, with M. Pabiniak. (Submitted) arXiv:1601.02825
Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots, with D. Bar-Natan, L. Leung, and F. Roukema. Experimental Mathematics 20-3 (2011), 282-287. arXiv:0909.5169

Talks

Some invited talks I have given:

2016/10 Crystals, the cactus group, and shift of argument algebras, Algebra seminar, University of York, UK. abstract
2016/07 An action of the cactus group on crystals, Representation Theory and Physics, University of Leeds, UK. handout
2016/03 Generalizing the Multivariable Alexander Polynomial, Advances in Quantum and Low-Dimensional Topology, University of Iowa, USA. handout
2016/02 The Gromov width via crystal bases, Symplectic geometry seminar, University of Toronto, Canada. slides
2016/02 The Gromov width of coadjoint orbits of the symplectic group, Geometry and topology seminar, McMaster University, Canada. abstract
2015/12 Two generalizations of the multivariable Alexander polynomial, Knots in Washington XLI, The George Washington University, USA. slides
2015/10 A cactus group action on crystals, AMS sectional meeting: Combinatorial and geometric representation theory, Loyola University Chicago, USA. slides
2015/06 Monodromy and cactus group actions on crystals, Geometry seminar, École Polytechnique Fédérale de Lausanne, Switzerland. abstract
2015/03 A cactus group action on crystals and the shift of argument algebras, Applied algebra seminar, York University, Canada. abstract
2014/12 Shift of argument algebras and the cactus group, Algebra seminar, Instituto Superior Técnico, Portugal. abstract
2014/03 A foray into knot theory: the Alexander polynomial, Graduate student seminar, University of Toronto, Canada. slides

Seminars

I have co-organized the following seminars:

Learning seminar on combinatorics and geometry of K-orbits on the flag manifold at Lancaster University, 2016.
Learning seminar on coideal subalgebras at the University of Toronto, 2016.
Learning seminar on affine structures and the affine Grassmannian at the University of Toronto, 2015.
Schubert calculus learning seminar at the Fields Institute, 2013-2014.

I have also participated in:

Knot at lunch at the University of Toronto.
Quantum algebra at the Fields Institute, 2013-2014.
Geometric representation theory at the Fields Institute.

Teaching

Instructor positions:

Teaching assistant positions: