59 citations · 281 across the 20 of their papers we have counts for
22 papers
Full twists and stability of knots and quivers
Sachin Chauhan, Piotr Kucharski, Dmitry Noshchenko +3
We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-P…
Quivers and BPS states in 3d and 4d
Piotr Kucharski, Pietro Longhi, Dmitry Noshchenko +2
We propose a symmetrization relation between BPS quivers encoding 4d theories and symmetric quivers associated to 3d theories. We analyse in detail…
Knot-quiver correspondence: a brief review
Piotr Kucharski, Dmitry Noshchenko
This note is an overview of the knot-quiver correspondence, which relates symmetric quivers and their partition functions, a.k.a. motivic Donaldson-Thomas generating series, to qua…
What makes math problems hard for reinforcement learning: a case study
Ali Shehper, Anibal M. Medina-Mardones, Lucas Fagan +6
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high…
3d Modularity Revisited
Miranda C. N. Cheng, Ioana Coman, Piotr Kucharski +2
The three-manifold topological invariants capture the half-index of the three-dimensional theory with supersymmetry obtained by compactifying the M5 bran…
Categorification of quiver diagonalization and Koszul algebras
Vladimir Dotsenko, Evgeny Feigin, Piotr Kucharski +1
In earlier work of three of the authors of the present paper, a supercommutative quadratic algebra was associated to each symmetric quiver, and a new proof of positivity of motivic…
Unlinking symmetric quivers
Piotr Kucharski, Hélder Larraguível, Dmitry Noshchenko +1
We analyse the structure of equivalence classes of symmetric quivers whose generating series are equal. We consider such classes constructed using the basic operation of unlinking,…
Quiver diagonalization and open BPS states
Jakub Jankowski, Piotr Kucharski, Hélder Larraguível +2
We show that motivic Donaldson-Thomas invariants of a~symmetric quiver , captured by the generating function , can be encoded in another quiver of (almost al…
Branches, quivers, and ideals for knot complements
Tobias Ekholm, Angus Gruen, Sergei Gukov +4
We generalize the invariant, i.e. for the complement of a knot in the 3-sphere, the knots-quivers correspondence, and -polynomials of knots, and find sev…
Knot homologies and generalized quiver partition functions
Tobias Ekholm, Piotr Kucharski, Pietro Longhi
We conjecture a relation between generalized quiver partition functions and generating functions for symmetrically colored HOMFLY-PT polynomials and corresponding HOMFLY-PT homolog…
Permutohedra for knots and quivers
Jakub Jankowski, Piotr Kucharski, Hélder Larraguível +2
The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this co…
at large : from curve counts to quantum modularity
Tobias Ekholm, Angus Gruen, Sergei Gukov +3
Reducing a 6d fivebrane theory on a 3-manifold gives a -series 3-manifold invariant . We analyse the large- behaviour of , where $M_…
Quivers for 3-manifolds: the correspondence, BPS states, and 3d =2 theories
Piotr Kucharski
We introduce and explore the relation between quivers and 3-manifolds with the topology of the knot complement. This idea can be viewed as an adaptation of the knots-quivers corres…
Multi-cover skeins, quivers, and 3d dualities
Tobias Ekholm, Piotr Kucharski, Pietro Longhi
The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cov…
invariants at rational
Piotr Kucharski
invariants of 3-manifolds were introduced as series in in order to categorify Witten-Reshetikhin-Turaev invariants corresponding to . However modulari…
Physics and geometry of knots-quivers correspondence
Tobias Ekholm, Piotr Kucharski, Pietro Longhi
The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot in the 3-sphere to representation theory of a quiver associated to th…
Knots-quivers correspondence
Piotr Kucharski, Markus Reineke, Marko Stosic +1
We introduce and explore the relation between knot invariants and quiver representation theory, which follows from the identification of quiver quantum mechanics in D-brane systems…
BPS states, knots and quivers
Piotr Kucharski, Markus Reineke, Marko Stosic +1
We argue how to identify supersymmetric quiver quantum mechanics description of BPS states, which arise in string theory in brane systems representing knots. This leads to a surpri…
The (2,0) Superalgebra, Null M-branes and Hitchin's System
Piotr Kucharski, Neil Lambert, Miles Owen
We present an interacting system of equations with sixteen supersymmetries and an R-symmetry where the fields depend on two space and one null dimensions that i…
BPS counting for knots and combinatorics on words
Piotr Kucharski, Piotr Sułkowski
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate…
Knots, BPS states, and algebraic curves
Stavros Garoufalidis, Piotr Kucharski, Piotr Sułkowski
We analyze relations between BPS degeneracies related to Labastida-Marino-Ooguri-Vafa (LMOV) invariants, and algebraic curves associated to knots. We introduce a new class of such…
Spin-k/2-spin-k/2 SU(2) two-point functions on the torus
Ingo Kirsch, Piotr Kucharski
We discuss a class of two-point functions on the torus of primary operators in the SU(2) Wess-Zumino-Witten model at integer level k. In particular, we construct an explicit expres…